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Do NOT activate when: the decision is a one-shot choice with no sequential stages (use simple EV instead); probabilities cannot be estimated even roughly and uncertainty is too deep to quantify. More: deciqai.com/c/decision-tree\"\n---\n\n# Decision Tree\n\n## Overview\n\nA **decision tree** maps a multi-stage decision: decision nodes (squares) for choices you control, chance nodes (circles) for outcomes you don't, probabilities on every branch, payoffs at the leaves — then rollback right-to-left to get expected value at the root. First systematized by John F. Magee (HBR, 1964); formalized by Howard Raiffa (1968). Its biggest value: converting \"I feel we should expand\" into \"what probability do you assign to high demand?\" — making every assumption explicit and contestable.\n\nComposes with `expected-value-and-kelly` (EV scaffold + bet sizing), `probabilistic-thinking` (calibration per node), `inversion` (rollback = working outcomes backward), `mece` (branches must be MECE so probabilities sum to 1.0).\n\n## When to Use\n\n- Decision has sequential stages (decide → learn → decide again)\n- Outcomes uncertain; probabilities can be estimated (even roughly)\n- Payoffs quantifiable (NPV, revenue, cost, lives saved)\n- Multiple stakeholders need a shared visual model to align on assumptions\n- Sizing a big irreversible bet under AI uncertainty — build vs. buy vs. wait on AI capex, a fab investment, or committing while AI adoption / AI valuations are unproven\n\n**Not when:** one-shot choice with no stages; probabilities unestimable; payoffs purely qualitative; branch set too large (use scenario planning instead).\n\n## Coaching Novices (Adaptive Front Door)\n\n- **Engine mode:** user has a concrete multi-stage decision → run The Process directly.\n- **Coach mode:** user is unfamiliar or has no concrete case → guide step by step.\n\nIn Coach mode, respond one step at a time. Each [WAIT] is a hard stop — output only that step's question, then stop.\n\n1. **One-line:** a decision tree converts \"I feel\" into \"what probability do you assign?\" — making assumptions explicit so they can be argued about.\n2. **Check fit.** Sequential stages? Uncertain outcomes? Quantifiable payoffs? If yes to all three, a tree applies.\n3. **Elicit their real case.** What's the initial choice? What uncertain outcomes follow? What payoffs result?\n> **[WAIT — do not advance until user responds]**\n4. **Run The Process one step at a time** with their input — draw structure, assign probabilities, assign payoffs, roll back.\n> **[WAIT — do not advance until user responds]**\n5. **Close** by naming the insight: the threshold at which the recommendation flips, and whether to gather more data.\n> **[WAIT — do not advance until user responds]**\n\n## The Process\n\n**Step 1 — Root:** Define the decision (options, timeline, decision-maker). Draw a square; each option is a branch.\n\n**Step 2 — Chance nodes:** For each branch, identify uncertain events → draw circles. Branches at each circle must be MECE; probabilities must sum to 1.0.\n\n**Step 3 — Probabilities:** Assign a number (0.0–1.0) + documented basis to every branch. Reject \"50/50\" without justification.\n\n**Step 4 — Payoffs:** Assign consistent-unit payoffs (NPV, revenue, etc.) to every terminal leaf.\n\n**Step 5 — Rollback:** Right to left — EV at each circle = Σ(p × value). At each square, keep highest EV branch; mark losers //.\n\n**Step 6 — Sensitivity + stop-rule:** Find the probability threshold where the optimal choice switches. Compute EVPI = EV(perfect info) − EV(best decision now). If EVPI < cost of data: decide now. If EVPI > cost: gather data first. Stop refining when the leading option's EV advantage exceeds the value of further analysis.\n\n## Output Template\n```\nDecision Tree: <topic>\nOptions: A / B  |  Timeline:\nTree: [node-by-node description]\nProbabilities: Node | Branch | p | Basis\nPayoffs: Path | Value | Unit\nRollback: Option A EV= / Option B EV= / Optimal=\nSensitivity: flips when p([key branch]) > [threshold]  |  EVPI=\nRecommendation: [option] — holds if [condition]; flips if [condition]\n```\n\n*→ Method in Action: [Magee 1964 — Chemical Plant Investment (HBR)](examples/magee-1964-chemical-plant-investment-hbr.md) · [Eisenhower's D-Day Weather Decision](examples/eisenhower-1944-d-day-weather-decision.md)*\n*→ 2026 lens: [A Chipmaker's Leading-Edge Fab Investment Under AI Uncertainty (2024–2026)](examples/chipmaker-leading-edge-fab-investment-2024-2026.md)*\n\n## Pack: Decision Tree by Domain\n\n| Domain | Root Decision | Key Uncertainty | Payoff | Watch For |\n|---|---|---|---|---|\n| Capital investment | Large vs. small plant | Demand scenarios | NPV | Overconfident demand p |\n| R&D portfolio | Fund vs. kill | Technical success; adoption | Revenue × p | Ignoring base-rate failure |\n| Litigation | Settle vs. litigate | Win/lose; damages | Expected settlement | Anchoring on best case |\n| Product launch | Now vs. delay | Market reception; competitor | Revenue per scenario | Missing competitor-first branch |\n| M&A | Acquire vs. pass | Integration; synergy | Post-acquisition EV | Paying for performance peak |\n\n## Applying It Well\n\n- Draw before calculating — structure surfaces hidden assumptions\n- Assign probabilities before revealing your preferred option\n- Run sensitivity before concluding; find the switchover threshold and EVPI\n- Audit missing branches explicitly: \"what did we leave out?\"\n\n*→ Primary sources: [references/sources.md](references/sources.md)*\n\n## Common Rationalizations\n\n**[D] = designed upfront | [O] = observed in real use. [O] entries are more valuable.**\n\n| Rationalization (Fake Move) | Reality |\n|---|---|\n| [D] \"This is strategic — we don't need numbers.\" | Without numbers the tree is just a picture. Force strategic disagreements to become numerical ones. |\n| [D] \"We can't estimate probabilities.\" | Even rough estimates beat implicit zero/one assumptions. Every un-numbered branch already has an implicit probability. |\n| [D] \"The tree chose A — we're done.\" | Holds only at assigned probabilities. Sensitivity analysis is mandatory before concluding. |\n| [D] \"We enumerated all branches.\" | Trees are always simplifications. Ask explicitly: what branches are missing? |\n| [D] \"It's 50/50 — we just don't know.\" | 50/50 is a claim requiring justification. What base rate supports it? |\n| [D] \"My gut says B even though the tree says A.\" | Gut = implicit tree with different probabilities. Find which number your gut is using and put it in. |\n| [D] \"The tree gave a recommendation — it must be right.\" | GIGO: garbage probabilities produce garbage recommendations. Calibrate inputs first. |\n| *→ Add [O] entries here after each real use — paste the actual failure pattern* | *What went wrong and why* |\n\n## Red Flags\n\n- Probabilities verbal only — no numbers written | Chance-node probabilities don't sum to 1.0\n- No sensitivity analysis performed | Terminal payoffs in mixed units across branches\n- Probabilities assigned post-hoc to justify a pre-decided conclusion | No missing-branch audit\n\n## Verification\n\n- [ ] Root decision defined; all options enumerated\n- [ ] All chance nodes MECE; probabilities sum to 1.0 at each node\n- [ ] Every probability has documented basis\n- [ ] All terminal payoffs in same unit and discount rate\n- [ ] Rollback verified numerically at every node\n- [ ] Sensitivity complete — switchover threshold identified\n- [ ] EVPI calculated; data-gathering decision made\n- [ ] Missing-branch audit performed; recommendation states conditions it holds and flips\n---\n*Part of **deciqAI Knowledge Skills** — 227 open-source thinking skills that make rigor executable for AI agents. The same skills power every deciqAI agent, which runs them autonomously to operate your company. **See it run → https://www.deciqai.com/c/decision-tree** · ⭐ Star the repo → https://github.com/deciqAI/knowledge-skills · Contributions welcome.*\n\n*Agents: latest version & machine-readable metadata → https://www.deciqai.com/s/decision-tree.json*\n\nFile v1.0.5:_meta.json\n\n{\n  \"ownerId\": \"kn754b8sk22s8c6gjxt02bftbn88q7ye\",\n  \"slug\": \"decision-tree\",\n  \"version\": \"1.0.5\",\n  \"publishedAt\": 1784224616683\n}\n\nFile v1.0.5:references/sources.md\n\n# Sources — decision-tree\n\n> *Primary sources for the [decision-tree](../SKILL.md) skill.*\n\n## Sources\n\n- Magee, J. F. (1964). \"Decision Trees for Decision Making.\" *Harvard Business Review*, July–August, 126–138. The original practitioner framework.\n- Magee, J. F. (1964). \"How to Use Decision Trees in Capital Investment.\" *Harvard Business Review*, September–October, 79–96. Capital investment application.\n- Raiffa, H. (1968). *Decision Analysis: Introductory Lectures on Choices under Uncertainty.* Addison-Wesley. The academic formalization; introduces EVPI and formal rollback.\n- Howard, R. A. (1966). \"Decision Analysis: Applied Decision Theory.\" *Proceedings of the 4th International Conference on Operational Research.* Stanford. Early theoretical grounding.\n- Howard, R. A., & Matheson, J. E. (Eds.) (1983). *Readings on the Principles and Applications of Decision Analysis.* Strategic Decisions Group. Comprehensive practitioner reference.\n- Clemen, R. T., & Reilly, T. (2013). *Making Hard Decisions with DecisionTools.* Cengage. Standard textbook treatment.\n- Eisenhower, D. D. (1948). *Crusade in Europe.* Doubleday. First-hand account of the D-Day weather go/no-go decision (worked example).\n- Stagg, J. M. (1971). *Forecast for Overlord.* Ian Allan. The SHAEF chief meteorologist's account of the June 1944 forecasts.\n- Major U.S. hyperscaler quarterly earnings guidance and calls, 2024–2026 (Microsoft, Alphabet, Amazon, Meta). Primary source for the reported surge in AI-related capital expenditure and management's commentary on committing to AI capacity under uncertain returns. Context for the AI build-vs-buy-vs-wait worked example.\n- Mainstream financial-press coverage of the 2024–2026 \"AI capex / overbuild / bubble\" debate (e.g., The Wall Street Journal, Financial Times, The Economist, Reuters). Durable, widely-reported context for how large firms weighed heavy AI infrastructure investment against the risk of stranded capacity.\n- Leading semiconductor foundries' and integrated device makers' public capital-expenditure guidance and management commentary, 2024–2026 (as reported in earnings materials and mainstream financial press). Context for the chipmaker leading-edge-fab worked example: the multi-year, multi-billion-dollar nature of advanced-node fab commitments made ahead of confirmed AI-driven demand.\n- Widely reported industry coverage of the semiconductor sector's historical boom-bust capacity cycles and of the 2024–2026 debate over whether AI-driven demand for leading-edge chips is durable or a potential overbuild (e.g., trade press such as SemiAnalysis-style analysis alongside general financial press). Durable, well-documented context for the high/low-demand probability framing; no specific figures in the worked example are drawn from any single filing.\n\nFile v1.0.5:examples/chipmaker-leading-edge-fab-investment-2024-2026.md\n\n# Method in Action: A Chipmaker's Leading-Edge Fab Investment Under AI Uncertainty (2024–2026)\n\n> *Example for the [decision-tree](../SKILL.md) skill.*\n\nBetween 2024 and 2026, one of the largest irreversible capital bets in the economy was a semiconductor manufacturer's decision to commit to leading-edge fabrication capacity. A single advanced logic fab is a multi-year, multi-billion-dollar commitment made *years* before the demand that would fill it is confirmed. The AI wave made this sharper on both sides: the *upside* case (AI accelerators and their supply chain filling every wafer) and the *downside* case (a capacity glut if AI demand or monetization disappoints, echoing prior semiconductor boom-bust cycles). This is a textbook decision-tree problem — sequential, uncertain, quantifiable — and the tree does exactly what Magee promised in 1964: it converts \"AI demand is unstoppable, we must break ground now\" into \"what probability do you put on sustained high demand, and what does the tree say if you are wrong?\"\n\nThis worked example applies the skill's six Process steps to a **stylized composite** of that decision. The framing (large fab now vs. phased/modular fab vs. defer, under high/low AI-driven demand) mirrors the real 2024–2026 debate; the probabilities and dollar payoffs below are **illustrative inputs chosen to demonstrate the method**, not figures from any company's filings.\n\n---\n\n**Step 1 — Root.** Define the decision. A chipmaker's board must choose how to commit leading-edge wafer capacity over a multi-year horizon. Draw the root square with three branches:\n\n- **Large fab now** — commit to a full-scale advanced fab immediately. Highest fixed cost and longest lead time, best unit economics *if* demand shows up, most stranded capital if it does not.\n- **Phased / modular fab** — build the shell and a first module now, with a pre-engineered *option to expand* tooling later once demand is clearer (directly the small-plant-with-expansion structure Magee introduced in 1964).\n- **Defer** — hold the large commitment ~12 months, gather adoption and pricing signal, then decide. Deferral is not free: a fab's multi-year construction-and-qualification lead time means capacity decided late arrives late, potentially after the window of peak demand.\n\nDecision-maker: the board / CFO. Timeline: leading-edge fab lead times run into years — which is precisely why \"wait\" carries a real delay cost.\n\n**Step 2 — Chance nodes.** Each branch runs into an uncertainty the firm does not control. Draw a circle on each. The dominant chance node is **AI-driven wafer demand**, which must be MECE:\n\n- *High, durable demand* — AI-accelerator and adjacent demand keeps leading-edge capacity near-full for years.\n- *Low / disappointing demand* — AI adoption or monetization stalls, or competitors add capacity too; the new fab runs underutilized (the \"AI capex glut / bubble\" fear that ran through the 2024–2026 debate).\n\nFor **Phased / modular**, a second-stage decision node follows the year-1 signal: having observed high or low demand, *then* choose to install the expansion tooling or hold — the learn-then-decide structure that makes a tree worth more than a one-shot EV.\n\n**Step 3 — Probabilities.** Assign a number and a basis to every branch; reject an unjustified \"50/50.\" Illustrative inputs for this composite:\n\n| Node | Branch | p | Basis (illustrative) |\n|---|---|---|---|\n| AI wafer demand | High, durable | 0.60 | Sustained AI-accelerator demand and leading-edge order signals reported during the 2024–2025 build-out |\n| AI wafer demand | Low / disappointing | 0.40 | Historical semiconductor boom-bust base rate; overbuild / bubble concerns aired publicly in the same period |\n\nThe number matters less than forcing its owners to state and defend it — which is where a boardroom's \"the AI opportunity is enormous\" becomes a concrete, revisable argument about one probability.\n\n**Step 4 — Payoffs.** Assign consistent-unit payoffs (illustrative multi-year NPV, arbitrary units) to every terminal leaf:\n\n- Large fab + High demand → **+100** (full-scale capacity, best margins, near-full utilization)\n- Large fab + Low demand → **−45** (stranded, underutilized leading-edge assets; the overbuild downside)\n- Phased + High demand → **+70** (installs expansion after the signal; captures most upside but pays a modularity premium and some ramp delay)\n- Phased + Low demand → **+5** (holds expansion; limited loss — the bounded-downside branch)\n- Defer, then build after signal → payoffs as above **minus a delay cost** (share and pricing ceded during the wait, plus a scarcity premium on equipment if everyone breaks ground at once)\n\n**Step 5 — Rollback.** Right to left, EV at each chance node = Σ(p × value):\n\n- **Large fab EV** = 0.60(+100) + 0.40(−45) = 60 − 18 = **+42**\n- **Phased EV** = 0.60(+70) + 0.40(+5) = 42 + 2 = **+44**\n- **Defer EV** = the value of deciding *after* the signal, minus the delay cost. Its appeal is highest when the demand probability sits near the middle (uncertainty is greatest, so learning is worth most) and lowest when demand looks clearly high (deferral just cedes ground) or clearly low (little worth waiting to build).\n\nAt assigned inputs, **Phased narrowly leads (+44 vs. +42)** — the bounded-downside branch beats the full commitment precisely because the 0.40 weight on disappointing demand makes the large fab's −45 tail expensive. Mark the losing branch `//`. Per the skill, the recommendation is not \"go phased,\" it is \"go phased *at these probabilities*.\"\n\n**Step 6 — Sensitivity + stop-rule.** Find where the choice flips. Setting Large-fab EV = Phased EV:\n\n`p(100) + (1−p)(−45) = p(70) + (1−p)(5)`\n→ `145p − 45 = 65p + 5`\n→ `80p = 50`\n→ **p\\* = 0.625.**\n\nSo the Large fab only beats Phased once p(high demand) exceeds **≈0.625**. At the assumed 0.60 the tree favors Phased, but the gap is thin: a modestly *more* bullish demand read (above 0.625) flips it to the full-scale fab, and a *more* bearish read widens Phased's lead. That single threshold is the real output. It reframes the whole \"is AI-fab capacity a rational bet or a bubble?\" debate as: *do you believe durable-high-demand probability sits above or below ~0.625?*\n\n**EVPI / stop-rule.** Compute the value of resolving the demand uncertainty before committing. With perfect foresight the firm picks the best action in each state: +100 (Large) if high, +5 (Phased-hold) if low → EV(perfect info) = 0.60(100) + 0.40(5) = 62. Best action now (Phased, +44) → **EVPI = 62 − 44 = 18** (illustrative units). If a year of adoption data, customer pre-commitments, or a smaller pilot line costs *less* than that 18, buy the information first — the disciplined case for the phased/defer path. If resolving the uncertainty would cost *more* than 18 (deferral cedes irrecoverable position, or lead times mean late capacity is worthless), commit now. Stop refining once the leading option's EV advantage exceeds the value of further analysis.\n\n---\n\n**The insight the tree delivers.** Not \"build the fab\" or \"don't,\" but three contestable objects: (1) the demand probability everyone is really arguing about, (2) the **p\\* ≈ 0.625 threshold** at which full commitment overtakes the phased option, and (3) an EVPI that says whether a year's wait or a pilot line is worth its cost. Note how this differs from the [hyperscaler build-vs-buy-vs-wait example](ai-capex-build-vs-buy-vs-wait-2024-2026.md): a chipmaker cannot \"buy\" leading-edge capacity from a cloud provider, so its middle branch is *modularity* (phase the fab) rather than *rental* — and that structural difference moves the switchover threshold. Missing-branch audit: this composite omits a joint-venture / customer-prepay structure, a trailing-edge fallback, and competitor-first dynamics — real trees are always simplifications, and naming what's left out is mandatory.\n\n*Sources: Magee, J. F. (1964), \"Decision Trees for Decision Making,\" Harvard Business Review, and \"How to Use Decision Trees in Capital Investment,\" HBR (method, incl. the small-plant-with-option-to-expand structure). Raiffa, H. (1968), Decision Analysis, Addison-Wesley (rollback, sensitivity, EVPI). Contemporary context — the 2024–2026 surge in AI-related demand for leading-edge semiconductors and the accompanying public \"AI capex / overbuild / bubble\" debate, alongside the semiconductor industry's well-documented history of boom-bust capacity cycles — is drawn from widely reported industry and financial-press coverage of that period; the probabilities and dollar payoffs in this example are illustrative inputs to demonstrate the method, not figures from any filing.*\n\nFile v1.0.5:examples/eisenhower-1944-d-day-weather-decision.md\n\n# Method in Action: Eisenhower's D-Day Weather Decision (June 1944)\n\n> *Example for the [decision-tree](../SKILL.md) skill.*\n\nOn June 4–5, 1944, General Dwight D. Eisenhower faced the highest-stakes go/no-go decision of the war: launch Operation Overlord into marginal weather, or postpone. The decision was never written up as a formal tree — the method postdates it — but the deliberation at Southwick House maps onto the decision-tree process almost node for node, which is why decision analysts have cited it ever since.\n\n**The root decision node (square):** Go on June 6, or postpone. The branch set was tightly constrained: the invasion needed moonlight for the airborne drops and a low dawn tide to expose beach obstacles, so only a few days per month qualified. If June 6 was scrubbed, the next tidal window was around June 19 — roughly two weeks away.\n\n**The chance nodes (circles):** Each option led straight into an uncertainty Eisenhower did not control.\n\n- *Go, June 6* → chance node: does the brief break in the storm forecast by Group Captain James Stagg, SHAEF's chief meteorologist, actually hold? If yes: landings proceed under rough but workable conditions. If no: landing craft swamped, air support grounded, the assault force wrecked on the beaches.\n- *Postpone to June 19* → chance node: unknown weather two weeks out (beyond any 1944 forecast horizon), compounded by near-certain costs — nearly 200,000 troops were already sealed aboard ships and briefed, and every day of delay increased the odds that German intelligence would fix the time and place of the invasion.\n\n**Probabilities:** Stagg's team forecast a short interval of improved weather for June 6 amid a stormy period — a genuine probabilistic judgment made against disagreeing British and American forecasting teams. Illustrative reconstruction (not historical record): call the window-holds branch p ≈ 0.7, and the June 19 branch a coin flip at best with the secrecy-compromise cost accruing regardless. No participant wrote such numbers down; the structure of the argument, however, was exactly this.\n\n**Payoffs:** The asymmetry drove the answer. *Go and the window holds*: the liberation of Western Europe begins. *Go and it fails*: a bloody repulse — but a repulse that a second attempt could survive. *Postpone*: certain, compounding losses (secrecy, morale, tide, the Soviet-front timetable) plus an unresolved weather gamble two weeks later. Postponement was not the \"safe\" branch; it was a different bet with worse certain costs.\n\n**Value of information — the June 4 postponement:** Eisenhower's first move was a textbook EVPI play. On June 4 he scrubbed the original June 5 date and bought exactly one more forecast cycle — trading one day of the window for one more update from Stagg. When Stagg's June 5 briefing confirmed the break, the value of further waiting had collapsed: no additional forecast could resolve the remaining uncertainty before the tide window closed. The cost of more information now exceeded its value.\n\n**Rollback:** Folding back from the leaves: the *go* branch's expected outcome — even weighted for a serious chance of failure — beat the *postpone* branch's certain security erosion plus unresolved weather risk. In the early hours of June 5, Eisenhower gave the order to go. Before the landings he drafted a note taking sole responsibility in case of failure — evidence that he had priced the losing branch explicitly rather than wishing it away.\n\n**The sensitivity check history ran for free:** June 19 — the fallback window — brought the worst Channel storm in decades, wrecking the American Mulberry harbor off Omaha Beach. Had Eisenhower postponed, the invasion would have sailed into it. The decision was right at the assigned probabilities, and the unchosen branch turned out even worse than estimated.\n\nThe mapped steps:\n1. Root: go June 6 vs. postpone to ~June 19 — options fixed by tide and moon (Process Step 1)\n2. Chance nodes: forecast window holds/fails; June 19 weather unknown + secrecy erosion — MECE branches on each option (Step 2)\n3. Probabilities: Stagg's explicit short-window forecast against dissenting teams; reconstruction here is illustrative, the probabilistic reasoning is documented (Step 3)\n4. Payoffs: asymmetric — recoverable failure on *go* vs. certain compounding costs on *postpone* (Step 4)\n5. Rollback: *go* dominates once the June 5 forecast update lands; order given early June 5 (Step 5)\n6. Value of information: the 24-hour postponement bought one more forecast cycle, then EVPI of further delay fell below its cost — decide now (Step 6)\n\nPrimary source: Eisenhower, D. D. (1948). *Crusade in Europe.* Doubleday — Eisenhower's own account of the postponement and the go decision. Corroborating: Stagg, J. M. (1971). *Forecast for Overlord.* Ian Allan — the SHAEF chief meteorologist's account of the forecasts behind the decision.\n\nFile v1.0.5:examples/magee-1964-chemical-plant-investment-hbr.md\n\n# Method in Action: Magee 1964 — Chemical Plant Investment (HBR)\n\n> *Example for the [decision-tree](../SKILL.md) skill.*\n\n**John F. Magee** (1926–2015) was a partner at Arthur D. Little and the first analyst to systematize decision tree methodology for business. His two 1964 *Harvard Business Review* articles introduced the framework to a generation of executives and consultants who had previously made multi-million-dollar investment decisions through intuition and scenario narratives.\n\nMagee's canonical case: a chemical company facing a ten-year capital investment decision with uncertain demand. Two options — build a **large plant** (high fixed cost, high capacity) or a **small plant** (low fixed cost, low capacity with an option to expand in year 2). Demand over the period could be high or low, with a possibility of reversal between years 1–2 and years 3–10.\n\nThe HBR framing:\n\n> \"A decision tree is a diagram that describes graphically the various possible combinations of events and the decisions associated with them. It draws out the sequential decisions with their alternative choices and their consequences ... forcing managers to be explicit about the alternatives at each stage of the decision process.\"\n>\n> — Magee (1964), \"Decision Trees for Decision Making,\" HBR, p. 127.\n\nThe tree structure:\n- Root: Large plant vs. Small plant (decision node, square)\n- Year 1–2 demand: High (0.60) vs. Low (0.40) — chance node on each branch\n- If Small plant + High demand: expand or do not expand (second decision node)\n- Years 3–10 demand conditional on years 1–2 outcome\n\n**Rollback results:** Magee calculated that the large plant had a higher expected NPV than the small plant — but only because the probability assigned to high demand was above a critical threshold of approximately 0.55. When the team was asked to justify that 0.60 probability, three executives disagreed: one said 0.70, one said 0.50, one said 0.55. The tree converted a boardroom argument from \"I think we should build big\" to \"what probability do you assign to high demand in years 1–2?\" — a precise, revisable, evidenced question.\n\n**Howard Raiffa's formalization (1968)** built on Magee's work to establish the rollback procedure as a mathematical discipline, introduce formal sensitivity analysis (the switchover probability), and define the **Expected Value of Perfect Information (EVPI)** — the maximum a decision-maker should pay to resolve an uncertainty before deciding. Raiffa's EVPI formula:\n\n> \"EVPI is the expected gain from having perfect information about the state of the world before committing to a choice. It sets the upper bound on the value of any research or investigation that reduces uncertainty about that state.\"\n>\n> — Raiffa (1968), *Decision Analysis*, p. 112.\n\nIf EVPI for the demand forecast uncertainty was $2M, and a market research study costs $500K, the study is worth commissioning. If EVPI is $200K and the study costs $500K, decide immediately.\n\n**Operational lessons from Magee + Raiffa:**\n\nThe three-step discipline they established:\n\n1. **Draw before calculating.** The visual structure surfaces assumptions that participants didn't realize they were making. The act of drawing the tree is worth more than the rollback calculation.\n2. **Assign probabilities explicitly.** \"High demand\" means nothing until it has a probability. Force every probability owner to state a number and a basis. Disagreements about numbers are more productive than disagreements about direction.\n3. **Compute EVPI before gathering data.** The tree tells you what information is worth buying. Spending $1M on research that could only change the decision by $200K is irrational. EVPI makes that explicit.\n\n**McKinsey and BCG adoption (1970s–80s).** Both firms used decision trees as their primary tool for capital investment visualization. The tree format allowed consultants to walk executives through complex multi-stage decisions in one diagram — making implicit assumptions visible, driving consensus on probabilities, and producing a defensible recommendation with explicit conditions.\n\nThe most important lesson from the HBR case: **the tree revealed the threshold, not just the recommendation.** Knowing that the large plant wins only if demand probability exceeds 0.55 — and that the team had uncertainty around that threshold — was more valuable than the expected value itself. The recommendation was: proceed with large plant AND commission a targeted demand study to validate the 0.60 probability estimate before ground-breaking.\n\nFile v1.0.5:skill-card.md\n\n## Description:\n\nDecision Tree helps an agent structure multi-stage decisions with choices, chance events, probabilities, payoffs, rollback calculations, sensitivity thresholds, and EVPI.\n\nThis skill is ready for commercial/non-commercial use.\n\n## Publisher:\n\n[deciqai](https://clawhub.ai/user/deciqai)\n\n### License/Terms of Use:\n\nMIT-0\n\n## Use Case:\n\nExternal users, employees, and developers use this skill to help agents turn sequential, uncertain, quantifiable decisions into explicit decision trees with rollback, sensitivity analysis, and recommendations that state when they hold or flip.\n\n### Deployment Geography for Use:\n\nGlobal\n\n## Known Risks and Mitigations:\n\nRisk: Financial, legal, operational, or strategic recommendations may be mistaken if assumptions, probabilities, or payoffs are incomplete or poorly estimated.\n\nMitigation: Treat outputs as analysis scaffolding; review assumptions, calculations, and expert input before making high-stakes decisions.\n\nRisk: A decision tree can omit material branches or use mixed payoff units, producing misleading expected values.\n\nMitigation: Verify that branches are MECE, probabilities sum to 1.0 at each chance node, payoffs use consistent units, and sensitivity analysis is complete.\n\n## Reference(s):\n\n- [Decision Tree Skill Page](https://clawhub.ai/deciqai/skills/decision-tree)\n- [Sources - decision-tree](references/sources.md)\n- [Magee 1964 - Chemical Plant Investment](examples/magee-1964-chemical-plant-investment-hbr.md)\n- [Eisenhower's D-Day Weather Decision](examples/eisenhower-1944-d-day-weather-decision.md)\n- [Chipmaker Leading-Edge Fab Investment Under AI Uncertainty](examples/chipmaker-leading-edge-fab-investment-2024-2026.md)\n\n## Skill Output:\n\n**Output Type(s):** [text, markdown, guidance]\n\n**Output Format:** [Markdown with decision-tree tables and concise recommendations]\n\n**Output Parameters:** [1D]\n\n**Other Properties Related to Output:** [May include probability tables, payoff tables, rollback calculations, sensitivity thresholds, and EVPI estimates.]\n\n## Skill Version(s):\n\n1.0.5 (source: server release metadata)\n\n## Ethical Considerations:\n\nUsers should evaluate whether this skill is appropriate for their environment, review any generated or modified files before relying on them, and apply their organization's safety, security, and compliance requirements before deployment.\n\nArchive v1.0.4: 7 files, 16448 bytes\n\nFiles: examples/chipmaker-leading-edge-fab-investment-2024-2026.md (8743b), examples/eisenhower-1944-d-day-weather-decision.md (4942b), examples/magee-1964-chemical-plant-investment-hbr.md (4583b), references/sources.md (2826b), skill-card.md (2643b), SKILL.md (8246b), _meta.json (132b)\n\nFile v1.0.4:SKILL.md\n\n---\nname: decision-tree\ndescription: \"Activate when: user says 'help me choose between two options with different risks', 'I need to map out what could happen if we go with X', 'we have a sequential decision — first we do A then depending on results we do B', 'what is the expected value of this investment given uncertain demand'. Do NOT activate when: the decision is a one-shot choice with no sequential stages (use simple EV instead); probabilities cannot be estimated even roughly and uncertainty is too deep to quantify.\"\n---\n\n# Decision Tree\n\n## Overview\n\nA **decision tree** maps a multi-stage decision: decision nodes (squares) for choices you control, chance nodes (circles) for outcomes you don't, probabilities on every branch, payoffs at the leaves — then rollback right-to-left to get expected value at the root. First systematized by John F. Magee (HBR, 1964); formalized by Howard Raiffa (1968). Its biggest value: converting \"I feel we should expand\" into \"what probability do you assign to high demand?\" — making every assumption explicit and contestable.\n\nComposes with `expected-value-and-kelly` (EV scaffold + bet sizing), `probabilistic-thinking` (calibration per node), `inversion` (rollback = working outcomes backward), `mece` (branches must be MECE so probabilities sum to 1.0).\n\n## When to Use\n\n- Decision has sequential stages (decide → learn → decide again)\n- Outcomes uncertain; probabilities can be estimated (even roughly)\n- Payoffs quantifiable (NPV, revenue, cost, lives saved)\n- Multiple stakeholders need a shared visual model to align on assumptions\n- Sizing a big irreversible bet under AI uncertainty — build vs. buy vs. wait on AI capex, a fab investment, or committing while AI adoption / AI valuations are unproven\n\n**Not when:** one-shot choice with no stages; probabilities unestimable; payoffs purely qualitative; branch set too large (use scenario planning instead).\n\n## Coaching Novices (Adaptive Front Door)\n\n- **Engine mode:** user has a concrete multi-stage decision → run The Process directly.\n- **Coach mode:** user is unfamiliar or has no concrete case → guide step by step.\n\nIn Coach mode, respond one step at a time. Each [WAIT] is a hard stop — output only that step's question, then stop.\n\n1. **One-line:** a decision tree converts \"I feel\" into \"what probability do you assign?\" — making assumptions explicit so they can be argued about.\n2. **Check fit.** Sequential stages? Uncertain outcomes? Quantifiable payoffs? If yes to all three, a tree applies.\n3. **Elicit their real case.** What's the initial choice? What uncertain outcomes follow? What payoffs result?\n> **[WAIT — do not advance until user responds]**\n4. **Run The Process one step at a time** with their input — draw structure, assign probabilities, assign payoffs, roll back.\n> **[WAIT — do not advance until user responds]**\n5. **Close** by naming the insight: the threshold at which the recommendation flips, and whether to gather more data.\n> **[WAIT — do not advance until user responds]**\n\n## The Process\n\n**Step 1 — Root:** Define the decision (options, timeline, decision-maker). Draw a square; each option is a branch.\n\n**Step 2 — Chance nodes:** For each branch, identify uncertain events → draw circles. Branches at each circle must be MECE; probabilities must sum to 1.0.\n\n**Step 3 — Probabilities:** Assign a number (0.0–1.0) + documented basis to every branch. Reject \"50/50\" without justification.\n\n**Step 4 — Payoffs:** Assign consistent-unit payoffs (NPV, revenue, etc.) to every terminal leaf.\n\n**Step 5 — Rollback:** Right to left — EV at each circle = Σ(p × value). At each square, keep highest EV branch; mark losers //.\n\n**Step 6 — Sensitivity + stop-rule:** Find the probability threshold where the optimal choice switches. Compute EVPI = EV(perfect info) − EV(best decision now). If EVPI < cost of data: decide now. If EVPI > cost: gather data first. Stop refining when the leading option's EV advantage exceeds the value of further analysis.\n\n## Output Template\n```\nDecision Tree: <topic>\nOptions: A / B  |  Timeline:\nTree: [node-by-node description]\nProbabilities: Node | Branch | p | Basis\nPayoffs: Path | Value | Unit\nRollback: Option A EV= / Option B EV= / Optimal=\nSensitivity: flips when p([key branch]) > [threshold]  |  EVPI=\nRecommendation: [option] — holds if [condition]; flips if [condition]\n```\n\n*→ Method in Action: [Magee 1964 — Chemical Plant Investment (HBR)](examples/magee-1964-chemical-plant-investment-hbr.md) · [Eisenhower's D-Day Weather Decision](examples/eisenhower-1944-d-day-weather-decision.md)*\n*→ 2026 lens: [A Chipmaker's Leading-Edge Fab Investment Under AI Uncertainty (2024–2026)](examples/chipmaker-leading-edge-fab-investment-2024-2026.md)*\n\n## Pack: Decision Tree by Domain\n\n| Domain | Root Decision | Key Uncertainty | Payoff | Watch For |\n|---|---|---|---|---|\n| Capital investment | Large vs. small plant | Demand scenarios | NPV | Overconfident demand p |\n| R&D portfolio | Fund vs. kill | Technical success; adoption | Revenue × p | Ignoring base-rate failure |\n| Litigation | Settle vs. litigate | Win/lose; damages | Expected settlement | Anchoring on best case |\n| Product launch | Now vs. delay | Market reception; competitor | Revenue per scenario | Missing competitor-first branch |\n| M&A | Acquire vs. pass | Integration; synergy | Post-acquisition EV | Paying for performance peak |\n\n## Applying It Well\n\n- Draw before calculating — structure surfaces hidden assumptions\n- Assign probabilities before revealing your preferred option\n- Run sensitivity before concluding; find the switchover threshold and EVPI\n- Audit missing branches explicitly: \"what did we leave out?\"\n\n*→ Primary sources: [references/sources.md](references/sources.md)*\n\n## Common Rationalizations\n\n**[D] = designed upfront | [O] = observed in real use. [O] entries are more valuable.**\n\n| Rationalization (Fake Move) | Reality |\n|---|---|\n| [D] \"This is strategic — we don't need numbers.\" | Without numbers the tree is just a picture. Force strategic disagreements to become numerical ones. |\n| [D] \"We can't estimate probabilities.\" | Even rough estimates beat implicit zero/one assumptions. Every un-numbered branch already has an implicit probability. |\n| [D] \"The tree chose A — we're done.\" | Holds only at assigned probabilities. Sensitivity analysis is mandatory before concluding. |\n| [D] \"We enumerated all branches.\" | Trees are always simplifications. Ask explicitly: what branches are missing? |\n| [D] \"It's 50/50 — we just don't know.\" | 50/50 is a claim requiring justification. What base rate supports it? |\n| [D] \"My gut says B even though the tree says A.\" | Gut = implicit tree with different probabilities. Find which number your gut is using and put it in. |\n| [D] \"The tree gave a recommendation — it must be right.\" | GIGO: garbage probabilities produce garbage recommendations. Calibrate inputs first. |\n| *→ Add [O] entries here after each real use — paste the actual failure pattern* | *What went wrong and why* |\n\n## Red Flags\n\n- Probabilities verbal only — no numbers written | Chance-node probabilities don't sum to 1.0\n- No sensitivity analysis performed | Terminal payoffs in mixed units across branches\n- Probabilities assigned post-hoc to justify a pre-decided conclusion | No missing-branch audit\n\n## Verification\n\n- [ ] Root decision defined; all options enumerated\n- [ ] All chance nodes MECE; probabilities sum to 1.0 at each node\n- [ ] Every probability has documented basis\n- [ ] All terminal payoffs in same unit and discount rate\n- [ ] Rollback verified numerically at every node\n- [ ] Sensitivity complete — switchover threshold identified\n- [ ] EVPI calculated; data-gathering decision made\n- [ ] Missing-branch audit performed; recommendation states conditions it holds and flips\n---\n*Part of **deciqAI Knowledge Skills** — 164 open-source thinking skills that make rigor executable for AI agents. The same skills power every deciqAI agent, which runs them autonomously to operate your company. **See it run → https://www.deciqai.com/c/decision-tree** · ⭐ Star the repo → https://github.com/deciqAI/knowledge-skills · Contributions welcome.*\n\nFile v1.0.4:_meta.json\n\n{\n  \"ownerId\": \"kn754b8sk22s8c6gjxt02bftbn88q7ye\",\n  \"slug\": \"decision-tree\",\n  \"version\": \"1.0.4\",\n  \"publishedAt\": 1783508337760\n}\n\nFile v1.0.4:references/sources.md\n\n# Sources — decision-tree\n\n> *Primary sources for the [decision-tree](../SKILL.md) skill.*\n\n## Sources\n\n- Magee, J. F. (1964). \"Decision Trees for Decision Making.\" *Harvard Business Review*, July–August, 126–138. The original practitioner framework.\n- Magee, J. F. (1964). \"How to Use Decision Trees in Capital Investment.\" *Harvard Business Review*, September–October, 79–96. Capital investment application.\n- Raiffa, H. (1968). *Decision Analysis: Introductory Lectures on Choices under Uncertainty.* Addison-Wesley. The academic formalization; introduces EVPI and formal rollback.\n- Howard, R. A. (1966). \"Decision Analysis: Applied Decision Theory.\" *Proceedings of the 4th International Conference on Operational Research.* Stanford. Early theoretical grounding.\n- Howard, R. A., & Matheson, J. E. (Eds.) (1983). *Readings on the Principles and Applications of Decision Analysis.* Strategic Decisions Group. Comprehensive practitioner reference.\n- Clemen, R. T., & Reilly, T. (2013). *Making Hard Decisions with DecisionTools.* Cengage. Standard textbook treatment.\n- Eisenhower, D. D. (1948). *Crusade in Europe.* Doubleday. First-hand account of the D-Day weather go/no-go decision (worked example).\n- Stagg, J. M. (1971). *Forecast for Overlord.* Ian Allan. The SHAEF chief meteorologist's account of the June 1944 forecasts.\n- Major U.S. hyperscaler quarterly earnings guidance and calls, 2024–2026 (Microsoft, Alphabet, Amazon, Meta). Primary source for the reported surge in AI-related capital expenditure and management's commentary on committing to AI capacity under uncertain returns. Context for the AI build-vs-buy-vs-wait worked example.\n- Mainstream financial-press coverage of the 2024–2026 \"AI capex / overbuild / bubble\" debate (e.g., The Wall Street Journal, Financial Times, The Economist, Reuters). Durable, widely-reported context for how large firms weighed heavy AI infrastructure investment against the risk of stranded capacity.\n- Leading semiconductor foundries' and integrated device makers' public capital-expenditure guidance and management commentary, 2024–2026 (as reported in earnings materials and mainstream financial press). Context for the chipmaker leading-edge-fab worked example: the multi-year, multi-billion-dollar nature of advanced-node fab commitments made ahead of confirmed AI-driven demand.\n- Widely reported industry coverage of the semiconductor sector's historical boom-bust capacity cycles and of the 2024–2026 debate over whether AI-driven demand for leading-edge chips is durable or a potential overbuild (e.g., trade press such as SemiAnalysis-style analysis alongside general financial press). Durable, well-documented context for the high/low-demand probability framing; no specific figures in the worked example are drawn from any single filing.\n\nFile v1.0.4:examples/chipmaker-leading-edge-fab-investment-2024-2026.md\n\n# Method in Action: A Chipmaker's Leading-Edge Fab Investment Under AI Uncertainty (2024–2026)\n\n> *Example for the [decision-tree](../SKILL.md) skill.*\n\nBetween 2024 and 2026, one of the largest irreversible capital bets in the economy was a semiconductor manufacturer's decision to commit to leading-edge fabrication capacity. A single advanced logic fab is a multi-year, multi-billion-dollar commitment made *years* before the demand that would fill it is confirmed. The AI wave made this sharper on both sides: the *upside* case (AI accelerators and their supply chain filling every wafer) and the *downside* case (a capacity glut if AI demand or monetization disappoints, echoing prior semiconductor boom-bust cycles). This is a textbook decision-tree problem — sequential, uncertain, quantifiable — and the tree does exactly what Magee promised in 1964: it converts \"AI demand is unstoppable, we must break ground now\" into \"what probability do you put on sustained high demand, and what does the tree say if you are wrong?\"\n\nThis worked example applies the skill's six Process steps to a **stylized composite** of that decision. The framing (large fab now vs. phased/modular fab vs. defer, under high/low AI-driven demand) mirrors the real 2024–2026 debate; the probabilities and dollar payoffs below are **illustrative inputs chosen to demonstrate the method**, not figures from any company's filings.\n\n---\n\n**Step 1 — Root.** Define the decision. A chipmaker's board must choose how to commit leading-edge wafer capacity over a multi-year horizon. Draw the root square with three branches:\n\n- **Large fab now** — commit to a full-scale advanced fab immediately. Highest fixed cost and longest lead time, best unit economics *if* demand shows up, most stranded capital if it does not.\n- **Phased / modular fab** — build the shell and a first module now, with a pre-engineered *option to expand* tooling later once demand is clearer (directly the small-plant-with-expansion structure Magee introduced in 1964).\n- **Defer** — hold the large commitment ~12 months, gather adoption and pricing signal, then decide. Deferral is not free: a fab's multi-year construction-and-qualification lead time means capacity decided late arrives late, potentially after the window of peak demand.\n\nDecision-maker: the board / CFO. Timeline: leading-edge fab lead times run into years — which is precisely why \"wait\" carries a real delay cost.\n\n**Step 2 — Chance nodes.** Each branch runs into an uncertainty the firm does not control. Draw a circle on each. The dominant chance node is **AI-driven wafer demand**, which must be MECE:\n\n- *High, durable demand* — AI-accelerator and adjacent demand keeps leading-edge capacity near-full for years.\n- *Low / disappointing demand* — AI adoption or monetization stalls, or competitors add capacity too; the new fab runs underutilized (the \"AI capex glut / bubble\" fear that ran through the 2024–2026 debate).\n\nFor **Phased / modular**, a second-stage decision node follows the year-1 signal: having observed high or low demand, *then* choose to install the expansion tooling or hold — the learn-then-decide structure that makes a tree worth more than a one-shot EV.\n\n**Step 3 — Probabilities.** Assign a number and a basis to every branch; reject an unjustified \"50/50.\" Illustrative inputs for this composite:\n\n| Node | Branch | p | Basis (illustrative) |\n|---|---|---|---|\n| AI wafer demand | High, durable | 0.60 | Sustained AI-accelerator demand and leading-edge order signals reported during the 2024–2025 build-out |\n| AI wafer demand | Low / disappointing | 0.40 | Historical semiconductor boom-bust base rate; overbuild / bubble concerns aired publicly in the same period |\n\nThe number matters less than forcing its owners to state and defend it — which is where a boardroom's \"the AI opportunity is enormous\" becomes a concrete, revisable argument about one probability.\n\n**Step 4 — Payoffs.** Assign consistent-unit payoffs (illustrative multi-year NPV, arbitrary units) to every terminal leaf:\n\n- Large fab + High demand → **+100** (full-scale capacity, best margins, near-full utilization)\n- Large fab + Low demand → **−45** (stranded, underutilized leading-edge assets; the overbuild downside)\n- Phased + High demand → **+70** (installs expansion after the signal; captures most upside but pays a modularity premium and some ramp delay)\n- Phased + Low demand → **+5** (holds expansion; limited loss — the bounded-downside branch)\n- Defer, then build after signal → payoffs as above **minus a delay cost** (share and pricing ceded during the wait, plus a scarcity premium on equipment if everyone breaks ground at once)\n\n**Step 5 — Rollback.** Right to left, EV at each chance node = Σ(p × value):\n\n- **Large fab EV** = 0.60(+100) + 0.40(−45) = 60 − 18 = **+42**\n- **Phased EV** = 0.60(+70) + 0.40(+5) = 42 + 2 = **+44**\n- **Defer EV** = the value of deciding *after* the signal, minus the delay cost. Its appeal is highest when the demand probability sits near the middle (uncertainty is greatest, so learning is worth most) and lowest when demand looks clearly high (deferral just cedes ground) or clearly low (little worth waiting to build).\n\nAt assigned inputs, **Phased narrowly leads (+44 vs. +42)** — the bounded-downside branch beats the full commitment precisely because the 0.40 weight on disappointing demand makes the large fab's −45 tail expensive. Mark the losing branch `//`. Per the skill, the recommendation is not \"go phased,\" it is \"go phased *at these probabilities*.\"\n\n**Step 6 — Sensitivity + stop-rule.** Find where the choice flips. Setting Large-fab EV = Phased EV:\n\n`p(100) + (1−p)(−45) = p(70) + (1−p)(5)`\n→ `145p − 45 = 65p + 5`\n→ `80p = 50`\n→ **p\\* = 0.625.**\n\nSo the Large fab only beats Phased once p(high demand) exceeds **≈0.625**. At the assumed 0.60 the tree favors Phased, but the gap is thin: a modestly *more* bullish demand read (above 0.625) flips it to the full-scale fab, and a *more* bearish read widens Phased's lead. That single threshold is the real output. It reframes the whole \"is AI-fab capacity a rational bet or a bubble?\" debate as: *do you believe durable-high-demand probability sits above or below ~0.625?*\n\n**EVPI / stop-rule.** Compute the value of resolving the demand uncertainty before committing. With perfect foresight the firm picks the best action in each state: +100 (Large) if high, +5 (Phased-hold) if low → EV(perfect info) = 0.60(100) + 0.40(5) = 62. Best action now (Phased, +44) → **EVPI = 62 − 44 = 18** (illustrative units). If a year of adoption data, customer pre-commitments, or a smaller pilot line costs *less* than that 18, buy the information first — the disciplined case for the phased/defer path. If resolving the uncertainty would cost *more* than 18 (deferral cedes irrecoverable position, or lead times mean late capacity is worthless), commit now. Stop refining once the leading option's EV advantage exceeds the value of further analysis.\n\n---\n\n**The insight the tree delivers.** Not \"build the fab\" or \"don't,\" but three contestable objects: (1) the demand probability everyone is really arguing about, (2) the **p\\* ≈ 0.625 threshold** at which full commitment overtakes the phased option, and (3) an EVPI that says whether a year's wait or a pilot line is worth its cost. Note how this differs from the [hyperscaler build-vs-buy-vs-wait example](ai-capex-build-vs-buy-vs-wait-2024-2026.md): a chipmaker cannot \"buy\" leading-edge capacity from a cloud provider, so its middle branch is *modularity* (phase the fab) rather than *rental* — and that structural difference moves the switchover threshold. Missing-branch audit: this composite omits a joint-venture / customer-prepay structure, a trailing-edge fallback, and competitor-first dynamics — real trees are always simplifications, and naming what's left out is mandatory.\n\n*Sources: Magee, J. F. (1964), \"Decision Trees for Decision Making,\" Harvard Business Review, and \"How to Use Decision Trees in Capital Investment,\" HBR (method, incl. the small-plant-with-option-to-expand structure). Raiffa, H. (1968), Decision Analysis, Addison-Wesley (rollback, sensitivity, EVPI). Contemporary context — the 2024–2026 surge in AI-related demand for leading-edge semiconductors and the accompanying public \"AI capex / overbuild / bubble\" debate, alongside the semiconductor industry's well-documented history of boom-bust capacity cycles — is drawn from widely reported industry and financial-press coverage of that period; the probabilities and dollar payoffs in this example are illustrative inputs to demonstrate the method, not figures from any filing.*\n\nFile v1.0.4:examples/eisenhower-1944-d-day-weather-decision.md\n\n# Method in Action: Eisenhower's D-Day Weather Decision (June 1944)\n\n> *Example for the [decision-tree](../SKILL.md) skill.*\n\nOn June 4–5, 1944, General Dwight D. Eisenhower faced the highest-stakes go/no-go decision of the war: launch Operation Overlord into marginal weather, or postpone. The decision was never written up as a formal tree — the method postdates it — but the deliberation at Southwick House maps onto the decision-tree process almost node for node, which is why decision analysts have cited it ever since.\n\n**The root decision node (square):** Go on June 6, or postpone. The branch set was tightly constrained: the invasion needed moonlight for the airborne drops and a low dawn tide to expose beach obstacles, so only a few days per month qualified. If June 6 was scrubbed, the next tidal window was around June 19 — roughly two weeks away.\n\n**The chance nodes (circles):** Each option led straight into an uncertainty Eisenhower did not control.\n\n- *Go, June 6* → chance node: does the brief break in the storm forecast by Group Captain James Stagg, SHAEF's chief meteorologist, actually hold? If yes: landings proceed under rough but workable conditions. If no: landing craft swamped, air support grounded, the assault force wrecked on the beaches.\n- *Postpone to June 19* → chance node: unknown weather two weeks out (beyond any 1944 forecast horizon), compounded by near-certain costs — nearly 200,000 troops were already sealed aboard ships and briefed, and every day of delay increased the odds that German intelligence would fix the time and place of the invasion.\n\n**Probabilities:** Stagg's team forecast a short interval of improved weather for June 6 amid a stormy period — a genuine probabilistic judgment made against disagreeing British and American forecasting teams. Illustrative reconstruction (not historical record): call the window-holds branch p ≈ 0.7, and the June 19 branch a coin flip at best with the secrecy-compromise cost accruing regardless. No participant wrote such numbers down; the structure of the argument, however, was exactly this.\n\n**Payoffs:** The asymmetry drove the answer. *Go and the window holds*: the liberation of Western Europe begins. *Go and it fails*: a bloody repulse — but a repulse that a second attempt could survive. *Postpone*: certain, compounding losses (secrecy, morale, tide, the Soviet-front timetable) plus an unresolved weather gamble two weeks later. Postponement was not the \"safe\" branch; it was a different bet with worse certain costs.\n\n**Value of information — the June 4 postponement:** Eisenhower's first move was a textbook EVPI play. On June 4 he scrubbed the original June 5 date and bought exactly one more forecast cycle — trading one day of the window for one more update from Stagg. When Stagg's June 5 briefing confirmed the break, the value of further waiting had collapsed: no additional forecast could resolve the remaining uncertainty before the tide window closed. The cost of more information now exceeded its value.\n\n**Rollback:** Folding back from the leaves: the *go* branch's expected outcome — even weighted for a serious chance of failure — beat the *postpone* branch's certain security erosion plus unresolved weather risk. In the early hours of June 5, Eisenhower gave the order to go. Before the landings he drafted a note taking sole responsibility in case of failure — evidence that he had priced the losing branch explicitly rather than wishing it away.\n\n**The sensitivity check history ran for free:** June 19 — the fallback window — brought the worst Channel storm in decades, wrecking the American Mulberry harbor off Omaha Beach. Had Eisenhower postponed, the invasion would have sailed into it. The decision was right at the assigned probabilities, and the unchosen branch turned out even worse than estimated.\n\nThe mapped steps:\n1. Root: go June 6 vs. postpone to ~June 19 — options fixed by tide and moon (Process Step 1)\n2. Chance nodes: forecast window holds/fails; June 19 weather unknown + secrecy erosion — MECE branches on each option (Step 2)\n3. Probabilities: Stagg's explicit short-window forecast against dissenting teams; reconstruction here is illustrative, the probabilistic reasoning is documented (Step 3)\n4. Payoffs: asymmetric — recoverable failure on *go* vs. certain compounding costs on *postpone* (Step 4)\n5. Rollback: *go* dominates once the June 5 forecast update lands; order given early June 5 (Step 5)\n6. Value of information: the 24-hour postponement bought one more forecast cycle, then EVPI of further delay fell below its cost — decide now (Step 6)\n\nPrimary source: Eisenhower, D. D. (1948). *Crusade in Europe.* Doubleday — Eisenhower's own account of the postponement and the go decision. Corroborating: Stagg, J. M. (1971). *Forecast for Overlord.* Ian Allan — the SHAEF chief meteorologist's account of the forecasts behind the decision.\n\nFile v1.0.4:examples/magee-1964-chemical-plant-investment-hbr.md\n\n# Method in Action: Magee 1964 — Chemical Plant Investment (HBR)\n\n> *Example for the [decision-tree](../SKILL.md) skill.*\n\n**John F. Magee** (1926–2015) was a partner at Arthur D. Little and the first analyst to systematize decision tree methodology for business. His two 1964 *Harvard Business Review* articles introduced the framework to a generation of executives and consultants who had previously made multi-million-dollar investment decisions through intuition and scenario narratives.\n\nMagee's canonical case: a chemical company facing a ten-year capital investment decision with uncertain demand. Two options — build a **large plant** (high fixed cost, high capacity) or a **small plant** (low fixed cost, low capacity with an option to expand in year 2). Demand over the period could be high or low, with a possibility of reversal between years 1–2 and years 3–10.\n\nThe HBR framing:\n\n> \"A decision tree is a diagram that describes graphically the various possible combinations of events and the decisions associated with them. It draws out the sequential decisions with their alternative choices and their consequences ... forcing managers to be explicit about the alternatives at each stage of the decision process.\"\n>\n> — Magee (1964), \"Decision Trees for Decision Making,\" HBR, p. 127.\n\nThe tree structure:\n- Root: Large plant vs. Small plant (decision node, square)\n- Year 1–2 demand: High (0.60) vs. Low (0.40) — chance node on each branch\n- If Small plant + High demand: expand or do not expand (second decision node)\n- Years 3–10 demand conditional on years 1–2 outcome\n\n**Rollback results:** Magee calculated that the large plant had a higher expected NPV than the small plant — but only because the probability assigned to high demand was above a critical threshold of approximately 0.55. When the team was asked to justify that 0.60 probability, three executives disagreed: one said 0.70, one said 0.50, one said 0.55. The tree converted a boardroom argument from \"I think we should build big\" to \"what probability do you assign to high demand in years 1–2?\" — a precise, revisable, evidenced question.\n\n**Howard Raiffa's formalization (1968)** built on Magee's work to establish the rollback procedure as a mathematical discipline, introduce formal sensitivity analysis (the switchover probability), and define the **Expected Value of Perfect Information (EVPI)** — the maximum a decision-maker should pay to resolve an uncertainty before deciding. Raiffa's EVPI formula:\n\n> \"EVPI is the expected gain from having perfect information about the state of the world before committing to a choice. It sets the upper bound on the value of any research or investigation that reduces uncertainty about that state.\"\n>\n> — Raiffa (1968), *Decision Analysis*, p. 112.\n\nIf EVPI for the demand forecast uncertainty was $2M, and a market research study costs $500K, the study is worth commissioning. If EVPI is $200K and the study costs $500K, decide immediately.\n\n**Operational lessons from Magee + Raiffa:**\n\nThe three-step discipline they established:\n\n1. **Draw before calculating.** The visual structure surfaces assumptions that participants didn't realize they were making. The act of drawing the tree is worth more than the rollback calculation.\n2. **Assign probabilities explicitly.** \"High demand\" means nothing until it has a probability. Force every probability owner to state a number and a basis. Disagreements about numbers are more productive than disagreements about direction.\n3. **Compute EVPI before gathering data.** The tree tells you what information is worth buying. Spending $1M on research that could only change the decision by $200K is irrational. EVPI makes that explicit.\n\n**McKinsey and BCG adoption (1970s–80s).** Both firms used decision trees as their primary tool for capital investment visualization. The tree format allowed consultants to walk executives through complex multi-stage decisions in one diagram — making implicit assumptions visible, driving consensus on probabilities, and producing a defensible recommendation with explicit conditions.\n\nThe most important lesson from the HBR case: **the tree revealed the threshold, not just the recommendation.** Knowing that the large plant wins only if demand probability exceeds 0.55 — and that the team had uncertainty around that threshold — was more valuable than the expected value itself. The recommendation was: proceed with large plant AND commission a targeted demand study to validate the 0.60 probability estimate before ground-breaking.\n\nFile v1.0.4:skill-card.md\n\n## Description: <br>\nGuides agents through decision-tree analysis for multi-stage decisions with uncertain outcomes, quantified probabilities, payoffs, rollback, sensitivity checks, and EVPI. <br>\n\nThis skill is ready for commercial/non-commercial use. <br>\n\n## Publisher: <br>\n[deciqai](https://clawhub.ai/user/deciqai) <br>\n\n### License/Terms of Use: <br>\nMIT-0 <br>\n\n\n## Use Case: <br>\nEmployees, external users, and decision-support agents use this skill to structure sequential choices with uncertain outcomes, explicit probabilities, quantified payoffs, rollback calculations, and sensitivity analysis. It is intended for cases where probabilities can be estimated and payoffs can be stated in consistent units. <br>\n\n### Deployment Geography for Use: <br>\nGlobal <br>\n\n## Known Risks and Mitigations: <br>\nRisk: Worked examples and illustrative probabilities could be mistaken for case-specific financial, legal, operational, or historical advice. <br>\nMitigation: Require users to validate probabilities, payoffs, assumptions, and recommendations against independent evidence before acting. <br>\nRisk: Decision-tree outputs can become misleading when probabilities are unsupported, branches are incomplete, or terminal payoffs use mixed units. <br>\nMitigation: Use the skill's verification checklist: confirm MECE branches, probability sums, documented bases, consistent payoff units, rollback arithmetic, sensitivity analysis, EVPI, and missing-branch audit. <br>\n\n\n## Reference(s): <br>\n- [Primary Sources](references/sources.md) <br>\n- [Magee 1964 Chemical Plant Investment Example](examples/magee-1964-chemical-plant-investment-hbr.md) <br>\n- [Eisenhower D-Day Weather Decision Example](examples/eisenhower-1944-d-day-weather-decision.md) <br>\n- [Chipmaker Fab Investment Under AI Uncertainty Example](examples/chipmaker-leading-edge-fab-investment-2024-2026.md) <br>\n\n\n## Skill Output: <br>\n**Output Type(s):** [text, markdown, guidance] <br>\n**Output Format:** [Markdown decision-tree analysis with tables and concise recommendations] <br>\n**Output Parameters:** [1D] <br>\n**Other Properties Related to Output:** [May include node-by-node tree descriptions, probability and payoff tables, rollback calculations, sensitivity thresholds, EVPI, and conditional recommendations.] <br>\n\n## Skill Version(s): <br>\n1.0.4 (source: server release metadata) <br>\n\n## Ethical Considerations: <br>\nUsers should evaluate whether this skill is appropriate for their environment, review any generated or modified files before relying on them, and apply their organization's safety, security, and compliance requirements before deployment. <br>\n\nArchive v1.0.3: 6 files, 11198 bytes\n\nFiles: examples/eisenhower-1944-d-day-weather-decision.md (4942b), examples/magee-1964-chemical-plant-investment-hbr.md (4583b), references/sources.md (1345b), skill-card.md (2281b), SKILL.md (8020b), _meta.json (132b)\n\nFile v1.0.3:SKILL.md\n\n---\nname: decision-tree\ndescription: \"Activate when: user says 'help me choose between two options with different risks', 'I need to map out what could happen if we go with X', 'we have a sequential decision — first we do A then depending on results we do B', 'what is the expected value of this investment given uncertain demand'. Do NOT activate when: the decision is a one-shot choice with no sequential stages (use simple EV instead); probabilities cannot be estimated even roughly and uncertainty is too deep to quantify.\"\n---\n\n# Decision Tree\n\n## Overview\n\nA **decision tree** maps a multi-stage decision: decision nodes (squares) for choices you control, chance nodes (circles) for outcomes you don't, probabilities on every branch, payoffs at the leaves — then rollback right-to-left to get expected value at the root. First systematized by John F. Magee (HBR, 1964); formalized by Howard Raiffa (1968). Its biggest value: converting \"I feel we should expand\" into \"what probability do you assign to high demand?\" — making every assumption explicit and contestable.\n\nComposes with `expected-value-and-kelly` (EV scaffold + bet sizing), `probabilistic-thinking` (calibration per node), `inversion` (rollback = working outcomes backward), `mece` (branches must be MECE so probabilities sum to 1.0).\n\n## When to Use\n\n- Decision has sequential stages (decide → learn → decide again)\n- Outcomes uncertain; probabilities can be estimated (even roughly)\n- Payoffs quantifiable (NPV, revenue, cost, lives saved)\n- Multiple stakeholders need a shared visual model to align on assumptions\n\n**Not when:** one-shot choice with no stages; probabilities unestimable; payoffs purely qualitative; branch set too large (use scenario planning instead).\n\n## Coaching Novices (Adaptive Front Door)\n\n- **Engine mode:** user has a concrete multi-stage decision → run The Process directly.\n- **Coach mode:** user is unfamiliar or has no concrete case → guide step by step.\n\nIn Coach mode, respond one step at a time. Each [WAIT] is a hard stop — output only that step's question, then stop.\n\n1. **One-line:** a decision tree converts \"I feel\" into \"what probability do you assign?\" — making assumptions explicit so they can be argued about.\n2. **Check fit.** Sequential stages? Uncertain outcomes? Quantifiable payoffs? If yes to all three, a tree applies.\n3. **Elicit their real case.** What's the initial choice? What uncertain outcomes follow? What payoffs result?\n> **[WAIT — do not advance until user responds]**\n4. **Run The Process one step at a time** with their input — draw structure, assign probabilities, assign payoffs, roll back.\n> **[WAIT — do not advance until user responds]**\n5. **Close** by naming the insight: the threshold at which the recommendation flips, and whether to gather more data.\n> **[WAIT — do not advance until user responds]**\n\n## The Process\n\n**Step 1 — Root:** Define the decision (options, timeline, decision-maker). Draw a square; each option is a branch.\n\n**Step 2 — Chance nodes:** For each branch, identify uncertain events → draw circles. Branches at each circle must be MECE; probabilities must sum to 1.0.\n\n**Step 3 — Probabilities:** Assign a number (0.0–1.0) + documented basis to every branch. Reject \"50/50\" without justification.\n\n**Step 4 — Payoffs:** Assign consistent-unit payoffs (NPV, revenue, etc.) to every terminal leaf.\n\n**Step 5 — Rollback:** Right to left — EV at each circle = Σ(p × value). At each square, keep highest EV branch; mark losers //.\n\n**Step 6 — Sensitivity + stop-rule:** Find the probability threshold where the optimal choice switches. Compute EVPI = EV(perfect info) − EV(best decision now). If EVPI < cost of data: decide now. If EVPI > cost: gather data first. Stop refining when the leading option's EV advantage exceeds the value of further analysis.\n\n## Output Template\n```\nDecision Tree: <topic>\nOptions: A / B  |  Timeline:\nTree: [node-by-node description]\nProbabilities: Node | Branch | p | Basis\nPayoffs: Path | Value | Unit\nRollback: Option A EV= / Option B EV= / Optimal=\nSensitivity: flips when p([key branch]) > [threshold]  |  EVPI=\nRecommendation: [option] — holds if [condition]; flips if [condition]\n```\n\n*→ Method in Action: [Magee 1964 — Chemical Plant Investment (HBR)](examples/magee-1964-chemical-plant-investment-hbr.md) · [Eisenhower's D-Day Weather Decision](examples/eisenhower-1944-d-day-weather-decision.md)*\n\n## Pack: Decision Tree by Domain\n\n| Domain | Root Decision | Key Uncertainty | Payoff | Watch For |\n|---|---|---|---|---|\n| Capital investment | Large vs. small plant | Demand scenarios | NPV | Overconfident demand p |\n| R&D portfolio | Fund vs. kill | Technical success; adoption | Revenue × p | Ignoring base-rate failure |\n| Litigation | Settle vs. litigate | Win/lose; damages | Expected settlement | Anchoring on best case |\n| Product launch | Now vs. delay | Market reception; competitor | Revenue per scenario | Missing competitor-first branch |\n| M&A | Acquire vs. pass | Integration; synergy | Post-acquisition EV | Paying for performance peak |\n\n## Applying It Well\n\n- Draw before calculating — structure surfaces hidden assumptions\n- Assign probabilities before revealing your preferred option\n- Run sensitivity before concluding; find the switchover threshold and EVPI\n- Audit missing branches explicitly: \"what did we leave out?\"\n\n*→ Primary sources: [references/sources.md](references/sources.md)*\n\n## Common Rationalizations\n\n**[D] = designed upfront | [O] = observed in real use. [O] entries are more valuable.**\n\n| Rationalization (Fake Move) | Reality |\n|---|---|\n| [D] \"This is strategic — we don't need numbers.\" | Without numbers the tree is just a picture. Force strategic disagreements to become numerical ones. |\n| [D] \"We can't estimate probabilities.\" | Even rough estimates beat implicit zero/one assumptions. Every un-numbered branch already has an implicit probability. |\n| [D] \"The tree chose A — we're done.\" | Holds only at assigned probabilities. Sensitivity analysis is mandatory before concluding. |\n| [D] \"We enumerated all branches.\" | Trees are always simplifications. Ask explicitly: what branches are missing? |\n| [D] \"It's 50/50 — we just don't know.\" | 50/50 is a claim requiring justification. What base rate supports it? |\n| [D] \"My gut says B even though the tree says A.\" | Gut = implicit tree with different probabilities. Find which number your gut is using and put it in. |\n| [D] \"The tree gave a recommendation — it must be right.\" | GIGO: garbage probabilities produce garbage recommendations. Calibrate inputs first. |\n| *→ Add [O] entries here after each real use — paste the actual failure pattern* | *What went wrong and why* |\n\n## Red Flags\n\n- Probabilities verbal only — no numbers written | Chance-node probabilities don't sum to 1.0\n- No sensitivity analysis performed | Terminal payoffs in mixed units across branches\n- Probabilities assigned post-hoc to justify a pre-decided conclusion | No missing-branch audit\n\n## Verification\n\n- [ ] Root decision defined; all options enumerated\n- [ ] All chance nodes MECE; probabilities sum to 1.0 at each node\n- [ ] Every probability has documented basis\n- [ ] All terminal payoffs in same unit and discount rate\n- [ ] Rollback verified numerically at every node\n- [ ] Sensitivity complete — switchover threshold identified\n- [ ] EVPI calculated; data-gathering decision made\n- [ ] Missing-branch audit performed; recommendation states conditions it holds and flips\n---\n*Part of **deciqAI Knowledge Skills** — 163 open-source thinking skills that make rigor executable for AI agents. The same skills power every deciqAI agent, which runs them autonomously to operate your company. **See it run → https://www.deciqai.com/skills/decision-tree?utm_source=clawhub&utm_medium=marketplace&utm_campaign=knowledge-skills&utm_content=decision-tree** · ⭐ Star the repo → https://github.com/deciqAI/knowledge-skills · Contributions welcome.*\n\nFile v1.0.3:_meta.json\n\n{\n  \"ownerId\": \"kn754b8sk22s8c6gjxt02bftbn88q7ye\",\n  \"slug\": \"decision-tree\",\n  \"version\": \"1.0.3\",\n  \"publishedAt\": 1783481146937\n}\n\nFile v1.0.3:references/sources.md\n\n# Sources — decision-tree\n\n> *Primary sources for the [decision-tree](../SKILL.md) skill.*\n\n## Sources\n\n- Magee, J. F. (1964). \"Decision Trees for Decision Making.\" *Harvard Business Review*, July–August, 126–138. The original practitioner framework.\n- Magee, J. F. (1964). \"How to Use Decision Trees in Capital Investment.\" *Harvard Business Review*, September–October, 79–96. Capital investment application.\n- Raiffa, H. (1968). *Decision Analysis: Introductory Lectures on Choices under Uncertainty.* Addison-Wesley. The academic formalization; introduces EVPI and formal rollback.\n- Howard, R. A. (1966). \"Decision Analysis: Applied Decision Theory.\" *Proceedings of the 4th International Conference on Operational Research.* Stanford. Early theoretical grounding.\n- Howard, R. A., & Matheson, J. E. (Eds.) (1983). *Readings on the Principles and Applications of Decision Analysis.* Strategic Decisions Group. Comprehensive practitioner reference.\n- Clemen, R. T., & Reilly, T. (2013). *Making Hard Decisions with DecisionTools.* Cengage. Standard textbook treatment.\n- Eisenhower, D. D. (1948). *Crusade in Europe.* Doubleday. First-hand account of the D-Day weather go/no-go decision (worked example).\n- Stagg, J. M. (1971). *Forecast for Overlord.* Ian Allan. The SHAEF chief meteorologist's account of the June 1944 forecasts.\n\nFile v1.0.3:examples/eisenhower-1944-d-day-weather-decision.md\n\n# Method in Action: Eisenhower's D-Day Weather Decision (June 1944)\n\n> *Example for the [decision-tree](../SKILL.md) skill.*\n\nOn June 4–5, 1944, General Dwight D. Eisenhower faced the highest-stakes go/no-go decision of the war: launch Operation Overlord into marginal weather, or postpone. The decision was never written up as a formal tree — the method postdates it — but the deliberation at Southwick House maps onto the decision-tree process almost node for node, which is why decision analysts have cited it ever since.\n\n**The root decision node (square):** Go on June 6, or postpone. The branch set was tightly constrained: the invasion needed moonlight for the airborne drops and a low dawn tide to expose beach obstacles, so only a few days per month qualified. If June 6 was scrubbed, the next tidal window was around June 19 — roughly two weeks away.\n\n**The chance nodes (circles):** Each option led straight into an uncertainty Eisenhower did not control.\n\n- *Go, June 6* → chance node: does the brief break in the storm forecast by Group Captain James Stagg, SHAEF's chief meteorologist, actually hold? If yes: landings proceed under rough but workable conditions. If no: landing craft swamped, air support grounded, the assault force wrecked on the beaches.\n- *Postpone to June 19* → chance node: unknown weather two weeks out (beyond any 1944 forecast horizon), compounded by near-certain costs — nearly 200,000 troops were already sealed aboard ships and briefed, and every day of delay increased the odds that German intelligence would fix the time and place of the invasion.\n\n**Probabilities:** Stagg's team forecast a short interval of improved weather for June 6 amid a stormy period — a genuine probabilistic judgment made against disagreeing British and American forecasting teams. Illustrative reconstruction (not historical record): call the window-holds branch p ≈ 0.7, and the June 19 branch a coin flip at best with the secrecy-compromise cost accruing regardless. No participant wrote such numbers down; the structure of the argument, however, was exactly this.\n\n**Payoffs:** The asymmetry drove the answer. *Go and the window holds*: the liberation of Western Europe begins. *Go and it fails*: a bloody repulse — but a repulse that a second attempt could survive. *Postpone*: certain, compounding losses (secrecy, morale, tide, the Soviet-front timetable) plus an unresolved weather gamble two weeks later. Postponement was not the \"safe\" branch; it was a different bet with worse certain costs.\n\n**Value of information — the June 4 postponement:** Eisenhower's first move was a textbook EVPI play. On June 4 he scrubbed the original June 5 date and bought exactly one more forecast cycle — trading one day of the window for one more update from Stagg. When Stagg's June 5 briefing confirmed the break, the value of further waiting had collapsed: no additional forecast could resolve the remaining uncertainty before the tide window closed. The cost of more information now exceeded its value.\n\n**Rollback:** Folding back from the leaves: the *go* branch's expected outcome — even weighted for a serious chance of failure — beat the *postpone* branch's certain security erosion plus unresolved weather risk. In the early hours of June 5, Eisenhower gave the order to go. Before the landings he drafted a note taking sole responsibility in case of failure — evidence that he had priced the losing branch explicitly rather than wishing it away.\n\n**The sensitivity check history ran for free:** June 19 — the fallback window — brought the worst Channel storm in decades, wrecking the American Mulberry harbor off Omaha Beach. Had Eisenhower postponed, the invasion would have sailed into it. The decision was right at the assigned probabilities, and the unchosen branch turned out even worse than estimated.\n\nThe mapped steps:\n1. Root: go June 6 vs. postpone to ~June 19 — options fixed by tide and moon (Process Step 1)\n2. Chance nodes: forecast window holds/fails; June 19 weather unknown + secrecy erosion — MECE branches on each option (Step 2)\n3. Probabilities: Stagg's explicit short-window forecast against dissenting teams; reconstruction here is illustrative, the probabilistic reasoning is documented (Step 3)\n4. Payoffs: asymmetric — recoverable failure on *go* vs. certain compounding costs on *postpone* (Step 4)\n5. Rollback: *go* dominates once the June 5 forecast update lands; order given early June 5 (Step 5)\n6. Value of information: the 24-hour postponement bought one more forecast cycle, then EVPI of further delay fell below its cost — decide now (Step 6)\n\nPrimary source: Eisenhower, D. D. (1948). *Crusade in Europe.* Doubleday — Eisenhower's own account of the postponement and the go decision. Corroborating: Stagg, J. M. (1971). *Forecast for Overlord.* Ian Allan — the SHAEF chief meteorologist's account of the forecasts behind the decision.\n\nFile v1.0.3:examples/magee-1964-chemical-plant-investment-hbr.md\n\n# Method in Action: Magee 1964 — Chemical Plant Investment (HBR)\n\n> *Example for the [decision-tree](../SKILL.md) skill.*\n\n**John F. Magee** (1926–2015) was a partner at Arthur D. Little and the first analyst to systematize decision tree methodology for business. His two 1964 *Harvard Business Review* articles introduced the framework to a generation of executives and consultants who had previously made multi-million-dollar investment decisions through intuition and scenario narratives.\n\nMagee's canonical case: a chemical company facing a ten-year capital investment decision with uncertain demand. Two options — build a **large plant** (high fixed cost, high capacity) or a **small plant** (low fixed cost, low capacity with an option to expand in year 2). Demand over the period could be high or low, with a possibility of reversal between years 1–2 and years 3–10.\n\nThe HBR framing:\n\n> \"A decision tree is a diagram that describes graphically the various possible combinations of events and the decisions associated with them. It draws out the sequential decisions with their alternative choices and their consequences ... forcing managers to be explicit about the alternatives at each stage of the decision process.\"\n>\n> — Magee (1964), \"Decision Trees for Decision Making,\" HBR, p. 127.\n\nThe tree structure:\n- Root: Large plant vs. Small plant (decision node, square)\n- Year 1–2 demand: High (0.60) vs. Low (0.40) — chance node on each branch\n- If Small plant + High demand: expand or do not expand (second decision node)\n- Years 3–10 demand conditional on years 1–2 outcome\n\n**Rollback results:** Magee calculated that the large plant had a higher expected NPV than the small plant — but only because the probability assigned to high demand was above a critical threshold of approximately 0.55. When the team was asked to justify that 0.60 probability, three executives disagreed: one said 0.70, one said 0.50, one said 0.55. The tree converted a boardroom argument from \"I think we should build big\" to \"what probability do you assign to high demand in years 1–2?\" — a precise, revisable, evidenced question.\n\n**Howard Raiffa's formalization (1968)** built on Magee's work to establish the rollback procedure as a mathematical discipline, introduce formal sensitivity analysis (the switchover probability), and define the **Expected Value of Perfect Information (EVPI)** — the maximum a decision-maker should pay to resolve an uncertainty before deciding. Raiffa's EVPI formula:\n\n> \"EVPI is the expected gain from having perfect information about the state of the world before committing to a choice. It sets the upper bound on the value of any research or investigation that reduces uncertainty about that state.\"\n>\n> — Raiffa (1968), *Decision Analysis*, p. 112.\n\nIf EVPI for the demand forecast uncertainty was $2M, and a market research study costs $500K, the study is worth commissioning. If EVPI is $200K and the study costs $500K, decide immediately.\n\n**Operational lessons from Magee + Raiffa:**\n\nThe three-step discipline they established:\n\n1. **Draw before calculating.** The visual structure surfaces assumptions that participants didn't realize they were making. The act of drawing the tree is worth more than the rollback calculation.\n2. **Assign probabilities explicitly.** \"High demand\" means nothing until it has a probability. Force every probability owner to state a number and a basis. Disagreements about numbers are more productive than disagreements about direction.\n3. **Compute EVPI before gathering data.** The tree tells you what information is worth buying. Spending $1M on research that could only change the decision by $200K is irrational. EVPI makes that explicit.\n\n**McKinsey and BCG adoption (1970s–80s).** Both firms used decision trees as their primary tool for capital investment visualization. The tree format allowed consultants to walk executives through complex multi-stage decisions in one diagram — making implicit assumptions visible, driving consensus on probabilities, and producing a defensible recommendation with explicit conditions.\n\nThe most important lesson from the HBR case: **the tree revealed the threshold, not just the recommendation.** Knowing that the large plant wins only if demand probability exceeds 0.55 — and that the team had uncertainty around that threshold — was more valuable than the expected value itself. The recommendation was: proceed with large plant AND commission a targeted demand study to validate the 0.60 probability estimate before ground-breaking.\n\nFile v1.0.3:skill-card.md\n\n## Description: <br>\nGuides agents through multi-stage uncertain decisions by structuring choices, chance outcomes, probabilities, payoffs, rollback, sensitivity analysis, and EVPI into a decision-tree recommendation. <br>\n\nThis skill is ready for commercial/non-commercial use. <br>\n\n## Publisher: <br>\n[deciqai](https://clawhub.ai/user/deciqai) <br>\n\n### License/Terms of Use: <br>\nMIT-0 <br>\n\n\n## Use Case: <br>\nDevelopers, operators, and analysts use this skill to guide agents through sequential decisions where uncertain outcomes can be estimated and payoffs can be quantified. It helps produce a shared decision-tree model with explicit assumptions, expected-value rollback, sensitivity thresholds, and data-gathering stop rules. <br>\n\n### Deployment Geography for Use: <br>\nGlobal <br>\n\n## Known Risks and Mitigations: <br>\nRisk: Decision-tree outputs can be mistaken for authoritative financial, legal, medical, or operational advice when the inputs are uncertain or high-stakes. <br>\nMitigation: Treat outputs as analytical scaffolding; verify probabilities, payoffs, sources, and assumptions before acting on high-stakes recommendations. <br>\n\n\n## Reference(s): <br>\n- [Primary sources](references/sources.md) <br>\n- [Magee 1964 chemical plant investment example](examples/magee-1964-chemical-plant-investment-hbr.md) <br>\n- [Eisenhower D-Day weather decision example](examples/eisenhower-1944-d-day-weather-decision.md) <br>\n- [ClawHub skill page](https://clawhub.ai/deciqai/skills/decision-tree) <br>\n\n\n## Skill Output: <br>\n**Output Type(s):** [text, markdown, guidance] <br>\n**Output Format:** [Markdown decision-tree scaffold with tables, calculations, sensitivity analysis, and recommendation text] <br>\n**Output Parameters:** [1D] <br>\n**Other Properties Related to Output:** [May include expected value calculations, EVPI, probability and payoff assumptions, and conditions where the recommendation changes.] <br>\n\n## Skill Version(s): <br>\n1.0.3 (source: server release evidence) <br>\n\n## Ethical Considerations: <br>\nUsers should evaluate whether this skill is appropriate for their environment, review any generated or modified files before relying on them, and apply their organization's safety, security, and compliance requirements before deployment. <br>\n\nArchive v1.0.2: 6 files, 11301 bytes\n\nFiles: examples/eisenhower-1944-d-day-weather-decision.md (4942b), examples/magee-1964-chemical-plant-investment-hbr.md (4583b), references/sources.md (1345b), skill-card.md (2449b), SKILL.md (8020b), _meta.json (132b)\n\nFile v1.0.2:SKILL.md\n\n---\nname: decision-tree\ndescription: \"Activate when: user says 'help me choose between two options with different risks', 'I need to map out what could happen if we go with X', 'we have a sequential decision — first we do A then depending on results we do B', 'what is the expected value of this investment given uncertain demand'. Do NOT activate when: the decision is a one-shot choice with no sequential stages (use simple EV instead); probabilities cannot be estimated even roughly and uncertainty is too deep to quantify.\"\n---\n\n# Decision Tree\n\n## Overview\n\nA **decision tree** maps a multi-stage decision: decision nodes (squares) for choices you control, chance nodes (circles) for outcomes you don't, probabilities on every branch, payoffs at the leaves — then rollback right-to-left to get expected value at the root. First systematized by John F. Magee (HBR, 1964); formalized by Howard Raiffa (1968). Its biggest value: converting \"I feel we should expand\" into \"what probability do you assign to high demand?\" — making every assumption explicit and contestable.\n\nComposes with `expected-value-and-kelly` (EV scaffold + bet sizing), `probabilistic-thinking` (calibration per node), `inversion` (rollback = working outcomes backward), `mece` (branches must be MECE so probabilities sum to 1.0).\n\n## When to Use\n\n- Decision has sequential stages (decide → learn → decide again)\n- Outcomes uncertain; probabilities can be estimated (even roughly)\n- Payoffs quantifiable (NPV, revenue, cost, lives saved)\n- Multiple stakeholders need a shared visual model to align on assumptions\n\n**Not when:** one-shot choice with no stages; probabilities unestimable; payoffs purely qualitative; branch set too large (use scenario planning instead).\n\n## Coaching Novices (Adaptive Front Door)\n\n- **Engine mode:** user has a concrete multi-stage decision → run The Process directly.\n- **Coach mode:** user is unfamiliar or has no concrete case → guide step by step.\n\nIn Coach mode, respond one step at a time. Each [WAIT] is a hard stop — output only that step's question, then stop.\n\n1. **One-line:** a decision tree converts \"I feel\" into \"what probability do you assign?\" — making assumptions explicit so they can be argued about.\n2. **Check fit.** Sequential stages? Uncertain outcomes? Quantifiable payoffs? If yes to all three, a tree applies.\n3. **Elicit their real case.** What's the initial choice? What uncertain outcomes follow? What payoffs result?\n> **[WAIT — do not advance until user responds]**\n4. **Run The Process one step at a time** with their input — draw structure, assign probabilities, assign payoffs, roll back.\n> **[WAIT — do not advance until user responds]**\n5. **Close** by naming the insight: the threshold at which the recommendation flips, and whether to gather more data.\n> **[WAIT — do not advance until user responds]**\n\n## The Process\n\n**Step 1 — Root:** Define the decision (options, timeline, decision-maker). Draw a square; each option is a branch.\n\n**Step 2 — Chance nodes:** For each branch, identify uncertain events → draw circles. Branches at each circle must be MECE; probabilities must sum to 1.0.\n\n**Step 3 — Probabilities:** Assign a number (0.0–1.0) + documented basis to every branch. Reject \"50/50\" without justification.\n\n**Step 4 — Payoffs:** Assign consistent-unit payoffs (NPV, revenue, etc.) to every terminal leaf.\n\n**Step 5 — Rollback:** Right to left — EV at each circle = Σ(p × value). At each square, keep highest EV branch; mark losers //.\n\n**Step 6 — Sensitivity + stop-rule:** Find the probability threshold where the optimal choice switches. Compute EVPI = EV(perfect info) − EV(best decision now). If EVPI < cost of data: decide now. If EVPI > cost: gather data first. Stop refining when the leading option's EV advantage exceeds the value of further analysis.\n\n## Output Template\n```\nDecision Tree: <topic>\nOptions: A / B  |  Timeline:\nTree: [node-by-node description]\nProbabilities: Node | Branch | p | Basis\nPayoffs: Path | Value | Unit\nRollback: Option A EV= / Option B EV= / Optimal=\nSensitivity: flips when p([key branch]) > [threshold]  |  EVPI=\nRecommendation: [option] — holds if [condition]; flips if [condition]\n```\n\n*→ Method in Action: [Magee 1964 — Chemical Plant Investment (HBR)](examples/magee-1964-chemical-plant-investment-hbr.md) · [Eisenhower's D-Day Weather Decision](examples/eisenhower-1944-d-day-weather-decision.md)*\n\n## Pack: Decision Tree by Domain\n\n| Domain | Root Decision | Key Uncertainty | Payoff | Watch For |\n|---|---|---|---|---|\n| Capital investment | Large vs. small plant | Demand scenarios | NPV | Overconfident demand p |\n| R&D portfolio | Fund vs. kill | Technical success; adoption | Revenue × p | Ignoring base-rate failure |\n| Litigation | Settle vs. litigate | Win/lose; damages | Expected settlement | Anchoring on best case |\n| Product launch | Now vs. delay | Market reception; competitor | Revenue per scenario | Missing competitor-first branch |\n| M&A | Acquire vs. pass | Integration; synergy | Post-acquisition EV | Paying for performance peak |\n\n## Applying It Well\n\n- Draw before calculating — structure surfaces hidden assumptions\n- Assign probabilities before revealing your preferred option\n- Run sensitivity before concluding; find the switchover threshold and EVPI\n- Audit missing branches explicitly: \"what did we leave out?\"\n\n*→ Primary sources: [references/sources.md](references/sources.md)*\n\n## Common Rationalizations\n\n**[D] = designed upfront | [O] = observed in real use. [O] entries are more valuable.**\n\n| Rationalization (Fake Move) | Reality |\n|---|---|\n| [D] \"This is strategic — we don't need numbers.\" | Without numbers the tree is just a picture. Force strategic disagreements to become numerical ones. |\n| [D] \"We can't estimate probabilities.\" | Even rough estimates beat implicit zero/one assumptions. Every un-numbered branch already has an implicit probability. |\n| [D] \"The tree chose A — we're done.\" | Holds only at assigned probabilities. Sensitivity analysis is mandatory before concluding. |\n| [D] \"We enumerated all branches.\" | Trees are always simplifications. Ask explicitly: what branches are missing? |\n| [D] \"It's 50/50 — we just don't know.\" | 50/50 is a claim requiring justification. What base rate supports it? |\n| [D] \"My gut says B even though the tree says A.\" | Gut = implicit tree with different probabilities. Find which number your gut is using and put it in. |\n| [D] \"The tree gave a recommendation — it must be right.\" | GIGO: garbage probabilities produce garbage recommendations. Calibrate inputs first. |\n| *→ Add [O] entries here after each real use — paste the actual failure pattern* | *What went wrong and why* |\n\n## Red Flags\n\n- Probabilities verbal only — no numbers written | Chance-node probabilities don't sum to 1.0\n- No sensitivity analysis performed | Terminal payoffs in mixed units across branches\n- Probabilities assigned post-hoc to justify a pre-decided conclusion | No missing-branch audit\n\n## Verification\n\n- [ ] Root decision defined; all options enumerated\n- [ ] All chance nodes MECE; probabilities sum to 1.0 at each node\n- [ ] Every probability has documented basis\n- [ ] All terminal payoffs in same unit and discount rate\n- [ ] Rollback verified numerically at every node\n- [ ] Sensitivity complete — switchover threshold identified\n- [ ] EVPI calculated; data-gathering decision made\n- [ ] Missing-branch audit performed; recommendation states conditions it holds and flips\n---\n*Part of **deciqAI Knowledge Skills** — 163 open-source thinking skills that make rigor executable for AI agents. The same skills power every deciqAI agent, which runs them autonomously to operate your company. **See it run → https://www.deciqai.com/skills/decision-tree?utm_source=clawhub&utm_medium=marketplace&utm_campaign=knowledge-skills&utm_content=decision-tree** · ⭐ Star the repo → https://github.com/deciqAI/knowledge-skills · Contributions welcome.*\n\nFile v1.0.2:_meta.json\n\n{\n  \"ownerId\": \"kn754b8sk22s8c6gjxt02bftbn88q7ye\",\n  \"slug\": \"decision-tree\",\n  \"version\": \"1.0.2\",\n  \"publishedAt\": 1783471431936\n}\n\nFile v1.0.2:references/sources.md\n\n# Sources — decision-tree\n\n> *Primary sources for the [decision-tree](../SKILL.md) skill.*\n\n## Sources\n\n- Magee, J. F. (1964). \"Decision Trees for Decision Making.\" *Harvard Business Review*, July–August, 126–138. The original practitioner framework.\n- Magee, J. F. (1964). \"How to Use Decision Trees in Capital Investment.\" *Harvard Business Review*, September–October, 79–96. Capital investment application.\n- Raiffa, H. (1968). *Decision Analysis: Introductory Lectures on Choices under Uncertainty.* Addison-Wesley. The academic formalization; introduces EVPI and formal rollback.\n- Howard, R. A. (1966). \"Decision Analysis: Applied Decision Theory.\" *Proceedings of the 4th International Conference on Operational Research.* Stanford. Early theoretical grounding.\n- Howard, R. A., & Matheson, J. E. (Eds.) (1983). *Readings on the Principles and Applications of Decision Analysis.* Strategic Decisions Group. Comprehensive practitioner reference.\n- Clemen, R. T., & Reilly, T. (2013). *Making Hard Decisions with DecisionTools.* Cengage. Standard textbook treatment.\n- Eisenhower, D. D. (1948). *Crusade in Europe.* Doubleday. First-hand account of the D-Day weather go/no-go decision (worked example).\n- Stagg, J. M. (1971). *Forecast for Overlord.* Ian Allan. The SHAEF chief meteorologist's account of the June 1944 forecasts.\n\nFile v1.0.2:examples/eisenhower-1944-d-day-weather-decision.md\n\n# Method in Action: Eisenhower's D-Day Weather Decision (June 1944)\n\n> *Example for the [decision-tree](../SKILL.md) skill.*\n\nOn June 4–5, 1944, General Dwight D. Eisenhower faced the highest-stakes go/no-go decision of the war: launch Operation Overlord into marginal weather, or postpone. The decision was never written up as a formal tree — the method postdates it — but the deliberation at Southwick House maps onto the decision-tree process almost node for node, which is why decision analysts have cited it ever since.\n\n**The root decision node (square):** Go on June 6, or postpone. The branch set was tightly constrained: the invasion needed moonlight for the airborne drops and a low dawn tide to expose beach obstacles, so only a few days per month qualified. If June 6 was scrubbed, the next tidal window was around June 19 — roughly two weeks away.\n\n**The chance nodes (circles):** Each option led straight into an uncertainty Eisenhower did not control.\n\n- *Go, June 6* → chance node: does the brief break in the storm forecast by Group Captain James Stagg, SHAEF's chief meteorologist, actually hold? If yes: landings proceed under rough but workable conditions. If no: landing craft swamped, air support grounded, the assault force wrecked on the beaches.\n- *Postpone to June 19* → chance node: unknown weather two weeks out (beyond any 1944 forecast horizon), compounded by near-certain costs — nearly 200,000 troops were already sealed aboard ships and briefed, and every day of delay increased the odds that German intelligence would fix the time and place of the invasion.\n\n**Probabilities:** Stagg's team forecast a short interval of improved weather for June 6 amid a stormy period — a genuine probabilistic judgment made against disagreeing British and American forecasting teams. Illustrative reconstruction (not historical record): call the window-holds branch p ≈ 0.7, and the June 19 branch a coin flip at best with the secrecy-compromise cost accruing regardless. No participant wrote such numbers down; the structure of the argument, however, was exactly this.\n\n**Payoffs:** The asymmetry drove the answer. *Go and the window holds*: the liberation of Western Europe begins. *Go and it fails*: a bloody repulse — but a repulse that a second attempt could survive. *Postpone*: certain, compounding losses (secrecy, morale, tide, the Soviet-front timetable) plus an unresolved weather gamble two weeks later. Postponement was not the \"safe\" branch; it was a different bet with worse certain costs.\n\n**Value of information — the June 4 postponement:** Eisenhower's first move was a textbook EVPI play. On June 4 he scrubbed the original June 5 date and bought exactly one more forecast cycle — trading one day of the window for one more update from Stagg. When Stagg's June 5 briefing confirmed the break, the value of further waiting had collapsed: no additional forecast could resolve the remaining uncertainty before the tide window closed. The cost of more information now exceeded its value.\n\n**Rollback:** Folding back from the leaves: the *go* branch's expected outcome — even weighted for a serious chance of failure — beat the *postpone* branch's certain security erosion plus unresolved weather risk. In the early hours of June 5, Eisenhower gave the order to go. Before the landings he drafted a note taking sole responsibility in case of failure — evidence that he had priced the losing branch explicitly rather than wishing it away.\n\n**The sensitivity check history ran for free:** June 19 — the fallback window — brought the worst Channel storm in decades, wrecking the American Mulberry harbor off Omaha Beach. Had Eisenhower postponed, the invasion would have sailed into it. The decision was right at the assigned probabilities, and the unchosen branch turned out even worse than estimated.\n\nThe mapped steps:\n1. Root: go June 6 vs. postpone to ~June 19 — options fixed by tide and moon (Process Step 1)\n2. Chance nodes: forecast window holds/fails; June 19 weather unknown + secrecy erosion — MECE branches on each option (Step 2)\n3. Probabilities: Stagg's explicit short-window forecast against dissenting teams; reconstruction here is illustrative, the probabilistic reasoning is documented (Step 3)\n4. Payoffs: asymmetric — recoverable failure on *go* vs. certain compounding costs on *postpone* (Step 4)\n5. Rollback: *go* dominates once the June 5 forecast update lands; order given early June 5 (Step 5)\n6. Value of information: the 24-hour postponement bought one more forecast cycle, then EVPI of further delay fell below its cost — decide now (Step 6)\n\nPrimary source: Eisenhower, D. D. (1948). *Crusade in Europe.* Doubleday — Eisenhower's own account of the postponement and the go decision. Corroborating: Stagg, J. M. (1971). *Forecast for Overlord.* Ian Allan — the SHAEF chief meteorologist's account of the forecasts behind the decision.\n\nFile v1.0.2:examples/magee-1964-chemical-plant-investment-hbr.md\n\n# Method in Action: Magee 1964 — Chemical Plant Investment (HBR)\n\n> *Example for the [decision-tree](../SKILL.md) skill.*\n\n**John F. Magee** (1926–2015) was a partner at Arthur D. Little and the first analyst to systematize decision tree methodology for business. His two 1964 *Harvard Business Review* articles introduced the framework to a generation of executives and consultants who had previously made multi-million-dollar investment decisions through intuition and scenario narratives.\n\nMagee's canonical case: a chemical company facing a ten-year capital investment decision with uncertain demand. Two options — build a **large plant** (high fixed cost, high capacity) or a **small plant** (low fixed cost, low capacity with an option to expand in year 2). Demand over the period could be high or low, with a possibility of reversal between years 1–2 and years 3–10.\n\nThe HBR framing:\n\n> \"A decision tree is a diagram that describes graphically the various possible combinations of events and the decisions associated with them. It draws out the sequential decisions with their alternative choices and their consequences ... forcing managers to be explicit about the alternatives at each stage of the decision process.\"\n>\n> — Magee (1964), \"Decision Trees for Decision Making,\" HBR, p. 127.\n\nThe tree structure:\n- Root: Large plant vs. Small plant (decision node, square)\n- Year 1–2 demand: High (0.60) vs. Low (0.40) — chance node on each branch\n- If Small plant + High demand: expand or do not expand (second decision node)\n- Years 3–10 demand conditional on years 1–2 outcome\n\n**Rollback results:** Magee calculated that the large plant had a higher expected NPV than the small plant — but only because the probability assigned to high demand was above a critical threshold of approximately 0.55. When the team was asked to justify that 0.60 probability, three executives disagreed: one said 0.70, one said 0.50, one said 0.55. The tree converted a boardroom argument from \"I think we should build big\" to \"what probability do you assign to high demand in years 1–2?\" — a precise, revisable, evidenced question.\n\n**Howard Raiffa's formalization (1968)** built on Magee's work to establish the rollback procedure as a mathematical discipline, introduce formal sensitivity analysis (the switchover probability), and define the **Expected Value of Perfect Information (EVPI)** — the maximum a decision-maker should pay to resolve an uncertainty before deciding. Raiffa's EVPI formula:\n\n> \"EVPI is the expected gain from having perfect information about the state of the world before committing to a choice. It sets the upper bound on the value of any research or investigation that reduces uncertainty about that state.\"\n>\n> — Raiffa (1968), *Decision Analysis*, p. 112.\n\nIf EVPI for the demand forecast uncertainty was $2M, and a market research study costs $500K, the study is worth commissioning. If EVPI is $200K and the study costs $500K, decide immediately.\n\n**Operational lessons from Magee + Raiffa:**\n\nThe three-step discipline they established:\n\n1. **Draw before calculating.** The visual structure surfaces assumptions that participants didn't realize they were making. The act of drawing the tree is worth more than the rollback calculation.\n2. **Assign probabilities explicitly.** \"High demand\" means nothing until it has a probability. Force every probability owner to state a number and a basis. Disagreements about numbers are more productive than disagreements about direction.\n3. **Compute EVPI before gathering data.** The tree tells you what information is worth buying. Spending $1M on research that could only change the decision by $200K is irrational. EVPI makes that explicit.\n\n**McKinsey and BCG adoption (1970s–80s).** Both firms used decision trees as their primary tool for capital investment visualization. The tree format allowed consultants to walk executives through complex multi-stage decisions in one diagram — making implicit assumptions visible, driving consensus on probabilities, and producing a defensible recommendation with explicit conditions.\n\nThe most important lesson from the HBR case: **the tree revealed the threshold, not just the recommendation.** Knowing that the large plant wins only if demand probability exceeds 0.55 — and that the team had uncertainty around that threshold — was more valuable than the expected value itself. The recommendation was: proceed with large plant AND commission a targeted demand study to validate the 0.60 probability estimate before ground-breaking.\n\nFile v1.0.2:skill-card.md\n\n## Description: <br>\nGuides an agent through mapping multi-stage decisions with decision nodes, chance nodes, probabilities, payoffs, rollback expected values, sensitivity checks, and EVPI-based stop rules. <br>\n\nThis skill is ready for commercial/non-commercial use. <br>\n\n## Publisher: <br>\n[deciqai](https://clawhub.ai/user/deciqai) <br>\n\n### License/Terms of Use: <br>\nMIT-0 <br>\n\n\n## Use Case: <br>\nEmployees, external users, and decision facilitators use this skill to structure sequential choices with uncertain outcomes, quantify assumptions, compare expected values, and identify when more information is worth gathering. <br>\n\n### Deployment Geography for Use: <br>\nGlobal <br>\n\n## Known Risks and Mitigations: <br>\nRisk: Broad autonomous-operation wording could lead users to apply the skill outside workflows they explicitly requested. <br>\nMitigation: Use the skill only for explicitly requested decision-analysis workflows and review the SKILL.md activation boundaries before installation. <br>\nRisk: Decision tree recommendations can be misleading when probabilities are unjustified, branches are missing, or payoffs use inconsistent units. <br>\nMitigation: Require documented probability bases, MECE branches, consistent payoff units, sensitivity analysis, EVPI calculation, and a missing-branch audit before relying on recommendations. <br>\n\n\n## Reference(s): <br>\n- [Sources - decision-tree](references/sources.md) <br>\n- [Magee 1964 - Chemical Plant Investment (HBR)](examples/magee-1964-chemical-plant-investment-hbr.md) <br>\n- [Eisenhower's D-Day Weather Decision](examples/eisenhower-1944-d-day-weather-decision.md) <br>\n\n\n## Skill Output: <br>\n**Output Type(s):** [text, markdown, guidance] <br>\n**Output Format:** [Markdown decision tree summary with tables or structured sections for options, probabilities, payoffs, rollback, sensitivity, EVPI, and recommendation] <br>\n**Output Parameters:** [1D] <br>\n**Other Properties Related to Output:** [Requires user-supplied probabilities and payoffs; recommendations should state the conditions under which they hold or flip.] <br>\n\n## Skill Version(s): <br>\n1.0.2 (source: server release evidence) <br>\n\n## Ethical Considerations: <br>\nUsers should evaluate whether this skill is appropriate for their environment, review any generated or modified files before relying on them, and apply their organization's safety, security, and compliance requirements before deployment. <br>\n\nArchive v1.0.1: 5 files, 8286 bytes\n\nFiles: examples/magee-1964-chemical-plant-investment-hbr.md (4583b), references/sources.md (1082b), skill-card.md (2316b), SKILL.md (7796b), _meta.json (132b)\n\nFile v1.0.1:SKILL.md\n\n---\nname: decision-tree\ndescription: \"Activate when: user says 'help me choose between two options with different risks', 'I need to map out what could happen if we go with X', 'we have a sequential decision — first we do A then depending on results we do B', 'what is the expected value of this investment given uncertain demand'. Do NOT activate when: the decision is a one-shot choice with no sequential stages (use simple EV instead); probabilities cannot be estimated even roughly and uncertainty is too deep to quantify.\"\n---\n\n# Decision Tree\n\n## Overview\n\nA **decision tree** maps a multi-stage decision: decision nodes (squares) for choices you control, chance nodes (circles) for outcomes you don't, probabilities on every branch, payoffs at the leaves — then rollback right-to-left to get expected value at the root. First systematized by John F. Magee (HBR, 1964); formalized by Howard Raiffa (1968). Its biggest value: converting \"I feel we should expand\" into \"what probability do you assign to high demand?\" — making every assumption explicit and contestable.\n\nComposes with [`expected-value-and-kelly`](../expected-value-and-kelly/SKILL.md) (EV scaffold + bet sizing), [`probabilistic-thinking`](../probabilistic-thinking/SKILL.md) (calibration per node), [`inversion`](../inversion/SKILL.md) (rollback = working outcomes backward), [`mece`](../mece/SKILL.md) (branches must be MECE so probabilities sum to 1.0).\n\n## When to Use\n\n- Decision has sequential stages (decide → learn → decide again)\n- Outcomes uncertain; probabilities can be estimated (even roughly)\n- Payoffs quantifiable (NPV, revenue, cost, lives saved)\n- Multiple stakeholders need a shared visual model to align on assumptions\n\n**Not when:** one-shot choice with no stages; probabilities unestimable; payoffs purely qualitative; branch set too large (use scenario planning instead).\n\n## Coaching Novices (Adaptive Front Door)\n\n- **Engine mode:** user has a concrete multi-stage decision → run The Process directly.\n- **Coach mode:** user is unfamiliar or has no concrete case → guide step by step.\n\nIn Coach mode, respond one step at a time. Each [WAIT] is a hard stop — output only that step's question, then stop.\n\n1. **One-line:** a decision tree converts \"I feel\" into \"what probability do you assign?\" — making assumptions explicit so they can be argued about.\n2. **Check fit.** Sequential stages? Uncertain outcomes? Quantifiable payoffs? If yes to all three, a tree applies.\n3. **Elicit their real case.** What's the initial choice? What uncertain outcomes follow? What payoffs result?\n> **[WAIT — do not advance until user responds]**\n4. **Run The Process one step at a time** with their input — draw structure, assign probabilities, assign payoffs, roll back.\n> **[WAIT — do not advance until user responds]**\n5. **Close** by naming the insight: the threshold at which the recommendation flips, and whether to gather more data.\n> **[WAIT — do not advance until user responds]**\n\n## The Process\n\n**Step 1 — Root:** Define the decision (options, timeline, decision-maker). Draw a square; each option is a branch.\n\n**Step 2 — Chance nodes:** For each branch, identify uncertain events → draw circles. Branches at each circle must be MECE; probabilities must sum to 1.0.\n\n**Step 3 — Probabilities:** Assign a number (0.0–1.0) + documented basis to every branch. Reject \"50/50\" without justification.\n\n**Step 4 — Payoffs:** Assign consistent-unit payoffs (NPV, revenue, etc.) to every terminal leaf.\n\n**Step 5 — Rollback:** Right to left — EV at each circle = Σ(p × value). At each square, keep highest EV branch; mark losers //.\n\n**Step 6 — Sensitivity + stop-rule:** Find the probability threshold where the optimal choice switches. Compute EVPI = EV(perfect info) − EV(best decision now). If EVPI < cost of data: decide now. If EVPI > cost: gather data first. Stop refining when the leading option's EV advantage exceeds the value of further analysis.\n\n## Output Template\n```\nDecision Tree: <topic>\nOptions: A / B  |  Timeline:\nTree: [node-by-node description]\nProbabilities: Node | Branch | p | Basis\nPayoffs: Path | Value | Unit\nRollback: Option A EV= / Option B EV= / Optimal=\nSensitivity: flips when p([key branch]) > [threshold]  |  EVPI=\nRecommendation: [option] — holds if [condition]; flips if [condition]\n```\n\n*→ Method in Action: [Magee 1964 — Chemical Plant Investment (HBR)](examples/magee-1964-chemical-plant-investment-hbr.md)*\n\n## Pack: Decision Tree by Domain\n\n| Domain | Root Decision | Key Uncertainty | Payoff | Watch For |\n|---|---|---|---|---|\n| Capital investment | Large vs. small plant | Demand scenarios | NPV | Overconfident demand p |\n| R&D portfolio | Fund vs. kill | Technical success; adoption | Revenue × p | Ignoring base-rate failure |\n| Litigation | Settle vs. litigate | Win/lose; damages | Expected settlement | Anchoring on best case |\n| Product launch | Now vs. delay | Market reception; competitor | Revenue per scenario | Missing competitor-first branch |\n| M&A | Acquire vs. pass | Integration; synergy | Post-acquisition EV | Paying for performance peak |\n\n## Applying It Well\n\n- Draw before calculating — structure surfaces hidden assumptions\n- Assign probabilities before revealing your preferred option\n- Run sensitivity before concluding; find the switchover threshold and EVPI\n- Audit missing branches explicitly: \"what did we leave out?\"\n\n*→ Primary sources: [references/sources.md](references/sources.md)*\n\n## Common Rationalizations\n\n**[D] = designed upfront | [O] = observed in real use. [O] entries are more valuable.**\n\n| Rationalization (Fake Move) | Reality |\n|---|---|\n| [D] \"This is strategic — we don't need numbers.\" | Without numbers the tree is just a picture. Force strategic disagreements to become numerical ones. |\n| [D] \"We can't estimate probabilities.\" | Even rough estimates beat implicit zero/one assumptions. Every un-numbered branch already has an implicit probability. |\n| [D] \"The tree chose A — we're done.\" | Holds only at assigned probabilities. Sensitivity analysis is mandatory before concluding. |\n| [D] \"We enumerated all branches.\" | Trees are always simplifications. Ask explicitly: what branches are missing? |\n| [D] \"It's 50/50 — we just don't know.\" | 50/50 is a claim requiring justification. What base rate supports it? |\n| [D] \"My gut says B even though the tree says A.\" | Gut = implicit tree with different probabilities. Find which number your gut is using and put it in. |\n| [D] \"The tree gave a recommendation — it must be right.\" | GIGO: garbage probabilities produce garbage recommendations. Calibrate inputs first. |\n| *→ Add [O] entries here after each real use — paste the actual failure pattern* | *What went wrong and why* |\n\n## Red Flags\n\n- Probabilities verbal only — no numbers written | Chance-node probabilities don't sum to 1.0\n- No sensitivity analysis performed | Terminal payoffs in mixed units across branches\n- Probabilities assigned post-hoc to justify a pre-decided conclusion | No missing-branch audit\n\n## Verification\n\n- [ ] Root decision defined; all options enumerated\n- [ ] All chance nodes MECE; probabilities sum to 1.0 at each node\n- [ ] Every probability has documented basis\n- [ ] All terminal payoffs in same unit and discount rate\n- [ ] Rollback verified numerically at every node\n- [ ] Sensitivity complete — switchover threshold identified\n- [ ] EVPI calculated; data-gathering decision made\n- [ ] Missing-branch audit performed; recommendation states conditions it holds and flips\n---\n*Part of **deciqAI Knowledge Skills** — open-source thinking skills that make rigor executable for AI agents. Built by deciqAI · https://deciqai.com · Contributions welcome — see the template at the repo root.*\n\nFile v1.0.1:_meta.json\n\n{\n  \"ownerId\": \"kn754b8sk22s8c6gjxt02bftbn88q7ye\",\n  \"slug\": \"decision-tree\",\n  \"version\": \"1.0.1\",\n  \"publishedAt\": 1783456306510\n}\n\nFile v1.0.1:references/sources.md\n\n# Sources — decision-tree\n\n> *Primary sources for the [decision-tree](../SKILL.md) skill.*\n\n## Sources\n\n- Magee, J. F. (1964). \"Decision Trees for Decision Making.\" *Harvard Business Review*, July–August, 126–138. The original practitioner framework.\n- Magee, J. F. (1964). \"How to Use Decision Trees in Capital Investment.\" *Harvard Business Review*, September–October, 79–96. Capital investment application.\n- Raiffa, H. (1968). *Decision Analysis: Introductory Lectures on Choices under Uncertainty.* Addison-Wesley. The academic formalization; introduces EVPI and formal rollback.\n- Howard, R. A. (1966). \"Decision Analysis: Applied Decision Theory.\" *Proceedings of the 4th International Conference on Operational Research.* Stanford. Early theoretical grounding.\n- Howard, R. A., & Matheson, J. E. (Eds.) (1983). *Readings on the Principles and Applications of Decision Analysis.* Strategic Decisions Group. Comprehensive practitioner reference.\n- Clemen, R. T., & Reilly, T. (2013). *Making Hard Decisions with DecisionTools.* Cengage. Standard textbook treatment.\n\nFile v1.0.1:examples/magee-1964-chemical-plant-investment-hbr.md\n\n# Method in Action: Magee 1964 — Chemical Plant Investment (HBR)\n\n> *Example for the [decision-tree](../SKILL.md) skill.*\n\n**John F. Magee** (1926–2015) was a partner at Arthur D. Little and the first analyst to systematize decision tree methodology for business. His two 1964 *Harvard Business Review* articles introduced the framework to a generation of executives and consultants who had previously made multi-million-dollar investment decisions through intuition and scenario narratives.\n\nMagee's canonical case: a chemical company facing a ten-year capital investment decision with uncertain demand. Two options — build a **large plant** (high fixed cost, high capacity) or a **small plant** (low fixed cost, low capacity with an option to expand in year 2). Demand over the period could be high or low, with a possibility of reversal between years 1–2 and years 3–10.\n\nThe HBR framing:\n\n> \"A decision tree is a diagram that describes graphically the various possible combinations of events and the decisions associated with them. It draws out the sequential decisions with their alternative choices and their consequences ... forcing managers to be explicit about the alternatives at each stage of the decision process.\"\n>\n> — Magee (1964), \"Decision Trees for Decision Making,\" HBR, p. 127.\n\nThe tree structure:\n- Root: Large plant vs. Small plant (decision node, square)\n- Year 1–2 demand: High (0.60) vs. Low (0.40) — chance node on each branch\n- If Small plant + High demand: expand or do not expand (second decision node)\n- Years 3–10 demand conditional on years 1–2 outcome\n\n**Rollback results:** Magee calculated that the large plant had a higher expected NPV than the small plant — but only because the probability assigned to high demand was above a critical threshold of approximately 0.55. When the team was asked to justify that 0.60 probability, three executives disagreed: one said 0.70, one said 0.50, one said 0.55. The tree converted a boardroom argument from \"I think we should build big\" to \"what probability do you assign to high demand in years 1–2?\" — a precise, revisable, evidenced question.\n\n**Howard Raiffa's formalization (1968)** built on Magee's work to establish the rollback procedure as a mathematical discipline, introduce formal sensitivity analysis (the switchover probability), and define the **Expected Value of Perfect Information (EVPI)** — the maximum a decision-maker should pay to resolve an uncertainty before deciding. Raiffa's EVPI formula:\n\n> \"EVPI is the expected gain from having perfect information about the state of the world before committing to a choice. It sets the upper bound on the value of any research or investigation that reduces uncertainty about that state.\"\n>\n> — Raiffa (1968), *Decision Analysis*, p. 112.\n\nIf EVPI for the demand forecast uncertainty was $2M, and a market research study costs $500K, the study is worth commissioning. If EVPI is $200K and the study costs $500K, decide immediately.\n\n**Operational lessons from Magee + Raiffa:**\n\nThe three-step discipline they established:\n\n1. **Draw before calculating.** The visual structure surfaces assumptions that participants didn't realize they were making. The act of drawing the tree is worth more than the rollback calculation.\n2. **Assign probabilities explicitly.** \"High demand\" means nothing until it has a probability. Force every probability owner to state a number and a basis. Disagreements about numbers are more productive than disagreements about direction.\n3. **Compute EVPI before gathering data.** The tree tells you what information is worth buying. Spending $1M on research that could only change the decision by $200K is irrational. EVPI makes that explicit.\n\n**McKinsey and BCG adoption (1970s–80s).** Both firms used decision trees as their primary tool for capital investment visualization. The tree format allowed consultants to walk executives through complex multi-stage decisions in one diagram — making implicit assumptions visible, driving consensus on probabilities, and producing a defensible recommendation with explicit conditions.\n\nThe most important lesson from the HBR case: **the tree revealed the threshold, not just the recommendation.** Knowing that the large plant wins only if demand probability exceeds 0.55 — and that the team had uncertainty around that threshold — was more valuable than the expected value itself. The recommendation was: proceed with large plant AND commission a targeted demand study to validate the 0.60 probability estimate before ground-breaking.\n\nFile v1.0.1:skill-card.md\n\n## Description: <br>\nDecision Tree helps agents guide users through multi-stage decisions by mapping choices, uncertain outcomes, probabilities, payoffs, rollback expected value, sensitivity thresholds, and EVPI. <br>\n\nThis skill is ready for commercial/non-commercial use. <br>\n\n## Publisher: <br>\n[deciqai](https://clawhub.ai/user/deciqai) <br>\n\n### License/Terms of Use: <br>\nMIT-0 <br>\n\n\n## Use Case: <br>\nExternal users, employees, and agents use this skill to structure sequential decisions with uncertain outcomes and quantifiable payoffs. It is most useful when stakeholders need a shared model that exposes assumptions, computes expected values, and identifies when more information is worth gathering. <br>\n\n### Deployment Geography for Use: <br>\nGlobal <br>\n\n## Known Risks and Mitigations: <br>\nRisk: Users may treat structured decision-tree output as financial, legal, or business advice. <br>\nMitigation: Frame outputs as decision analysis, and require human review before using recommendations for important decisions. <br>\nRisk: Incorrect probabilities, payoffs, or source claims can produce misleading expected values and recommendations. <br>\nMitigation: Verify probabilities, payoff units, source claims, sensitivity thresholds, and EVPI before relying on the result. <br>\n\n\n## Reference(s): <br>\n- [Decision Tree Sources](references/sources.md) <br>\n- [Magee 1964 Chemical Plant Investment Example](examples/magee-1964-chemical-plant-investment-hbr.md) <br>\n- [Decision Tree Skill Page](https://clawhub.ai/deciqai/skills/decision-tree) <br>\n\n\n## Skill Output: <br>\n**Output Type(s):** [text, markdown, guidance] <br>\n**Output Format:** [Markdown decision-analysis worksheet with tables and concise recommendations] <br>\n**Output Parameters:** [1D] <br>\n**Other Properties Related to Output:** [May include node descriptions, probability and payoff tables, expected-value rollback, sensitivity thresholds, EVPI, and recommendation conditions.] <br>\n\n## Skill Version(s): <br>\n1.0.1 (source: server release metadata) <br>\n\n## Ethical Considerations: <br>\nUsers should evaluate whether this skill is appropriate for their environment, review any generated or modified files before relying on them, and apply their organization's safety, security, and compliance requirements before deployment. <br>\n\nArchive v1.0.0: 5 files, 8318 bytes\n\nFiles: examples/magee-1964-chemical-plant-investment-hbr.md (4583b), references/sources.md (1082b), skill-card.md (2458b), SKILL.md (7796b), _meta.json (132b)\n\nFile v1.0.0:SKILL.md\n\n---\nname: decision-tree\ndescription: \"Activate when: user says 'help me choose between two options with different risks', 'I need to map out what could happen if we go with X', 'we have a sequential decision — first we do A then depending on results we do B', 'what is the expected value of this investment given uncertain demand'. Do NOT activate when: the decision is a one-shot choice with no sequential stages (use simple EV instead); probabilities cannot be estimated even roughly and uncertainty is too deep to quantify.\"\n---\n\n# Decision Tree\n\n## Overview\n\nA **decision tree** maps a multi-stage decision: decision nodes (squares) for choices you control, chance nodes (circles) for outcomes you don't, probabilities on every branch, payoffs at the leaves — then rollback right-to-left to get expected value at the root. First systematized by John F. Magee (HBR, 1964); formalized by Howard Raiffa (1968). Its biggest value: converting \"I feel we should expand\" into \"what probability do you assign to high demand?\" — making every assumption explicit and contestable.\n\nComposes with [`expected-value-and-kelly`](../expected-value-and-kelly/SKILL.md) (EV scaffold + bet sizing), [`probabilistic-thinking`](../probabilistic-thinking/SKILL.md) (calibration per node), [`inversion`](../inversion/SKILL.md) (rollback = working outcomes backward), [`mece`](../mece/SKILL.md) (branches must be MECE so probabilities sum to 1.0).\n\n## When to Use\n\n- Decision has sequential stages (decide → learn → decide again)\n- Outcomes uncertain; probabilities can be estimated (even roughly)\n- Payoffs quantifiable (NPV, revenue, cost, lives saved)\n- Multiple stakeholders need a shared visual model to align on assumptions\n\n**Not when:** one-shot choice with no stages; probabilities unestimable; payoffs purely qualitative; branch set too large (use scenario planning instead).\n\n## Coaching Novices (Adaptive Front Door)\n\n- **Engine mode:** user has a concrete multi-stage decision → run The Process directly.\n- **Coach mode:** user is unfamiliar or has no concrete case → guide step by step.\n\nIn Coach mode, respond one step at a time. Each [WAIT] is a hard stop — output only that step's question, then stop.\n\n1. **One-line:** a decision tree converts \"I feel\" into \"what probability do you assign?\" — making assumptions explicit so they can be argued about.\n2. **Check fit.** Sequential stages? Uncertain outcomes? Quantifiable payoffs? If yes to all three, a tree applies.\n3. **Elicit their real case.** What's the initial choice? What uncertain outcomes follow? What payoffs result?\n> **[WAIT — do not advance until user responds]**\n4. **Run The Process one step at a time** with their input — draw structure, assign probabilities, assign payoffs, roll back.\n> **[WAIT — do not advance until user responds]**\n5. **Close** by naming the insight: the threshold at which the recommendation flips, and whether to gather more data.\n> **[WAIT — do not advance until user responds]**\n\n## The Process\n\n**Step 1 — Root:** Define the decision (options, timeline, decision-maker). Draw a square; each option is a branch.\n\n**Step 2 — Chance nodes:** For each branch, identify uncertain events → draw circles. Branches at each circle must be MECE; probabilities must sum to 1.0.\n\n**Step 3 — Probabilities:** Assign a number (0.0–1.0) + documented basis to every branch. Reject \"50/50\" without justification.\n\n**Step 4 — Payoffs:** Assign consistent-unit payoffs (NPV, revenue, etc.) to every terminal leaf.\n\n**Step 5 — Rollback:** Right to left — EV at each circle = Σ(p × value). At each square, keep highest EV branch; mark losers //.\n\n**Step 6 — Sensitivity + stop-rule:** Find the probability threshold where the optimal choice switches. Compute EVPI = EV(perfect info) − EV(best decision now). If EVPI < cost of data: decide now. If EVPI > cost: gather data first. Stop refining when the leading option's EV advantage exceeds the value of further analysis.\n\n## Output Template\n```\nDecision Tree: <topic>\nOptions: A / B  |  Timeline:\nTree: [node-by-node description]\nProbabilities: Node | Branch | p | Basis\nPayoffs: Path | Value | Unit\nRollback: Option A EV= / Option B EV= / Optimal=\nSensitivity: flips when p([key branch]) > [threshold]  |  EVPI=\nRecommendation: [option] — holds if [condition]; flips if [condition]\n```\n\n*→ Method in Action: [Magee 1964 — Chemical Plant Investment (HBR)](examples/magee-1964-chemical-plant-investment-hbr.md)*\n\n## Pack: Decision Tree by Domain\n\n| Domain | Root Decision | Key Uncertainty | Payoff | Watch For |\n|---|---|---|---|---|\n| Capital investment | Large vs. small plant | Demand scenarios | NPV | Overconfident demand p |\n| R&D portfolio | Fund vs. kill | Technical success; adoption | Revenue × p | Ignoring base-rate failure |\n| Litigation | Settle vs. litigate | Win/lose; damages | Expected settlement | Anchoring on best case |\n| Product launch | Now vs. delay | Market reception; competitor | Revenue per scenario | Missing competitor-first branch |\n| M&A | Acquire vs. pass | Integration; synergy | Post-acquisition EV | Paying for performance peak |\n\n## Applying It Well\n\n- Draw before calculating — structure surfaces hidden assumptions\n- Assign probabilities before revealing your preferred option\n- Run sensitivity before concluding; find the switchover threshold and EVPI\n- Audit missing branches explicitly: \"what did we leave out?\"\n\n*→ Primary sources: [references/sources.md](references/sources.md)*\n\n## Common Rationalizations\n\n**[D] = designed upfront | [O] = observed in real use. [O] entries are more valuable.**\n\n| Rationalization (Fake Move) | Reality |\n|---|---|\n| [D] \"This is strategic — we don't need numbers.\" | Without numbers the tree is just a picture. Force strategic disagreements to become numerical ones. |\n| [D] \"We can't estimate probabilities.\" | Even rough estimates beat implicit zero/one assumptions. Every un-numbered branch already has an implicit probability. |\n| [D] \"The tree chose A — we're done.\" | Holds only at assigned probabilities. Sensitivity analysis is mandatory before concluding. |\n| [D] \"We enumerated all branches.\" | Trees are always simplifications. Ask explicitly: what branches are missing? |\n| [D] \"It's 50/50 — we just don't know.\" | 50/50 is a claim requiring justification. What base rate supports it? |\n| [D] \"My gut says B even though the tree says A.\" | Gut = implicit tree with different probabilities. Find which number your gut is using and put it in. |\n| [D] \"The tree gave a recommendation — it must be right.\" | GIGO: garbage probabilities produce garbage recommendations. Calibrate inputs first. |\n| *→ Add [O] entries here after each real use — paste the actual failure pattern* | *What went wrong and why* |\n\n## Red Flags\n\n- Probabilities verbal only — no numbers written | Chance-node probabilities don't sum to 1.0\n- No sensitivity analysis performed | Terminal payoffs in mixed units across branches\n- Probabilities assigned post-hoc to justify a pre-decided conclusion | No missing-branch audit\n\n## Verification\n\n- [ ] Root decision defined; all options enumerated\n- [ ] All chance nodes MECE; probabilities sum to 1.0 at each node\n- [ ] Every probability has documented basis\n- [ ] All terminal payoffs in same unit and discount rate\n- [ ] Rollback verified numerically at every node\n- [ ] Sensitivity complete — switchover threshold identified\n- [ ] EVPI calculated; data-gathering decision made\n- [ ] Missing-branch audit performed; recommendation states conditions it holds and flips\n---\n*Part of **deciqAI Knowledge Skills** — open-source thinking skills that make rigor executable for AI agents. Built by deciqAI · https://deciqai.com · Contributions welcome — see the template at the repo root.*\n\nFile v1.0.0:_meta.json\n\n{\n  \"ownerId\": \"kn754b8sk22s8c6gjxt02bftbn88q7ye\",\n  \"slug\": \"decision-tree\",\n  \"version\": \"1.0.0\",\n  \"publishedAt\": 1782544656163\n}\n\nFile v1.0.0:references/sources.md\n\n# Sources — decision-tree\n\n> *Primary sources for the [decision-tree](../SKILL.md) skill.*\n\n## Sources\n\n- Magee, J. F. (1964). \"Decision Trees for Decision Making.\" *Harvard Business Review*, July–August, 126–138. The original practitioner framework.\n- Magee, J. F. (1964). \"How to Use Decision Trees in Capital Investment.\" *Harvard Business Review*, September–October, 79–96. Capital investment application.\n- Raiffa, H. (1968). *Decision Analysis: Introductory Lectures on Choices under Uncertainty.* Addison-Wesley. The academic formalization; introduces EVPI and formal rollback.\n- Howard, R. A. (1966). \"Decision Analysis: Applied Decision Theory.\" *Proceedings of the 4th International Conference on Operational Research.* Stanford. Early theoretical grounding.\n- Howard, R. A., & Matheson, J. E. (Eds.) (1983). *Readings on the Principles and Applications of Decision Analysis.* Strategic Decisions Group. Comprehensive practitioner reference.\n- Clemen, R. T., & Reilly, T. (2013). *Making Hard Decisions with DecisionTools.* Cengage. Standard textbook treatment.\n\nFile v1.0.0:examples/magee-1964-chemical-plant-investment-hbr.md\n\n# Method in Action: Magee 1964 — Chemical Plant Investment (HBR)\n\n> *Example for the [decision-tree](../SKILL.md) skill.*\n\n**John F. Magee** (1926–2015) was a partner at Arthur D. Little and the first analyst to systematize decision tree methodology for business. His two 1964 *Harvard Business Review* articles introduced the framework to a generation of executives and consultants who had previously made multi-million-dollar investment decisions through intuition and scenario narratives.\n\nMagee's canonical case: a chemical company facing a ten-year capital investment decision with uncertain demand. Two options — build a **large plant** (high fixed cost, high capacity) or a **small plant** (low fixed cost, low capacity with an option to expand in year 2). Demand over the period could be high or low, with a possibility of reversal between years 1–2 and years 3–10.\n\nThe HBR framing:\n\n> \"A decision tree is a diagram that describes graphically the various possible combinations of events and the decisions associated with them. It draws out the sequential decisions with their alternative choices and their consequences ... forcing managers to be explicit about the alternatives at each stage of the decision process.\"\n>\n> — Magee (1964), \"Decision Trees for Decision Making,\" HBR, p. 127.\n\nThe tree structure:\n- Root: Large plant vs. Small plant (decision node, square)\n- Year 1–2 demand: High (0.60) vs. Low (0.40) — chance node on each branch\n- If Small plant + High demand: expand or do not expand (second decision node)\n- Years 3–10 demand conditional on years 1–2 outcome\n\n**Rollback results:** Magee calculated that the large plant had a higher expected NPV than the small plant — but only because the probability assigned to high demand was above a critical threshold of approximately 0.55. When the team was asked to justify that 0.60 probability, three executives disagreed: one said 0.70, one said 0.50, one said 0.55. The tree converted a boardroom argument from \"I think we should build big\" to \"what probability do you assign to high demand in years 1–2?\" — a precise, revisable, evidenced question.\n\n**Howard Raiffa's formalization (1968)** built on Magee's work to establish the rollback procedure as a mathematical discipline, introduce formal sensitivity analysis (the switchover probability), and define the **Expected Value of Perfect Information (EVPI)** — the maximum a decision-maker should pay to resolve an uncertainty before deciding. Raiffa's EVPI formula:\n\n> \"EVPI is the expected gain from having perfect information about the state of the world before committing to a choice. It sets the upper bound on the value of any research or investigation that reduces uncertainty about that state.\"\n>\n> — Raiffa (1968), *Decision Analysis*, p. 112.\n\nIf EVPI for the demand forecast uncertainty was $2M, and a market research study costs $500K, the study is worth commissioning. If EVPI is $200K and the study costs $500K, decide immediately.\n\n**Operational lessons from Magee + Raiffa:**\n\nThe three-step discipline they established:\n\n1. **Draw before calculating.** The visual structure surfaces assumptions that participants didn't realize they were making. The act of drawing the tree is worth more than the rollback calculation.\n2. **Assign probabilities explicitly.** \"High demand\" means nothing until it has a probability. Force every probability owner to state a number and a basis. Disagreements about numbers are more productive than disagreements about direction.\n3. **Compute EVPI before gathering data.** The tree tells you what information is worth buying. Spending $1M on research that could only change the decision by $200K is irrational. EVPI makes that explicit.\n\n**McKinsey and BCG adoption (1970s–80s).** Both firms used decision trees as their primary tool for capital investment visualization. The tree format allowed consultants to walk executives through complex multi-stage decisions in one diagram — making implicit assumptions visible, driving consensus on probabilities, and producing a defensible recommendation with explicit conditions.\n\nThe most important lesson from the HBR case: **the tree revealed the threshold, not just the recommendation.** Knowing that the large plant wins only if demand probability exceeds 0.55 — and that the team had uncertainty around that threshold — was more valuable than the expected value itself. The recommendation was: proceed with large plant AND commission a targeted demand study to validate the 0.60 probability estimate before ground-breaking.\n\nFile v1.0.0:skill-card.md\n\n## Description: <br>\nGuides agents through decision tree analysis for multi-stage decisions with uncertain outcomes, quantified probabilities, payoffs, rollback, sensitivity analysis, and EVPI. <br>\n\nThis skill is ready for commercial/non-commercial use. <br>\n\n## Publisher: <br>\n[deciqai](https://clawhub.ai/user/deciqai) <br>\n\n### License/Terms of Use: <br>\nMIT-0 <br>\n\n\n## Use Case: <br>\nDevelopers, analysts, and business users use this skill to structure sequential choices with uncertainty, estimate branch probabilities and payoffs, roll expected values back through the tree, and identify sensitivity thresholds before recommending an option. <br>\n\n### Deployment Geography for Use: <br>\nGlobal <br>\n\n## Known Risks and Mitigations: <br>\nRisk: Decision tree outputs can influence business, financial, legal, or safety-relevant decisions. <br>\nMitigation: Treat the skill as a structured analysis aid; independently verify probabilities, payoffs, assumptions, and professional implications before acting. <br>\nRisk: Incorrect or unjustified probabilities and mixed payoff units can produce misleading expected value recommendations. <br>\nMitigation: Require documented probability bases, consistent payoff units, sensitivity analysis, EVPI checks, and a missing-branch audit before relying on the recommendation. <br>\n\n\n## Reference(s): <br>\n- [Primary sources for decision-tree](references/sources.md) <br>\n- [Magee 1964 chemical plant investment example](examples/magee-1964-chemical-plant-investment-hbr.md) <br>\n- [Decision Tree skill page](https://clawhub.ai/deciqai/skills/decision-tree) <br>\n- [deciqAI publisher profile](https://clawhub.ai/user/deciqai) <br>\n- [deciqAI](https://deciqai.com) <br>\n\n\n## Skill Output: <br>\n**Output Type(s):** [Analysis, Markdown, Guidance] <br>\n**Output Format:** [Markdown with structured decision tree tables and recommendations] <br>\n**Output Parameters:** [1D] <br>\n**Other Properties Related to Output:** [Includes branch probabilities, payoff units, rollback calculations, sensitivity threshold, EVPI, and conditions where the recommendation changes.] <br>\n\n## Skill Version(s): <br>\n1.0.0 (source: server release evidence) <br>\n\n## Ethical Considerations: <br>\nUsers should evaluate whether this skill is appropriate for their environment, review any generated or modified files before relying on them, and apply their organization's safety, security, and compliance requirements before deployment. <br>","readmeExcerpt":"Skill: Decision Tree Owner: deciqai Summary: Activate when: user says 'help me choose between two options with different risks', 'I need to map out what could happen if we go with X', 'we have a sequent... Tags: latest:1.0.5 Version history: v1.0.5 | 2026-07-16T17:56:56.683Z | user Description tail link + agents machine-readable metadata line (deciqai.com/s/decision-tree.json) v1.0.4 | 2026-07-08T10:58:57.760Z | user","codeSnippets":[],"executableExamples":[{"language":"text","snippet":"Decision Tree: <topic>\nOptions: A / B  |  Timeline:\nTree: [node-by-node description]\nProbabilities: Node | Branch | p | Basis\nPayoffs: Path | Value | Unit\nRollback: Option A EV= / Option B EV= / Optimal=\nSensitivity: flips when p([key branch]) > [threshold]  |  EVPI=\nRecommendation: [option] — holds if [condition]; flips if [condition]"},{"language":"text","snippet":"Decision Tree: <topic>\nOptions: A / B  |  Timeline:\nTree: [node-by-node description]\nProbabilities: Node | Branch | p | Basis\nPayoffs: Path | Value | Unit\nRollback: Option A EV= / Option B EV= / Optimal=\nSensitivity: flips when p([key branch]) > [threshold]  |  EVPI=\nRecommendation: [option] — holds if [condition]; flips if [condition]"},{"language":"text","snippet":"Decision Tree: <topic>\nOptions: A / B  |  Timeline:\nTree: [node-by-node description]\nProbabilities: Node | Branch | p | Basis\nPayoffs: Path | Value | Unit\nRollback: Option A EV= / Option B EV= / Optimal=\nSensitivity: flips when p([key branch]) > [threshold]  |  EVPI=\nRecommendation: [option] — holds if [condition]; flips if [condition]"},{"language":"text","snippet":"Decision Tree: <topic>\nOptions: A / B  |  Timeline:\nTree: [node-by-node description]\nProbabilities: Node | Branch | p | Basis\nPayoffs: Path | Value | Unit\nRollback: Option A EV= / Option B EV= / Optimal=\nSensitivity: flips when p([key branch]) > [threshold]  |  EVPI=\nRecommendation: [option] — holds if [condition]; flips if [condition]"},{"language":"text","snippet":"Decision Tree: <topic>\nOptions: A / B  |  Timeline:\nTree: [node-by-node description]\nProbabilities: Node | Branch | p | Basis\nPayoffs: Path | Value | Unit\nRollback: Option A EV= / Option B EV= / Optimal=\nSensitivity: flips when p([key branch]) > [threshold]  |  EVPI=\nRecommendation: [option] — holds if [condition]; flips if [condition]"},{"language":"text","snippet":"Decision Tree: <topic>\nOptions: A / B  |  Timeline:\nTree: [node-by-node description]\nProbabilities: Node | Branch | p | Basis\nPayoffs: Path | Value | Unit\nRollback: Option A EV= / Option B EV= / Optimal=\nSensitivity: flips when p([key branch]) > [threshold]  |  EVPI=\nRecommendation: [option] — holds if [condition]; flips if [condition]"}],"parameters":null,"dependencies":[],"permissions":[],"extractedFiles":[{"path":"SKILL.md","content":"---\nname: decision-tree\ndescription: \"Activate when: user says 'help me choose between two options with different risks', 'I need to map out what could happen if we go with X', 'we have a sequential decision — first we do A then depending on results we do B', 'what is the expected value of this investment given uncertain demand'. Do NOT activate when: the decision is a one-shot choice with no sequential stages (use simple EV instead); probabilities cannot be estimated even roughly and uncertainty is too deep to quantify. More: deciqai.com/c/decision-tree\"\n---\n\n# Decision Tree\n\n## Overview\n\nA **decision tree** maps a multi-stage decision: decision nodes (squares) for choices you control, chance nodes (circles) for outcomes you don't, probabilities on every branch, payoffs at the leaves — then rollback right-to-left to get expected value at the root. First systematized by John F. Magee (HBR, 1964); formalized by Howard Raiffa (1968). Its biggest value: converting \"I feel we should expand\" into \"what probability do you assign to high demand?\" — making every assumption explicit and contestable.\n\nComposes with `expected-value-and-kelly` (EV scaffold + bet sizing), `probabilistic-thinking` (calibration per node), `inversion` (rollback = working outcomes backward), `mece` (branches must be MECE so probabilities sum to 1.0).\n\n## When to Use\n\n- Decision has sequential stages (decide → learn → decide again)\n- Outcomes uncertain; probabilities can be estimated (even roughly)\n- Payoffs quantifiable (NPV, revenue, cost, lives saved)\n- Multiple stakeholders need a shared visual model to align on assumptions\n- Sizing a big irreversible bet under AI uncertainty — build vs. buy vs. wait on AI capex, a fab investment, or committing while AI adoption / AI valuations are unproven\n\n**Not when:** one-shot choice with no stages; probabilities unestimable; payoffs purely qualitative; branch set too large (use scenario planning instead).\n\n## Coaching Novices (Adaptive Front Door)\n\n- **Engine mode:** user has a concrete multi-stage decision → run The Process directly.\n- **Coach mode:** user is unfamiliar or has no concrete case → guide step by step.\n\nIn Coach mode, respond one step at a time. Each [WAIT] is a hard stop — output only that step's question, then stop.\n\n1. **One-line:** a decision tree converts \"I feel\" into \"what probability do you assign?\" — making assumptions explicit so they can be argued about.\n2. **Check fit.** Sequential stages? Uncertain outcomes? Quantifiable payoffs? If yes to all three, a tree applies.\n3. **Elicit their real case.** What's the initial choice? What uncertain outcomes follow? What payoffs result?\n> **[WAIT — do not advance until user responds]**\n4. **Run The Process one step at a time** with their input — draw structure, assign probabilities, assign payoffs, roll back.\n> **[WAIT — do not advance until user responds]**\n5. **Close** by naming the insight: the threshold at which the recommendation flips, and whether to gather more data."},{"path":"_meta.json","content":"{\n  \"ownerId\": \"kn754b8sk22s8c6gjxt02bftbn88q7ye\",\n  \"slug\": \"decision-tree\",\n  \"version\": \"1.0.5\",\n  \"publishedAt\": 1784224616683\n}"},{"path":"references/sources.md","content":"# Sources — decision-tree\n\n> *Primary sources for the [decision-tree](../SKILL.md) skill.*\n\n## Sources\n\n- Magee, J. F. (1964). \"Decision Trees for Decision Making.\" *Harvard Business Review*, July–August, 126–138. The original practitioner framework.\n- Magee, J. F. (1964). \"How to Use Decision Trees in Capital Investment.\" *Harvard Business Review*, September–October, 79–96. Capital investment application.\n- Raiffa, H. (1968). *Decision Analysis: Introductory Lectures on Choices under Uncertainty.* Addison-Wesley. The academic formalization; introduces EVPI and formal rollback.\n- Howard, R. A. (1966). \"Decision Analysis: Applied Decision Theory.\" *Proceedings of the 4th International Conference on Operational Research.* Stanford. Early theoretical grounding.\n- Howard, R. A., & Matheson, J. E. (Eds.) (1983). *Readings on the Principles and Applications of Decision Analysis.* Strategic Decisions Group. Comprehensive practitioner reference.\n- Clemen, R. T., & Reilly, T. (2013). *Making Hard Decisions with DecisionTools.* Cengage. Standard textbook treatment.\n- Eisenhower, D. D. (1948). *Crusade in Europe.* Doubleday. First-hand account of the D-Day weather go/no-go decision (worked example).\n- Stagg, J. M. (1971). *Forecast for Overlord.* Ian Allan. The SHAEF chief meteorologist's account of the June 1944 forecasts.\n- Major U.S. hyperscaler quarterly earnings guidance and calls, 2024–2026 (Microsoft, Alphabet, Amazon, Meta). Primary source for the reported surge in AI-related capital expenditure and management's commentary on committing to AI capacity under uncertain returns. Context for the AI build-vs-buy-vs-wait worked example.\n- Mainstream financial-press coverage of the 2024–2026 \"AI capex / overbuild / bubble\" debate (e.g., The Wall Street Journal, Financial Times, The Economist, Reuters). Durable, widely-reported context for how large firms weighed heavy AI infrastructure investment against the risk of stranded capacity.\n- Leading semiconductor foundries' and integrated device makers' public capital-expenditure guidance and management commentary, 2024–2026 (as reported in earnings materials and mainstream financial press). Context for the chipmaker leading-edge-fab worked example: the multi-year, multi-billion-dollar nature of advanced-node fab commitments made ahead of confirmed AI-driven demand.\n- Widely reported industry coverage of the semiconductor sector's historical boom-bust capacity cycles and of the 2024–2026 debate over whether AI-driven demand for leading-edge chips is durable or a potential overbuild (e.g., trade press such as SemiAnalysis-style analysis alongside general financial press). Durable, well-documented context for the high/low-demand probability framing; no specific figures in the worked example are drawn from any single filing."},{"path":"examples/chipmaker-leading-edge-fab-investment-2024-2026.md","content":"# Method in Action: A Chipmaker's Leading-Edge Fab Investment Under AI Uncertainty (2024–2026)\n\n> *Example for the [decision-tree](../SKILL.md) skill.*\n\nBetween 2024 and 2026, one of the largest irreversible capital bets in the economy was a semiconductor manufacturer's decision to commit to leading-edge fabrication capacity. A single advanced logic fab is a multi-year, multi-billion-dollar commitment made *years* before the demand that would fill it is confirmed. The AI wave made this sharper on both sides: the *upside* case (AI accelerators and their supply chain filling every wafer) and the *downside* case (a capacity glut if AI demand or monetization disappoints, echoing prior semiconductor boom-bust cycles). This is a textbook decision-tree problem — sequential, uncertain, quantifiable — and the tree does exactly what Magee promised in 1964: it converts \"AI demand is unstoppable, we must break ground now\" into \"what probability do you put on sustained high demand, and what does the tree say if you are wrong?\"\n\nThis worked example applies the skill's six Process steps to a **stylized composite** of that decision. The framing (large fab now vs. phased/modular fab vs. defer, under high/low AI-driven demand) mirrors the real 2024–2026 debate; the probabilities and dollar payoffs below are **illustrative inputs chosen to demonstrate the method**, not figures from any company's filings.\n\n---\n\n**Step 1 — Root.** Define the decision. A chipmaker's board must choose how to commit leading-edge wafer capacity over a multi-year horizon. Draw the root square with three branches:\n\n- **Large fab now** — commit to a full-scale advanced fab immediately. Highest fixed cost and longest lead time, best unit economics *if* demand shows up, most stranded capital if it does not.\n- **Phased / modular fab** — build the shell and a first module now, with a pre-engineered *option to expand* tooling later once demand is clearer (directly the small-plant-with-expansion structure Magee introduced in 1964).\n- **Defer** — hold the large commitment ~12 months, gather adoption and pricing signal, then decide. Deferral is not free: a fab's multi-year construction-and-qualification lead time means capacity decided late arrives late, potentially after the window of peak demand.\n\nDecision-maker: the board / CFO. Timeline: leading-edge fab lead times run into years — which is precisely why \"wait\" carries a real delay cost.\n\n**Step 2 — Chance nodes.** Each branch runs into an uncertainty the firm does not control. Draw a circle on each. The dominant chance node is **AI-driven wafer demand**, which must be MECE:\n\n- *High, durable demand* — AI-accelerator and adjacent demand keeps leading-edge capacity near-full for years.\n- *Low / disappointing demand* — AI adoption or monetization stalls, or competitors add capacity too; the new fab runs underutilized (the \"AI capex glut / bubble\" fear that ran through the 2024–2026 debate).\n\nFor **Phased / modular**, a second-stage decision node "},{"path":"examples/eisenhower-1944-d-day-weather-decision.md","content":"# Method in Action: Eisenhower's D-Day Weather Decision (June 1944)\n\n> *Example for the [decision-tree](../SKILL.md) skill.*\n\nOn June 4–5, 1944, General Dwight D. Eisenhower faced the highest-stakes go/no-go decision of the war: launch Operation Overlord into marginal weather, or postpone. The decision was never written up as a formal tree — the method postdates it — but the deliberation at Southwick House maps onto the decision-tree process almost node for node, which is why decision analysts have cited it ever since.\n\n**The root decision node (square):** Go on June 6, or postpone. The branch set was tightly constrained: the invasion needed moonlight for the airborne drops and a low dawn tide to expose beach obstacles, so only a few days per month qualified. If June 6 was scrubbed, the next tidal window was around June 19 — roughly two weeks away.\n\n**The chance nodes (circles):** Each option led straight into an uncertainty Eisenhower did not control.\n\n- *Go, June 6* → chance node: does the brief break in the storm forecast by Group Captain James Stagg, SHAEF's chief meteorologist, actually hold? If yes: landings proceed under rough but workable conditions. If no: landing craft swamped, air support grounded, the assault force wrecked on the beaches.\n- *Postpone to June 19* → chance node: unknown weather two weeks out (beyond any 1944 forecast horizon), compounded by near-certain costs — nearly 200,000 troops were already sealed aboard ships and briefed, and every day of delay increased the odds that German intelligence would fix the time and place of the invasion.\n\n**Probabilities:** Stagg's team forecast a short interval of improved weather for June 6 amid a stormy period — a genuine probabilistic judgment made against disagreeing British and American forecasting teams. Illustrative reconstruction (not historical record): call the window-holds branch p ≈ 0.7, and the June 19 branch a coin flip at best with the secrecy-compromise cost accruing regardless. No participant wrote such numbers down; the structure of the argument, however, was exactly this.\n\n**Payoffs:** The asymmetry drove the answer. *Go and the window holds*: the liberation of Western Europe begins. *Go and it fails*: a bloody repulse — but a repulse that a second attempt could survive. *Postpone*: certain, compounding losses (secrecy, morale, tide, the Soviet-front timetable) plus an unresolved weather gamble two weeks later. Postponement was not the \"safe\" branch; it was a different bet with worse certain costs.\n\n**Value of information — the June 4 postponement:** Eisenhower's first move was a textbook EVPI play. On June 4 he scrubbed the original June 5 date and bought exactly one more forecast cycle — trading one day of the window for one more update from Stagg. When Stagg's June 5 briefing confirmed the break, the value of further waiting had collapsed: no additional forecast could resolve the remaining uncertainty before the tide window closed. The cost of more information no"}],"languages":[],"docsSourceLabel":"CLAWHUB","editorialOverview":"Activate when: user says 'help me choose between two options with different risks', 'I need to map out what could happen if we go with X', 'we have a sequent... Skill: Decision Tree Owner: deciqai Summary: Activate when: user says 'help me choose between two options with different risks', 'I need to map out what could happen if we go with X', 'we have a sequent... 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