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+---
+name: expected-value
+description: Use when making decisions under uncertainty with quantifiable outcomes, comparing risky options (investments, product bets, strategic choices), prioritizing projects by expected return, assessing whether to take a gamble, or when user mentions expected value, EV calculation, risk-adjusted return, probability-weighted outcomes, decision tree, or needs to choose between uncertain alternatives.
+---
+# Expected Value
+
+## Table of Contents
+- [Purpose](#purpose)
+- [When to Use](#when-to-use)
+- [What Is It?](#what-is-it)
+- [Workflow](#workflow)
+- [Common Patterns](#common-patterns)
+- [Guardrails](#guardrails)
+- [Quick Reference](#quick-reference)
+
+## Purpose
+
+Expected Value (EV) provides a framework for making rational decisions under uncertainty by calculating the probability-weighted average of all possible outcomes. This skill guides you through identifying scenarios, estimating probabilities and payoffs, computing expected values, and interpreting results while accounting for risk preferences and real-world constraints.
+
+## When to Use
+
+Use this skill when:
+
+- **Investment decisions**: Should we invest in project A (high risk, high return) or project B (low risk, low return)?
+- **Product bets**: Launch feature X (uncertain adoption) or focus on feature Y (safer bet)?
+- **Resource allocation**: Which initiatives have highest expected return given limited budget?
+- **Go/no-go decisions**: Is expected value of launching positive after accounting for probabilities of success/failure?
+- **Pricing & negotiation**: What's expected value of accepting vs. rejecting an offer?
+- **Insurance & hedging**: Should we buy insurance (guaranteed small loss) vs. risk large loss?
+- **A/B test interpretation**: Which variant has higher expected conversion rate accounting for uncertainty?
+- **Portfolio optimization**: Diversify to maximize expected return for given risk tolerance?
+
+Trigger phrases: "expected value", "EV calculation", "risk-adjusted return", "probability-weighted outcomes", "decision tree", "should I take this gamble", "compare risky options"
+
+## What Is It?
+
+**Expected Value (EV)** = Σ (Probability of outcome × Value of outcome)
+
+For each possible outcome, multiply its probability by its value (payoff), then sum across all outcomes.
+
+**Core formula**:
+```
+EV = (p₁ × v₁) + (p₂ × v₂) + ... + (pₙ × vₙ)
+
+where:
+- p₁, p₂, ..., pₙ are probabilities of each outcome (must sum to 1.0)
+- v₁, v₂, ..., vₙ are values (payoffs) of each outcome
+```
+
+**Quick example:**
+
+**Scenario**: Launch new product feature. Estimate 60% chance of success ($100k revenue), 40% chance of failure (-$20k sunk cost).
+
+**Calculation**:
+- EV = (0.6 × $100k) + (0.4 × -$20k)
+- EV = $60k - $8k = **$52k**
+
+**Interpretation**: On average, launching this feature yields $52k. Positive EV → launch is rational choice (if risk tolerance allows).
+
+**Core benefits:**
+- **Quantitative comparison**: Compare disparate options on same scale (expected return)
+- **Explicit uncertainty**: Forces estimation of probabilities instead of gut feel
+- **Repeatable framework**: Same method applies to investments, products, hiring, etc.
+- **Risk-adjusted**: Weights outcomes by likelihood, not just best/worst case
+- **Portfolio thinking**: Optimal long-term strategy is maximize expected value over many decisions
+
+## Workflow
+
+Copy this checklist and track your progress:
+
+```
+Expected Value Analysis Progress:
+- [ ] Step 1: Define decision and alternatives
+- [ ] Step 2: Identify possible outcomes
+- [ ] Step 3: Estimate probabilities
+- [ ] Step 4: Estimate payoffs (values)
+- [ ] Step 5: Calculate expected values
+- [ ] Step 6: Interpret and adjust for risk preferences
+```
+
+**Step 1: Define decision and alternatives**
+
+What decision are you making? What are the mutually exclusive options? See [resources/template.md](resources/template.md#decision-framing-template).
+
+**Step 2: Identify possible outcomes**
+
+For each alternative, what could happen? List scenarios from best case to worst case. See [resources/template.md](resources/template.md#outcome-identification-template).
+
+**Step 3: Estimate probabilities**
+
+What's the probability of each outcome? Use base rates, reference classes, expert judgment, data. See [resources/methodology.md](resources/methodology.md#1-probability-estimation-techniques).
+
+**Step 4: Estimate payoffs (values)**
+
+What's the value (gain or loss) of each outcome? Quantify in dollars, time, utility. See [resources/methodology.md](resources/methodology.md#2-payoff-quantification).
+
+**Step 5: Calculate expected values**
+
+Multiply probabilities by payoffs, sum across outcomes for each alternative. See [resources/template.md](resources/template.md#ev-calculation-template).
+
+**Step 6: Interpret and adjust for risk preferences**
+
+Choose option with highest EV? Or adjust for risk aversion, non-monetary factors, strategic value. See [resources/methodology.md](resources/methodology.md#4-risk-preferences-and-utility).
+
+Validate using [resources/evaluators/rubric_expected_value.json](resources/evaluators/rubric_expected_value.json). **Minimum standard**: Average score ≥ 3.5.
+
+## Common Patterns
+
+**Pattern 1: Investment Decision (Discrete Outcomes)**
+- **Structure**: Go/no-go choice with 3-5 discrete scenarios (best, base, worst case)
+- **Use case**: Product launch, hire vs. not hire, accept investment offer, buy vs. lease
+- **Pros**: Simple, intuitive, easy to communicate (decision tree visualization)
+- **Cons**: Oversimplifies continuous distributions, binary framing may miss nuance
+- **Example**: Launch product feature (60% success $100k, 40% fail -$20k) → EV = $52k
+
+**Pattern 2: Portfolio Allocation (Multiple Options)**
+- **Structure**: Allocate budget across N projects, each with own EV and risk profile
+- **Use case**: Venture portfolio, R&D budget, marketing spend allocation, team capacity
+- **Pros**: Diversification reduces variance, can optimize for risk/return tradeoff
+- **Cons**: Requires estimates for many variables, correlations matter (not independent)
+- **Example**: Invest in 3 startups ($50k each), EVs = [$20k, $15k, -$10k]. Total EV = $25k. Diversified portfolio reduces risk vs. single $150k bet.
+
+**Pattern 3: Sequential Decision (Decision Tree)**
+- **Structure**: Series of decisions over time, outcomes of early decisions affect later options
+- **Use case**: Clinical trials (Phase I → II → III), staged investment, explore then exploit
+- **Pros**: Captures optionality (can stop if early results bad), fold-back induction finds optimal strategy
+- **Cons**: Tree grows exponentially, need probabilities for all branches
+- **Example**: Phase I drug trial (70% pass, $1M cost) → if pass, Phase II (50% pass, $5M) → if pass, Phase III (40% approve, $50M revenue). Calculate EV working backwards.
+
+**Pattern 4: Continuous Distribution (Monte Carlo)**
+- **Structure**: Outcomes are continuous (revenue could be $0-$1M), use probability distributions
+- **Use case**: Financial modeling, project timelines, resource planning, sensitivity analysis
+- **Pros**: Captures full uncertainty, avoids discrete scenario bias, provides confidence intervals
+- **Cons**: Requires distributional assumptions, computationally intensive, harder to communicate
+- **Example**: Revenue ~ Normal($500k, $100k std dev). Run 10,000 simulations → mean = $510k, 90% CI = [$350k, $670k].
+
+**Pattern 5: Competitive Game (Payoff Matrix)**
+- **Structure**: Your outcome depends on competitor's choice, create payoff matrix
+- **Use case**: Pricing strategy, product launch timing, negotiation, auction bidding
+- **Pros**: Incorporates strategic interaction, finds Nash equilibrium
+- **Cons**: Requires estimating competitor's probabilities and payoffs, game-theoretic complexity
+- **Example**: Price high vs. low, competitor prices high vs. low → 2×2 matrix. Calculate EV for each strategy given beliefs about competitor.
+
+## Guardrails
+
+**Critical requirements:**
+
+1. **Probabilities must sum to 1.0**: If you list outcomes, their probabilities must be exhaustive (cover all possibilities) and mutually exclusive (no overlap). Check: p₁ + p₂ + ... + pₙ = 1.0.
+
+2. **Don't use EV for one-shot, high-stakes decisions without risk adjustment**: EV is long-run average. For rare, irreversible decisions (bet life savings, critical surgery), consider risk aversion. A 1% chance of $1B (EV = $10M) doesn't mean you should bet your house.
+
+3. **Quantify uncertainty, don't hide it**: Probabilities and payoffs are estimates, often uncertain. Use ranges (optimistic/pessimistic), sensitivity analysis, or distributions. Don't pretend false precision.
+
+4. **Consider non-monetary value**: EV in dollars is convenient, but some outcomes have utility not captured by money (reputation, learning, optionality, morale). Convert to common scale or use multi-attribute utility.
+
+5. **Probabilities must be calibrated**: Don't use gut-feel probabilities without grounding. Use base rates, reference classes, data, expert forecasts. Test: are your "70% confident" predictions right 70% of the time?
+
+6. **Account for correlated outcomes**: If outcomes aren't independent (economic downturn affects all portfolio companies), correlation reduces diversification benefit. Model dependencies.
+
+7. **Time value of money**: Payoffs at different times aren't equivalent. Discount future cash flows to present value (NPV = Σ CF_t / (1+r)^t). EV should use NPV, not nominal values.
+
+8. **Stopping rules and option value**: In sequential decisions, fold-back induction finds optimal strategy. Don't ignore option to stop early, pivot, or wait for more information.
+
+**Common pitfalls:**
+
+- ❌ **Ignoring risk aversion**: EV($100k, 50/50) = EV($50k, certain) but most prefer certain $50k. Use utility functions for risk-averse agents.
+- ❌ **Anchor on single scenario**: "Best case is $1M!" → but probability is 5%. Focus on EV, not cherry-picked scenarios.
+- ❌ **False precision**: "Probability = 67.3%" when you're guessing. Use ranges, express uncertainty.
+- ❌ **Sunk cost fallacy**: Past costs are sunk, don't include in forward-looking EV. Only future costs/benefits matter.
+- ❌ **Ignoring tail risk**: Low-probability, high-impact events (0.1% chance of -$10M) can dominate EV. Don't round to zero.
+- ❌ **Static analysis**: Assume you can't update beliefs or change course. Real decisions allow learning and pivoting.
+
+## Quick Reference
+
+**Key formulas:**
+
+**Expected Value**: EV = Σ (pᵢ × vᵢ) where p = probability, v = value
+
+**Expected Utility** (for risk aversion): EU = Σ (pᵢ × U(vᵢ)) where U = utility function
+- Risk-neutral: U(x) = x (EV = EU)
+- Risk-averse: U(x) = √x or U(x) = log(x) (concave)
+- Risk-seeking: U(x) = x² (convex)
+
+**Net Present Value**: NPV = Σ (CF_t / (1+r)^t) where CF = cash flow, r = discount rate, t = time period
+
+**Variance** (risk measure): Var = Σ (pᵢ × (vᵢ - EV)²)
+
+**Standard Deviation**: σ = √Var
+
+**Coefficient of Variation** (risk/return ratio): CV = σ / EV (lower = better risk-adjusted return)
+
+**Breakeven probability**: p* where EV = 0. Solve: p* × v_success + (1-p*) × v_failure = 0.
+
+**Decision rules**:
+- **Maximize EV**: Choose option with highest EV (risk-neutral, repeated decisions)
+- **Maximize EU**: Choose option with highest expected utility (risk-averse, incorporates preferences)
+- **Minimax regret**: Minimize maximum regret across scenarios (conservative, avoid worst mistake)
+- **Satisficing**: Choose first option above threshold EV (bounded rationality)
+
+**Sensitivity analysis questions**:
+- How much do probabilities need to change to flip decision?
+- What's EV in best case? Worst case? Which variables have most impact?
+- At what probability does EV break even (EV = 0)?
+
+**Key resources:**
+- **[resources/template.md](resources/template.md)**: Decision framing, outcome identification, EV calculation templates, sensitivity analysis
+- **[resources/methodology.md](resources/methodology.md)**: Probability estimation, payoff quantification, decision tree analysis, utility functions
+- **[resources/evaluators/rubric_expected_value.json](resources/evaluators/rubric_expected_value.json)**: Quality criteria (scenario completeness, probability calibration, payoff quantification, EV interpretation)
+
+**Inputs required:**
+- **Decision**: What are you choosing between? (2+ mutually exclusive alternatives)
+- **Outcomes**: For each alternative, what could happen? (3-5 scenarios typical)
+- **Probabilities**: How likely is each outcome? (sum to 1.0)
+- **Payoffs**: What's the value (gain/loss) of each outcome? (dollars, time, utility)
+
+**Outputs produced:**
+- `expected-value-analysis.md`: Decision framing, outcome scenarios with probabilities and payoffs, EV calculations, sensitivity analysis, recommendation with risk considerations
--- a/skills/expected-value/resources/evaluators/rubric_expected_value.json
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+{
+  "criteria": [
+    {
+      "name": "Scenario Completeness",
+      "1": "Only 1-2 scenarios considered (best case or base case only), missing tail risk or critical scenarios, outcomes not mutually exclusive or exhaustive",
+      "3": "3-4 scenarios covering best/base/worst cases, mostly exhaustive, some overlap or gaps",
+      "5": "Comprehensive scenario set (4-6 outcomes), exhaustive and mutually exclusive, covers full range including tail risks, explicit check that probabilities sum to 1.0"
+    },
+    {
+      "name": "Probability Calibration",
+      "1": "Gut-feel probabilities with no grounding, no base rates or reference classes used, probabilities arbitrary or don't sum to 1.0",
+      "3": "Probabilities estimated using 1-2 methods (inside view or expert judgment), some grounding in data or reference classes, sum to 1.0",
+      "5": "Probabilities triangulated using multiple methods (base rates, inside view, expert judgment, data/models), weighted reconciliation across methods, explicit confidence ranges, historical calibration checked"
+    },
+    {
+      "name": "Payoff Quantification",
+      "1": "Vague payoffs ('good' vs 'bad'), no dollar amounts or quantification, non-monetary factors ignored, no time value of money",
+      "3": "Payoffs quantified in dollars for monetary components, rough estimates for non-monetary (time, reputation), NPV mentioned if multi-period",
+      "5": "Comprehensive payoff quantification: monetary (revenue, costs, opportunity cost) with NPV for multi-period (discount rate justified), non-monetary (time, reputation, learning, strategic) converted to $ or utility, uncertainty expressed (ranges or distributions)"
+    },
+    {
+      "name": "EV Calculation Accuracy",
+      "1": "No formal EV calculation, 'seems like good idea', or calculation errors (wrong formula, arithmetic mistakes, probabilities don't sum to 1.0)",
+      "3": "EV calculated correctly (Σ p×v), shown for all alternatives, comparison table present, minor errors",
+      "5": "EV calculated correctly with full transparency (table showing outcomes, probabilities, payoffs, p×v for each), variance and standard deviation computed (risk measures), coefficient of variation for risk-adjusted comparison, all calculations verified"
+    },
+    {
+      "name": "Sensitivity Analysis",
+      "1": "No sensitivity analysis, assumes point estimates are certain, no breakeven analysis",
+      "3": "One-way sensitivity for 1-2 key variables, breakeven calculation (at what probability does decision flip?), some scenario analysis",
+      "5": "Comprehensive sensitivity: one-way for all key variables, tornado diagram (ranked by impact), scenario analysis (optimistic/base/pessimistic), breakeven probabilities, identifies which assumptions matter most, robustness of decision across scenarios"
+    },
+    {
+      "name": "Risk Adjustment",
+      "1": "No consideration of risk aversion, assumes maximize EV regardless of stakes, one-shot high-stakes decision treated as repeated bet",
+      "3": "Risk profile mentioned (one-shot vs repeated, risk-averse vs neutral), some adjustment for risk (prefer lower variance option if EVs close)",
+      "5": "Explicit risk adjustment: utility function specified if risk-averse, expected utility (EU) calculated in addition to EV, certainty equivalent and risk premium computed, decision maker profile assessed (one-shot/repeated, stakes, risk tolerance), recommendation accounts for both EV and risk"
+    },
+    {
+      "name": "Decision Tree Use (if sequential)",
+      "1": "Sequential decision treated as simultaneous (ignores optionality), no fold-back induction, optimal strategy not found",
+      "3": "Decision tree drawn for sequential decisions, fold-back induction attempted, optimal strategy identified, some errors in calculation",
+      "5": "Decision tree correctly structured (decision nodes, chance nodes, terminal payoffs), fold-back induction performed correctly, optimal strategy clearly stated (which choices at each decision point), value of information (EVPI) calculated if relevant, optionality value quantified"
+    },
+    {
+      "name": "Bias Mitigation",
+      "1": "Probabilities show clear biases (overconfidence, anchoring, availability), sunk costs included in forward-looking EV, no acknowledgment of bias risk",
+      "3": "Biases mentioned (overconfidence, anchoring), some mitigation (use base rates, triangulate estimates), sunk costs excluded from EV",
+      "5": "Comprehensive bias mitigation: probabilities calibrated (base rates used, confidence ranges specified, multiple methods triangulate), anchoring avoided (independent estimates before seeing others), availability bias checked (not overweighting vivid examples), sunk costs explicitly excluded, tail risks not rounded to zero, uncertainty expressed (no false precision)"
+    },
+    {
+      "name": "Non-Monetary Factors",
+      "1": "Only monetary payoffs considered, strategic value / learning / reputation ignored or mentioned as afterthought without quantification",
+      "3": "Non-monetary factors mentioned qualitatively (strategic value, learning), rough $ equivalents or scoring (1-10), incorporated into final recommendation",
+      "5": "Non-monetary factors systematically quantified: time (hours × rate), reputation (CLV impact, premium pricing), learning (option value of skills), strategic positioning (market share × profit), morale (productivity impact), either converted to $ or incorporated via multi-attribute utility, weighting justified"
+    },
+    {
+      "name": "Recommendation Clarity",
+      "1": "No clear recommendation, presents EV but doesn't say which option to choose, recommendation contradicts EV without explanation",
+      "3": "Recommendation stated (choose Alt X), rationale references EV and risk, some explanation of factors beyond EV",
+      "5": "Clear, actionable recommendation with full rationale: highest EV alternative identified, risk considerations explained (EU if risk-averse), non-monetary factors weighted in, contingencies specified (if Outcome Y occurs, we'll pivot to...), sensitivity and robustness discussed, confidence level stated, next steps / action plan provided"
+    }
+  ],
+  "guidance_by_type": {
+    "Investment Decision": {
+      "target_score": 4.0,
+      "key_requirements": [
+        "Payoff Quantification (≥4): NPV calculated with justified discount rate (WACC, hurdle rate), multi-period cash flows discounted",
+        "Probability Calibration (≥4): Base rates from similar investments, triangulation across methods",
+        "Risk Adjustment (≥4): One-shot high-stakes → expected utility, certainty equivalent, risk premium calculated",
+        "Sensitivity Analysis (≥4): IRR, payback period, breakeven analysis, scenario stress tests"
+      ],
+      "common_pitfalls": [
+        "Ignoring time value of money (using nominal cash flows without discounting)",
+        "Optimism bias (probabilities skewed toward success)",
+        "Sunk cost fallacy (including past investments in forward-looking EV)"
+      ]
+    },
+    "Product / Feature Launch": {
+      "target_score": 3.8,
+      "key_requirements": [
+        "Scenario Completeness (≥4): Best (viral success), base (expected adoption), worst (flop), partial success scenarios",
+        "Non-Monetary Factors (≥4): Learning value (customer insights), strategic positioning (competitive response), brand impact",
+        "Sensitivity Analysis (≥4): Adoption rate, willingness to pay, churn rate, development cost overruns",
+        "Decision Tree (≥3 if staged): Pilot → measure → decide to scale or kill"
+      ],
+      "common_pitfalls": [
+        "Ignoring opportunity cost (what else could team build?)",
+        "Treating as pure monetary decision (missing strategic / learning value)",
+        "Binary framing (launch or don't) when staged rollout is option"
+      ]
+    },
+    "Resource Allocation (Portfolio)": {
+      "target_score": 4.1,
+      "key_requirements": [
+        "EV Calculation (≥5): EV computed for each project, ranked by EV, marginal vs. total EV if budget constrained",
+        "Risk Adjustment (≥4): Portfolio variance (correlation between projects), diversification benefit, risk-return frontier",
+        "Sensitivity Analysis (≥4): How does ranking change if key assumptions vary? Robust winners vs. fragile",
+        "Non-Monetary Factors (≥4): Strategic balance (explore vs exploit), team capacity, dependency sequencing"
+      ],
+      "common_pitfalls": [
+        "Assuming independence (projects often correlated, especially in downturn)",
+        "Ignoring constraints (budget, team capacity, sequencing dependencies)",
+        "Marginal analysis error (choosing projects by EV/cost ratio when should use knapsack optimization)"
+      ]
+    },
+    "Sequential Decision (Decision Tree)": {
+      "target_score": 4.2,
+      "key_requirements": [
+        "Decision Tree Use (≥5): Correctly structured tree, fold-back induction, optimal strategy, value of optionality",
+        "Scenario Completeness (≥4): All branches labeled with probabilities and payoffs, paths to terminal nodes complete",
+        "Sensitivity Analysis (≥4): Value of information (EVPI), when to stop vs continue, option value quantified",
+        "Risk Adjustment (≥3): Risk aversion may favor stopping early (take certain intermediate payoff vs gamble on later stages)"
+      ],
+      "common_pitfalls": [
+        "Ignoring optionality (treating as upfront all-or-nothing decision)",
+        "Not working backwards (trying to solve forward instead of fold-back induction)",
+        "Forgetting to subtract costs at each decision node (costs are sunk for later nodes)"
+      ]
+    },
+    "Competitive / Game-Theoretic": {
+      "target_score": 3.9,
+      "key_requirements": [
+        "Probability Calibration (≥4): Estimate opponent's strategy probabilities (beliefs or mixed strategy), justify via game theory or behavioral model",
+        "Payoff Quantification (≥4): Payoff matrix (your payoff for each combination of strategies), account for opponent's response",
+        "Sensitivity Analysis (≥4): How does optimal strategy change if opponent's probabilities shift? Robust strategies (good across many opponent behaviors)",
+        "Recommendation (≥4): Nash equilibrium identified if relevant, best response given beliefs, contingency if opponent deviates"
+      ],
+      "common_pitfalls": [
+        "Assuming rational opponent (real opponents may be irrational, vindictive, or mistaken)",
+        "Ignoring signaling / credibility (opponent may learn from your choice, affecting their future strategy)",
+        "Static analysis (in repeated games, cooperation / retaliation dynamics matter)"
+      ]
+    }
+  },
+  "guidance_by_complexity": {
+    "Simple": {
+      "target_score": 3.5,
+      "description": "2 alternatives, 3-4 discrete scenarios per alternative, monetary payoffs, single-period, no sequential decisions",
+      "key_requirements": [
+        "Scenario Completeness (≥3): Best, base, worst cases identified, probabilities sum to 1.0",
+        "Probability Calibration (≥3): At least one grounding method (base rates or inside view or expert judgment)",
+        "Payoff Quantification (≥3): Monetary payoffs in dollars, rough estimates acceptable",
+        "EV Calculation (≥5): Correct formula, transparent table, comparison across alternatives",
+        "Sensitivity Analysis (≥3): Breakeven probability calculated",
+        "Recommendation (≥4): Clear choice with rationale"
+      ],
+      "time_estimate": "1-3 hours",
+      "examples": [
+        "Accept job offer ($120k certain) vs stay ($100k + 20% chance of promotion to $140k)",
+        "Buy insurance ($5k premium) vs risk loss (5% chance of -$80k repair)",
+        "Launch feature (60% success $100k, 40% fail -$20k) vs don't launch ($0)"
+      ]
+    },
+    "Standard": {
+      "target_score": 4.0,
+      "description": "3-4 alternatives, 4-6 scenarios per alternative, monetary + non-monetary payoffs, multi-period (NPV), sensitivity analysis, may be sequential",
+      "key_requirements": [
+        "Scenario Completeness (≥4): Comprehensive scenarios including tail risks, explicit exhaustiveness check",
+        "Probability Calibration (≥4): Multiple methods (base rates, inside view, experts, data), triangulation, confidence ranges",
+        "Payoff Quantification (≥4): NPV for multi-period, non-monetary factors quantified (time, reputation, learning)",
+        "EV Calculation (≥5): Correct with variance/std dev, coefficient of variation for risk comparison",
+        "Sensitivity Analysis (≥4): One-way for key variables, tornado diagram, scenario analysis, breakeven",
+        "Risk Adjustment (≥4): Utility function if risk-averse, EU calculated, risk premium",
+        "Bias Mitigation (≥4): Base rates used, sunk costs excluded, tail risks not ignored",
+        "Recommendation (≥5): Clear choice, full rationale (EV + risk + strategic), contingencies, confidence"
+      ],
+      "time_estimate": "6-12 hours",
+      "examples": [
+        "Invest in project A (high risk, high return) vs B (low risk, low return) vs C (medium) with NPV",
+        "Product roadmap: Feature X vs Y vs Z, multi-period revenue, strategic value, team capacity",
+        "Market expansion: Enter country A vs B vs wait, staged rollout (pilot → scale), learning value"
+      ]
+    },
+    "Complex": {
+      "target_score": 4.3,
+      "description": "5+ alternatives, continuous distributions (Monte Carlo), sequential multi-stage decisions (decision tree), game-theoretic interactions, portfolio optimization, high-stakes",
+      "key_requirements": [
+        "Scenario Completeness (≥5): Continuous distributions or 6+ discrete scenarios, Monte Carlo simulation if appropriate",
+        "Probability Calibration (≥5): Rigorous triangulation, data-driven models, historical calibration checked, explicit uncertainty quantification",
+        "Payoff Quantification (≥5): Comprehensive monetary + non-monetary, NPV with justified discount rate, option value / real options analysis",
+        "EV Calculation (≥5): Monte Carlo or decision tree with fold-back induction, variance/correlation if portfolio, percentile outputs (5th-95th)",
+        "Sensitivity Analysis (≥5): Comprehensive tornado, scenario stress tests, value of information (EVPI), robustness analysis",
+        "Risk Adjustment (≥5): Expected utility with calibrated utility function, certainty equivalent, risk-return frontier if portfolio, loss aversion (Prospect Theory)",
+        "Decision Tree (≥5 if sequential): Multi-stage tree, optimal strategy, optionality value, stopping rules",
+        "Bias Mitigation (≥5): Full calibration protocol, independent probability estimates, outside view anchored, no tail risk neglect",
+        "Non-Monetary Factors (≥5): Multi-attribute utility or systematic $ conversion, strategic value quantified",
+        "Recommendation (≥5): Detailed action plan, contingencies, monitoring plan (what metrics to track, triggers for pivot)"
+      ],
+      "time_estimate": "20-40 hours, specialized expertise",
+      "examples": [
+        "Venture portfolio allocation: Optimize across 10 startups with correlated downside risk, different stages (seed/A/B)",
+        "Pharmaceutical R&D: Phase I/II/III sequential decision tree, option to stop or continue, EVPI for clinical trial",
+        "Competitive pricing: Game-theoretic analysis (your price vs competitor's response), Nash equilibrium, signaling",
+        "Major capital investment: Monte Carlo NPV with uncertain demand, costs, timeline; real options (defer, expand, abandon)"
+      ]
+    }
+  },
+  "common_failure_modes": [
+    {
+      "failure": "Incomplete scenarios (missing tail risk)",
+      "symptom": "Only best/base/worst cases, no intermediate scenarios, tail risks (low prob, high impact) not modeled or rounded to zero",
+      "detection": "Ask 'What else could happen? What's the 1% worst case?' Check if probabilities leave room for tail (p_best + p_base + p_worst < 1.0 → missing scenarios).",
+      "fix": "Add 4th-6th scenarios (partial success, catastrophic failure, unexpected upside). Explicitly model tail risks even if low probability (0.1% × -$10M = -$10k EV, material)."
+    },
+    {
+      "failure": "Gut-feel probabilities with no calibration",
+      "symptom": "Probabilities like '70%' with no justification, no base rates, no reference to similar situations, overconfidence (80% when should be 60%)",
+      "detection": "Ask 'Where does 70% come from? What's the reference class? How often are you right when you say 70%?' If no answer → gut-feel.",
+      "fix": "Use base rates (historical frequency in similar cases), inside view (decompose into factors), expert judgment (average multiple experts), data/models. Triangulate. Widen ranges if uncertain."
+    },
+    {
+      "failure": "Ignoring time value of money",
+      "symptom": "Multi-period cash flows treated as equivalent (Year 1 revenue and Year 5 revenue added directly without discounting), no NPV calculation",
+      "detection": "Check if payoffs occur over multiple periods. If yes and no discounting → ignoring time value.",
+      "fix": "Discount future cash flows to present value: NPV = Σ (CF_t / (1+r)^t). Justify discount rate (WACC, risk-free + risk premium). Use NPV in EV calculation."
+    },
+    {
+      "failure": "Sunk cost fallacy",
+      "symptom": "'We've already spent $1M, can't stop now' → includes past costs in forward-looking EV, escalation of commitment",
+      "detection": "Check if past costs mentioned in recommendation ('We've invested so much'). If yes → sunk cost fallacy.",
+      "fix": "Sunk costs are sunk. Only future costs and benefits matter for decision. EV = future payoff - future cost. Ignore past investments."
+    },
+    {
+      "failure": "No risk adjustment for one-shot high-stakes decisions",
+      "symptom": "Recommendation to 'maximize EV' for decision that could bankrupt (bet life savings), no mention of risk aversion or utility",
+      "detection": "Ask 'Is this decision repeated or one-shot? Can we afford to lose?' If one-shot high-stakes and only EV considered → missing risk adjustment.",
+      "fix": "Use expected utility (EU) instead of EV. Specify utility function (U(x) = √x or log(x) for risk aversion). Calculate EU, certainty equivalent, risk premium. Recommendation: Choose based on EU, not just EV."
+    },
+    {
+      "failure": "Ignoring optionality in sequential decisions",
+      "symptom": "Sequential decision (pilot → scale) treated as upfront all-or-nothing choice, no decision tree, no fold-back induction, value of learning not quantified",
+      "detection": "Ask 'Can we stop/pivot/wait for more info?' If yes but not modeled → ignoring optionality.",
+      "fix": "Build decision tree with decision nodes (choose) and chance nodes (uncertain outcomes). Fold-back induction to find optimal strategy (when to stop, continue, pivot). Quantify option value."
+    },
+    {
+      "failure": "False precision in probabilities",
+      "symptom": "'Probability = 67.32%' when estimate is rough guess, no uncertainty expressed, point estimates treated as certain",
+      "detection": "Ask 'How certain are you? Could this be 60% or 75%?' If wide range but point estimate given → false precision.",
+      "fix": "Express uncertainty: probability range (60-75%), confidence intervals, distributions. Don't pretend more precision than you have. Sensitivity analysis shows impact of uncertainty."
+    },
+    {
+      "failure": "Anchoring bias in probability estimation",
+      "symptom": "First estimate (or number mentioned) biases final estimate, adjust insufficiently from anchor ('Is success rate > 50%?' → estimate ends up ~50% even if should be 20%)",
+      "detection": "Compare independent estimates (before/after seeing anchor). If large shift toward anchor → anchoring bias.",
+      "fix": "Generate independent estimate before seeing others' numbers. Use base rates as anchor (better anchor than arbitrary number). Triangulate across multiple methods."
+    },
+    {
+      "failure": "Ignoring non-monetary factors",
+      "symptom": "Only dollar payoffs considered, strategic value / learning / reputation mentioned as afterthought but not quantified or weighted in decision",
+      "detection": "Check if non-monetary factors listed but EV calculation only uses $. If yes → ignored in quantitative analysis.",
+      "fix": "Quantify non-monetary: time (hours × rate), reputation (CLV impact), learning (option value), strategic (market share × profit). Convert to $ or use multi-attribute utility with weights."
+    },
+    {
+      "failure": "No sensitivity analysis (decision fragile to assumptions)",
+      "symptom": "Single EV calculation, no 'what-if' analysis, don't know how decision changes if assumptions vary, breakeven not calculated",
+      "detection": "Ask 'At what probability does decision flip? What if payoff is 30% lower?' If no answer → no sensitivity.",
+      "fix": "One-way sensitivity (vary each variable), tornado diagram (rank by impact), scenario analysis (optimistic/base/pessimistic), breakeven calculations. Identify robust vs. fragile decisions."
+    }
+  ]
+}
--- a/skills/expected-value/resources/methodology.md
+++ b/skills/expected-value/resources/methodology.md
@@ -0,0 +1,384 @@
+# Expected Value Methodology
+
+Advanced techniques for probability estimation, payoff quantification, utility theory, decision trees, and bias mitigation.
+
+## Workflow
+
+```
+Expected Value Analysis Progress:
+- [ ] Step 1: Define decision and alternatives
+- [ ] Step 2: Identify possible outcomes
+- [ ] Step 3: Estimate probabilities
+- [ ] Step 4: Estimate payoffs (values)
+- [ ] Step 5: Calculate expected values
+- [ ] Step 6: Interpret and adjust for risk preferences
+```
+
+**Step 1-2**: Define decision, identify outcomes → See [resources/template.md](template.md)
+
+**Step 3**: Estimate probabilities → See [1. Probability Estimation Techniques](#1-probability-estimation-techniques)
+
+**Step 4**: Estimate payoffs → See [2. Payoff Quantification](#2-payoff-quantification)
+
+**Step 5**: Calculate EV → See [3. Decision Tree Analysis](#3-decision-tree-analysis) for sequential decisions
+
+**Step 6**: Adjust for risk → See [4. Risk Preferences and Utility](#4-risk-preferences-and-utility)
+
+---
+
+## 1. Probability Estimation Techniques
+
+### Base Rates (Outside View)
+
+**Principle**: Use historical frequency from similar situations (reference class forecasting).
+
+**Process**:
+1. **Identify reference class**: What category of events does this belong to? (e.g., "tech startup launches", "enterprise software migrations", "clinical trials for this disease")
+2. **Gather data**: How many cases in the reference class? How many succeeded vs. failed?
+3. **Calculate base rate**: p(success) = # successes / # total cases
+4. **Adjust for differences**: Is your case typical or atypical for the reference class? (Use inside view to adjust, but anchor on base rate.)
+
+**Example**: Startup success rate. Reference class = "SaaS B2B startups, 2015-2020". Data: 10,000 launches, 1,500 reached $1M ARR. Base rate = 15%. Your startup: Similar profile → start with 15%, then adjust for unique factors.
+
+**Cautions**: Reference class selection matters. Too broad (all startups) misses nuance. Too narrow (exactly like us) has no data.
+
+### Inside View (Causal Decomposition)
+
+**Principle**: Break outcome into necessary conditions, estimate probability of each, combine.
+
+**Process**:
+1. **Causal chain**: What needs to happen for this outcome? (A and B and C...)
+2. **Estimate each link**: What's p(A)? p(B|A)? p(C|A,B)?
+3. **Combine**: If independent: p(Outcome) = p(A) × p(B) × p(C). If conditional: p(Outcome) = p(A) × p(B|A) × p(C|A,B).
+
+**Example**: Product launch success requires: (1) feature ships on time (80%), (2) marketing campaign reaches target audience (70%), (3) product-market fit (50%). If independent: p(success) = 0.8 × 0.7 × 0.5 = 28%. If dependent (late ship → poor marketing → worse fit): adjust.
+
+**Cautions**: Overconfidence in ability to model all links. Conjunction fallacy (underestimate how probabilities multiply, 80% × 80% × 80% = 51%).
+
+### Expert Judgment Aggregation
+
+**Methods**:
+- **Simple average**: Mean of expert estimates. Works well if experts are independent and equally calibrated.
+- **Weighted average**: Weight experts by track record (past calibration score). More weight to well-calibrated forecasters.
+- **Median**: Robust to outliers. Use if some experts give extreme estimates.
+- **Delphi method**: Multiple rounds. Experts see others' estimates (anonymized), revise their own, converge.
+
+**Calibration scoring**: Expert says "70% confident" → are they right 70% of the time? Track record via Brier score = Σ (p_i - outcome_i)² / N. Lower = better.
+
+**Cautions**: Group-think if experts see each other's estimates before forming own. Anchoring on first estimate heard.
+
+### Data-Driven Models
+
+**Regression**: Predict outcome probability from features. Logistic regression for binary (success/fail). Linear for continuous (revenue).
+
+**Time series**: If outcome is repeating event (monthly sales, weekly sign-ups), use time series (ARIMA, exponential smoothing) to forecast.
+
+**Machine learning**: If rich data, use ML (random forest, gradient boosting, neural nets). Provides predicted probability + confidence intervals.
+
+**Backtesting**: Test model on historical data. What would model have predicted vs. actual outcomes? Calibration plot: predicted 70% → actually 70%?
+
+**Cautions**: Overfitting (model fits noise, not signal). Out-of-distribution (future may differ from past). Need enough data (small N → high variance).
+
+### Combining Methods (Triangulation)
+
+**Best practice**: Don't rely on single method. Estimate probability using 2-4 methods, compare.
+
+- If estimates converge (all ~60%) → confidence high.
+- If estimates diverge (base rate = 20%, inside view = 60%) → investigate why. Which assumptions differ? Truth likely in between.
+
+**Weighted combination**: Base rate (50% weight), Inside view (30%), Expert judgment (20%) → final estimate.
+
+**Update with new info**: Start with base rate (prior), update with inside view / expert / data (evidence) using Bayes theorem: p(A|B) = p(B|A) × p(A) / p(B).
+
+---
+
+## 2. Payoff Quantification
+
+### Monetary Valuation
+
+**Direct cash flows**: Revenue, costs, savings. Straightforward to quantify.
+
+**Opportunity cost**: What are you giving up? (Time, resources, alternative investments). Cost = value of best alternative foregone.
+
+**Option value**: Does this create future options? (Pilot project → if successful, can scale. Value of option > value of pilot alone.) Use real options analysis or decision tree.
+
+**Time value of money**: $1 today ≠ $1 next year. Discount future cash flows to present value.
+
+**NPV formula**: NPV = Σ (CF_t / (1+r)^t) where CF_t = cash flow in period t, r = discount rate (WACC, hurdle rate, or risk-free + risk premium).
+
+**Discount rate selection**:
+- Risk-free rate (US Treasury): ~3-5%
+- Corporate projects: WACC (weighted average cost of capital), typically 7-12%
+- Venture / high-risk: 20-40%
+- Personal decisions: Opportunity cost of capital (what else could you invest in?)
+
+**Inflation**: Use real cash flows (inflation-adjusted) or nominal cash flows with nominal discount rate. Don't mix.
+
+### Non-Monetary Valuation
+
+**Time**: Convert to dollars. Your hourly rate (salary / hours or freelance rate). Time saved = hours × rate. Or use opportunity cost (what else could you do with time?).
+
+**Reputation / brand**: Harder to quantify. Approaches:
+- Proxy: How much would you pay to prevent reputation damage? (e.g., PR crisis costs $X to fix → value of avoiding = $X)
+- Customer lifetime value: Better reputation → higher retention → $Y in CLV
+- Premium pricing: Strong brand → can charge Z% more → $W in extra revenue
+
+**Learning / optionality**: Value of information or skills gained. Enables future opportunities. Hard to quantify exactly, but can bound:
+- Conservative: $0 (ignore)
+- Optimistic: Value of best future opportunity enabled × probability you pursue it
+- Expected: Sum of option values across multiple future paths
+
+**Strategic**: Competitive advantage, market position. Quantify via:
+- Market share ×Average profit per point of share
+- Defensive: How much would competitor pay to block this move?
+- Offensive: How much extra profit from improved position?
+
+**Utility**: Some outcomes have intrinsic value not captured by money (autonomy, impact, meaning). Use utility functions or qualitative scoring (1-10 scale).
+
+### Handling Uncertainty in Payoffs
+
+**Point estimate**: Single number (expected case). Simple but hides uncertainty.
+
+**Range**: Optimistic / base / pessimistic (three-point estimate). Captures uncertainty. Can convert to distribution (triangular or PERT).
+
+**Distribution**: Full probability distribution over payoffs (normal, lognormal, beta). Most accurate but requires assumptions. Use Monte Carlo simulation.
+
+**Sensitivity analysis**: How much does EV change if payoff varies ±20%? Identifies which payoffs matter most.
+
+---
+
+## 3. Decision Tree Analysis
+
+### Building Decision Trees
+
+**Nodes**:
+- **Decision node** (square): You make a choice. Branches = alternatives.
+- **Chance node** (circle): Uncertain event. Branches = possible outcomes with probabilities.
+- **Terminal node** (triangle): End of path. Payoff specified.
+
+**Structure**:
+- Start at left (initial decision), move right through chance and decision nodes, end at right (payoffs).
+- Label all branches (decision choices, outcome names, probabilities).
+- Assign payoffs to terminal nodes.
+
+**Conventions**:
+- Probabilities on branches from chance nodes must sum to 1.0.
+- Decision branches have no probabilities (you control which to take).
+
+### Fold-Back Induction (Solving Trees)
+
+**Algorithm**: Work backwards from terminal nodes to find optimal strategy.
+
+1. **At terminal nodes**: Payoff given.
+2. **At chance nodes**: EV = Σ (p_i × payoff_i). Replace node with EV.
+3. **At decision nodes**: Choose branch with highest EV. Replace node with max EV, note optimal choice.
+4. **Repeat** until you reach initial decision node.
+
+**Result**: Optimal strategy (which choices to make at each decision node) and overall EV of following that strategy.
+
+**Example**:
+```
+Decision 1: [Invest $100k or Don't]
+  If Invest → Chance: [Success 60% → $300k, Fail 40% → $0]
+    EV(Invest) = 0.6 × $300k + 0.4 × $0 = $180k. Net = $180k - $100k = $80k.
+  If Don't → $0
+  Optimal: Invest (EV = $80k > $0)
+```
+
+### Value of Information
+
+**Perfect information**: If you could learn outcome of uncertain event before deciding, how much would that be worth?
+
+**EVPI** (Expected Value of Perfect Information):
+- **With perfect info**: Choose optimal decision for each outcome. EV = Σ (p_i × best_payoff_i).
+- **Without info**: EV of optimal strategy under uncertainty.
+- **EVPI** = EV(with info) - EV(without info).
+
+**Interpretation**: Maximum you'd pay to eliminate uncertainty. If actual cost of info < EVPI, worth buying (run experiment, hire consultant, do research).
+
+**Partial information**: If info is imperfect (e.g., test with 80% accuracy), use Bayes theorem to update probabilities, calculate EV with updated beliefs, subtract cost of test.
+
+### Sequential vs. Simultaneous Decisions
+
+**Sequential**: Make choice, observe outcome, make next choice. Fold-back induction finds optimal strategy. Captures optionality (can stop, pivot, wait).
+
+**Simultaneous**: Make all choices upfront, then outcomes resolve. Less flexible but sometimes unavoidable (commit to strategy before seeing results).
+
+**Design for learning**: Structure decisions sequentially when possible (pilot before full launch, Phase I/II/III trials, MVP before scale). Preserves options, reduces downside.
+
+---
+
+## 4. Risk Preferences and Utility
+
+### Risk Neutrality vs. Risk Aversion
+
+**Risk-neutral**: Only care about EV, not variance. EV($100k, 50/50) = EV($50k, certain) → indifferent.
+
+**Risk-averse**: Prefer certainty, willing to sacrifice EV to reduce variance. Prefer $50k certain over $100k gamble even though EV equal.
+
+**Risk-seeking**: Enjoy uncertainty, prefer high-variance gambles. Rare for most people/organizations.
+
+**When does risk matter?**
+- **One-shot, high-stakes**: Can't afford to lose (bet life savings, critical product launch). Risk aversion matters.
+- **Repeated, portfolio**: Many independent bets, law of large numbers. EV dominates (VCs, insurance companies, diversified portfolios).
+
+### Utility Functions
+
+**Utility** U(x): Subjective value of outcome x. For risk-averse agents, U is concave (diminishing marginal utility).
+
+**Common functions**:
+- **Linear**: U(x) = x. Risk-neutral (EU = EV).
+- **Square root**: U(x) = √x. Moderate risk aversion.
+- **Logarithmic**: U(x) = log(x). Strong risk aversion (common in economics).
+- **Exponential**: U(x) = -e^(-ax). Constant absolute risk aversion (CARA), parameter a = risk aversion coefficient.
+
+**Expected Utility**: EU = Σ (p_i × U(v_i)). Choose option with highest EU.
+
+**Certainty Equivalent** (CE): The guaranteed amount you'd accept instead of the gamble. Solve: U(CE) = EU. For risk-averse agents, CE < EV.
+
+**Risk Premium**: RP = EV - CE. How much you'd pay to eliminate risk.
+
+**Example**: Gamble: 50% $100k, 50% $0. EV = $50k.
+- If U(x) = √x, then EU = 0.5 × √100k + 0.5 × √0 = 0.5 × 316.2 = 158.1.
+- CE: √CE = 158.1 → CE = 158.1² = $25k.
+- RP = $50k - $25k = $25k. Would pay up to $25k to avoid gamble, take guaranteed $50k instead.
+
+### Calibrating Your Utility Function
+
+**Questions to reveal risk aversion**:
+1. "Gamble: 50% $100k, 50% $0 vs. Certain $40k. Which?" → If prefer certain $40k, you're risk-averse (CE < $50k).
+2. "Gamble: 50% $200k, 50% $0 vs. Certain $X. At what X are you indifferent?" → X = CE for this gamble.
+3. Repeat for several gambles, fit utility curve to your choices.
+
+**Organization risk tolerance**: Depends on reserves, ability to absorb loss, stakeholder expectations (public company vs. startup founder). Quantify via "How much can we afford to lose?" and "What's minimum acceptable return?"
+
+### Non-Linear Utility (Prospect Theory)
+
+**Observations** (Kahneman & Tversky):
+- **Loss aversion**: Losses hurt more than equivalent gains feel good. U(loss) < -U(gain) in absolute terms. Ratio ~2:1 (losing $100 feels 2× worse than gaining $100).
+- **Reference dependence**: Utility depends on change from reference point (status quo), not absolute wealth.
+- **Probability weighting**: Overweight small probabilities (1% feels > 1%), underweight large probabilities (99% feels < 99%).
+
+**Implications**: People are risk-averse for gains, risk-seeking for losses (gamble to avoid sure loss). Framing matters (80% success vs. 20% failure).
+
+**Practical**: If stakeholders are loss-averse, emphasize downside protection (hedges, insurance, diversification) even if it reduces EV.
+
+---
+
+## 5. Common Biases and Pitfalls
+
+### Overconfidence
+
+**Problem**: Estimated probabilities too extreme (80% when should be 60%). Underestimate uncertainty.
+
+**Detection**: Track calibration. Are your "70% confident" predictions right 70% of the time? Most people are overconfident (right 60% when say 70%).
+
+**Fix**: Widen probability ranges. Use reference classes (base rates). Ask "How often am I this confident and wrong?"
+
+### Anchoring
+
+**Problem**: First number you hear (or think of) biases estimate. Adjust insufficiently from anchor.
+
+**Example**: "Is revenue > $500k?" → even if you say no, your estimate will be anchored near $500k.
+
+**Fix**: Generate estimate independently before seeing anchors. Use multiple methods to triangulate (outside view, inside view, experts).
+
+### Availability Bias
+
+**Problem**: Overweight recent or vivid events. "Startup X just failed, so all startups fail" (ignoring base rate of thousands of startups).
+
+**Fix**: Use data / base rates, not anecdotes. Ask "How representative is this example?"
+
+### Sunk Cost Fallacy
+
+**Problem**: Include past costs in forward-looking EV. "We've already spent $1M, can't stop now!"
+
+**Fix**: Sunk costs are sunk. Only future costs/benefits matter. EV = future payoff - future cost. Ignore past.
+
+### Neglecting Tail Risk
+
+**Problem**: Round low-probability, high-impact events to zero. "0.1% chance of -$10M? I'll call it 0%."
+
+**Fix**: Don't ignore tail risk. 0.1% × -$10M = -$10k in EV (material). Sensitivity: What if probability is 1%?
+
+### False Precision
+
+**Problem**: "Probability = 67.3%, payoff = $187,432.17" when you're guessing.
+
+**Fix**: Express uncertainty. Use ranges (55-75%, $150k-$200k). Don't pretend more precision than you have.
+
+### Static Analysis (Ignoring Optionality)
+
+**Problem**: Assume you make all decisions upfront, can't update or pivot. Misses value of learning.
+
+**Fix**: Use decision trees for sequential decisions. Model optionality (stop early, wait for info, pivot). Often shifts optimal strategy.
+
+---
+
+## 6. Advanced Topics
+
+### Correlation and Diversification
+
+**Independent outcomes**: If portfolio of uncorrelated bets, variance decreases with N (Var_portfolio = Var_single / N). Diversification works.
+
+**Correlated outcomes**: If outcomes move together (economic downturn hurts all investments), correlation reduces diversification benefit. Model dependencies (correlation coefficient, copulas).
+
+**Portfolio EV**: Sum of individual EVs (always true). Portfolio variance: More complex, depends on correlations.
+
+### Monte Carlo Simulation
+
+**When to use**: Continuous distributions, many uncertain variables, complex interactions.
+
+**Process**:
+1. Define distributions for each uncertain variable (normal, lognormal, beta, etc.).
+2. Sample randomly from each distribution (draw one value per variable).
+3. Calculate outcome (payoff) for that sample.
+4. Repeat 10,000+ times.
+5. Analyze results: Mean = EV, percentiles = confidence intervals (5th-95th), plot histogram.
+
+**Pros**: Captures full uncertainty, no need for discrete scenarios, provides distribution of outcomes.
+
+**Cons**: Requires distributional assumptions (which may be wrong), computationally intensive, harder to communicate.
+
+**Tools**: Excel (@RISK, Crystal Ball), Python (NumPy, SciPy), R (mc2d).
+
+### Multi-Attribute Utility
+
+**When**: Multiple objectives (profit, risk, strategic value, ethics) that can't all be converted to dollars.
+
+**Approaches**:
+- **Weighted scoring**: Score each option on each attribute (1-10), multiply by weight, sum. Choose highest total.
+- **Utility surface**: Define utility over multiple dimensions U(x, y, z) where x=profit, y=risk, z=strategy.
+- **Pareto frontier**: Identify non-dominated options (no option strictly better on all dimensions). Choose from frontier based on preferences.
+
+**Example**: Investment A (high profit, high risk, low strategic value), Investment B (medium profit, medium risk, high strategic value). Can't say one is objectively better. Depends on weights.
+
+### Game Theory (Strategic Interactions)
+
+**When**: Outcome depends on competitor's choice (pricing, product launch, negotiation).
+
+**Payoff matrix**: Rows = your choices, columns = competitor's choices, cells = your payoff given both choices.
+
+**Nash equilibrium**: Strategy pair where neither player wants to deviate given other's strategy. May not maximize joint value.
+
+**Expected value in games**: Estimate opponent's probabilities (mixed strategy or beliefs about their choice), calculate EV for each of your strategies, choose best response.
+
+**Cautions**: Assumes rational opponent. Real opponents may be irrational, vindictive, or making mistakes. Model their actual behavior, not ideal.
+
+---
+
+## Summary
+
+**Probability estimation**: Use multiple methods (base rates, inside view, experts, data), triangulate. Avoid overconfidence, anchoring, availability bias.
+
+**Payoff quantification**: Include monetary (revenue, costs, NPV) and non-monetary (time, reputation, learning, strategic). Handle uncertainty with ranges or distributions.
+
+**Decision trees**: Fold-back induction for sequential decisions. Calculate EVPI for value of information. Structure for learning (sequential > simultaneous).
+
+**Risk preferences**: Risk-neutral → maximize EV. Risk-averse → maximize expected utility (EU). Calibrate utility function via elicitation. Account for loss aversion (Prospect Theory).
+
+**Biases**: Overconfidence, anchoring, availability, sunk cost, tail risk neglect, false precision, static analysis. Mitigate via calibration, base rates, ranges, optionality.
+
+**Advanced**: Correlation in portfolios, Monte Carlo for continuous distributions, multi-attribute utility for multiple objectives, game theory for strategic interactions.
+
+**Final principle**: EV analysis structures thinking, not mechanizes decisions. Probabilities and payoffs are estimates. Sensitivity analysis reveals robustness. Combine quantitative EV with qualitative judgment (strategic fit, alignment with values, regret minimization).
--- a/skills/expected-value/resources/template.md
+++ b/skills/expected-value/resources/template.md
@@ -0,0 +1,338 @@
+# Expected Value Templates
+
+Quick-start templates for decision framing, outcome identification, probability estimation, payoff quantification, EV calculation, and sensitivity analysis.
+
+## Workflow
+
+```
+Expected Value Analysis Progress:
+- [ ] Step 1: Define decision and alternatives
+- [ ] Step 2: Identify possible outcomes
+- [ ] Step 3: Estimate probabilities
+- [ ] Step 4: Estimate payoffs (values)
+- [ ] Step 5: Calculate expected values
+- [ ] Step 6: Interpret and adjust for risk preferences
+```
+
+**Step 1: Define decision and alternatives** → Use [Decision Framing Template](#decision-framing-template)
+
+**Step 2: Identify possible outcomes** → Use [Outcome Identification Template](#outcome-identification-template)
+
+**Step 3: Estimate probabilities** → Use [Probability Estimation Template](#probability-estimation-template)
+
+**Step 4: Estimate payoffs** → Use [Payoff Quantification Template](#payoff-quantification-template)
+
+**Step 5: Calculate expected values** → Use [EV Calculation Template](#ev-calculation-template)
+
+**Step 6: Interpret and adjust for risk** → Use [Risk Adjustment Template](#risk-adjustment-template) and [Sensitivity Analysis Template](#sensitivity-analysis-template)
+
+---
+
+## Decision Framing Template
+
+**Decision to be made**: [Clear statement of the choice]
+
+**Context**: [Why are you making this decision? What's the deadline? What constraints exist?]
+
+**Alternatives** (mutually exclusive options):
+1. **[Alternative 1]**: [Brief description]
+2. **[Alternative 2]**: [Brief description]
+3. **[Alternative 3]**: [Brief description, if applicable]
+4. **Do nothing / status quo**: [Always consider baseline]
+
+**Success criteria**: [How will you know if this was a good decision? What are you optimizing for?]
+
+**Assumptions**:
+- [Key assumption 1]
+- [Key assumption 2]
+- [Key assumption 3]
+
+**Out of scope** (not considering):
+- [Factor 1 you're explicitly not modeling]
+- [Factor 2]
+
+---
+
+## Outcome Identification Template
+
+For each alternative, identify 3-5 possible outcomes (scenarios).
+
+### Alternative: [Name]
+
+**Outcome 1: Best case**
+- **Description**: [What happens in optimistic scenario?]
+- **Key drivers**: [What needs to go right?]
+- **Likelihood indicator**: [Rough sense: common, uncommon, rare?]
+
+**Outcome 2: Base case**
+- **Description**: [What happens in most likely scenario?]
+- **Key drivers**: [What's the typical path?]
+- **Likelihood indicator**: [Should be most probable]
+
+**Outcome 3: Worst case**
+- **Description**: [What happens in pessimistic scenario?]
+- **Key drivers**: [What needs to go wrong?]
+- **Likelihood indicator**: [How bad could it get?]
+
+**Outcome 4: [Other scenario, if needed]**
+- **Description**:
+- **Key drivers**:
+- **Likelihood indicator**:
+
+**Check**: Do these outcomes cover the full range of possibilities? Are they mutually exclusive (no overlap)?
+
+---
+
+## Probability Estimation Template
+
+Estimate probability for each outcome using multiple methods, then reconcile.
+
+### Outcome: [Name]
+
+| Method | Estimate | Notes |
+|--------|----------|-------|
+| **Base rates** (reference class) | [X%] | [Similar situations: N cases, frequency] |
+| **Inside view** (causal model) | [Y%] | [Key factors: p_A × p_B × p_C] |
+| **Expert judgment** | [Z%] | [Average of expert estimates] |
+| **Data/model** | [W%] | [Forecast, confidence interval] |
+
+**Final estimate**: [Weighted average] **Confidence**: [Range if uncertain]
+
+**All outcomes** (must sum to 1.0):
+- Outcome 1: [p₁], Outcome 2: [p₂], Outcome 3: [p₃]. **Total**: [p₁+p₂+p₃ = 1.0 ✓]
+
+---
+
+## Payoff Quantification Template
+
+### Outcome: [Name]
+
+**Monetary**: Revenue [+$X], Cost [-$Y], Savings [+$Z], Opp. cost [-$W]. **Net**: [Sum]
+
+**Non-monetary** (convert to $ or utility): Time [X hrs × $rate], Reputation [$Z], Learning [$W], Strategic [qualitative or $], Morale [qualitative or $]
+
+**Time horizon**: [When?] **Discount rate**: [r%/yr if multi-period]
+
+**NPV** (if multi-period): Yr0 [$X/(1+r)⁰], Yr1 [$Y/(1+r)¹], Yr2 [$Z/(1+r)²]. **Total NPV**: [Sum]
+
+**Total Payoff**: [$ or utility] **Uncertainty**: [Point estimate or range: low-high]
+
+---
+
+## EV Calculation Template
+
+Calculate expected value for each alternative.
+
+### Alternative: [Name]
+
+| Outcome | Probability (p) | Payoff (v) | p × v |
+|---------|----------------|-----------|-------|
+| [Outcome 1] | [p₁] | [v₁] | [p₁ × v₁] |
+| [Outcome 2] | [p₂] | [v₂] | [p₂ × v₂] |
+| [Outcome 3] | [p₃] | [v₃] | [p₃ × v₃] |
+| **Total** | **1.0** | | **EV = Σ (p × v)** |
+
+**Expected Value**: [EV = p₁×v₁ + p₂×v₂ + p₃×v₃]
+
+**Variance**: Var = Σ (pᵢ × (vᵢ - EV)²)
+- (v₁ - EV)² × p₁ = [X]
+- (v₂ - EV)² × p₂ = [Y]
+- (v₃ - EV)² × p₃ = [Z]
+- **Variance** = [X + Y + Z]
+
+**Standard Deviation**: σ = √Var = [σ]
+
+**Coefficient of Variation**: CV = σ / EV = [CV] (lower = better risk-adjusted return)
+
+### Comparison Across Alternatives
+
+| Alternative | EV | σ (risk) | CV | Rank by EV |
+|-------------|-------|----------|-----|------------|
+| [Alt 1] | [EV₁] | [σ₁] | [CV₁] | [1] |
+| [Alt 2] | [EV₂] | [σ₂] | [CV₂] | [2] |
+| [Alt 3] | [EV₃] | [σ₃] | [CV₃] | [3] |
+
+**Preliminary recommendation** (based on EV): [Highest EV alternative]
+
+---
+
+## Sensitivity Analysis Template
+
+Test how sensitive the decision is to changes in key assumptions.
+
+### One-Way Sensitivity (vary one variable at a time)
+
+**Variable**: Probability of [Outcome X]
+
+| p(Outcome X) | EV(Alt 1) | EV(Alt 2) | Best choice |
+|-------------|-----------|-----------|-------------|
+| [Low: p-20%] | [EV] | [EV] | [Alt] |
+| [Base: p] | [EV] | [EV] | [Alt] |
+| [High: p+20%] | [EV] | [EV] | [Alt] |
+
+**Breakeven**: At what probability does decision flip? Solve: EV(Alt 1) = EV(Alt 2).
+
+**Variable**: Payoff of [Outcome Y]
+
+| v(Outcome Y) | EV(Alt 1) | EV(Alt 2) | Best choice |
+|-------------|-----------|-----------|-------------|
+| [Low: v-30%] | [EV] | [EV] | [Alt] |
+| [Base: v] | [EV] | [EV] | [Alt] |
+| [High: v+30%] | [EV] | [EV] | [Alt] |
+
+### Tornado Diagram (which variables have most impact on EV?)
+
+| Variable | Range tested | Impact on EV (swing) | Rank |
+|----------|-------------|---------------------|------|
+| [Var 1] | [low-high] | [±$X] | [1 (highest impact)] |
+| [Var 2] | [low-high] | [±$Y] | [2] |
+| [Var 3] | [low-high] | [±$Z] | [3] |
+
+**Interpretation**: Focus on high-impact variables. Get better estimates for top 2-3.
+
+### Scenario Analysis (vary multiple variables together)
+
+| Scenario | Assumptions | EV(Alt 1) | EV(Alt 2) | Best |
+|----------|------------|-----------|-----------|------|
+| **Optimistic** | [High demand, low cost, no delays] | [EV] | [EV] | [Alt] |
+| **Base** | [Expected values] | [EV] | [EV] | [Alt] |
+| **Pessimistic** | [Low demand, high cost, delays] | [EV] | [EV] | [Alt] |
+
+**Robustness**: Does the decision hold across scenarios? If different winners in different scenarios → decision is fragile, more info needed.
+
+---
+
+## Risk Adjustment Template
+
+**Risk profile**: Risk-neutral / Risk-averse / Risk-seeking? One-shot or repeated decision?
+
+**Utility function** (if risk-averse): U(x) = x (neutral), √x (moderate aversion), log(x) (strong aversion)
+
+### Expected Utility (if risk-averse)
+
+| Outcome | p | v | U(v) | p × U(v) |
+|---------|---|---|------|----------|
+| [Out 1] | [p₁] | [v₁] | [U(v₁)] | [p₁ × U(v₁)] |
+| [Out 2] | [p₂] | [v₂] | [U(v₂)] | [p₂ × U(v₂)] |
+| **Total** | **1.0** | | | **EU = Σ** |
+
+**Certainty Equivalent**: CE = U⁻¹(EU). **Risk Premium**: EV - CE.
+
+**Non-monetary factors**: Strategic value [$/qualitative], Alignment with mission [score 1-5], Regret [low/med/high]
+
+**Recommendation**: Highest EV [Alt X], Highest EU [Alt Y], **Final choice**: [Alt Z with rationale]
+
+---
+
+## Decision Tree Template
+
+For sequential decisions (make choice, observe outcome, make another choice).
+
+### Tree Structure
+
+```
+[Decision 1] → [Outcome A] → [Decision 2a] → [Outcome C]
+                                           → [Outcome D]
+             → [Outcome B] → [Decision 2b] → [Outcome E]
+                                           → [Outcome F]
+```
+
+### Fold-Back Induction (work backwards from end)
+
+**Step 1: Calculate EV at terminal nodes** (final outcomes)
+- Outcome C: [payoff = $X]
+- Outcome D: [payoff = $Y]
+- Outcome E: [payoff = $Z]
+- Outcome F: [payoff = $W]
+
+**Step 2: Calculate EV at Decision 2a**
+- If choose path to C: [p(C) × $X]
+- If choose path to D: [p(D) × $Y]
+- **Optimal Decision 2a**: [Choose whichever has higher EV]
+- **EV(Decision 2a)**: [max of the two]
+
+**Step 3: Calculate EV at Decision 2b**
+- If choose path to E: [p(E) × $Z]
+- If choose path to F: [p(F) × $W]
+- **Optimal Decision 2b**: [Choose whichever has higher EV]
+- **EV(Decision 2b)**: [max of the two]
+
+**Step 4: Calculate EV at Decision 1**
+- If choose path to A: [p(A) × EV(Decision 2a)]
+- If choose path to B: [p(B) × EV(Decision 2b)]
+- **Optimal Decision 1**: [Choose whichever has higher EV]
+- **Overall EV**: [max of the two]
+
+**Optimal Strategy**:
+1. At Decision 1: [Choose A or B]
+2. If A occurs, at Decision 2a: [Choose path to C or D]
+3. If B occurs, at Decision 2b: [Choose path to E or F]
+
+**Value of Information**: If you could know outcome before Decision 1, how much would that be worth?
+- EVPI = EV(with perfect info) - EV(current decision)
+
+---
+
+## Complete EV Analysis Template
+
+**Decision**: [Name]
+
+**Date**: [Date]
+
+**Decision maker**: [Name/Team]
+
+### 1. Decision Framing
+
+**Alternatives**:
+1. [Alt 1]
+2. [Alt 2]
+3. [Alt 3]
+
+**Success criteria**: [What are you optimizing for?]
+
+### 2. Outcomes and Probabilities
+
+| Alternative | Outcome | Probability | Payoff | p × v |
+|-------------|---------|------------|--------|-------|
+| **[Alt 1]** | [Outcome 1] | [p₁] | [v₁] | [p₁ × v₁] |
+|  | [Outcome 2] | [p₂] | [v₂] | [p₂ × v₂] |
+|  | [Outcome 3] | [p₃] | [v₃] | [p₃ × v₃] |
+|  | **EV(Alt 1)** | | | **[EV₁]** |
+| **[Alt 2]** | [Outcome 1] | [p₁] | [v₁] | [p₁ × v₁] |
+|  | [Outcome 2] | [p₂] | [v₂] | [p₂ × v₂] |
+|  | [Outcome 3] | [p₃] | [v₃] | [p₃ × v₃] |
+|  | **EV(Alt 2)** | | | **[EV₂]** |
+
+### 3. Comparison
+
+| Alternative | EV | σ (risk) | CV |
+|-------------|-------|----------|-----|
+| [Alt 1] | [EV₁] | [σ₁] | [CV₁] |
+| [Alt 2] | [EV₂] | [σ₂] | [CV₂] |
+
+**Highest EV**: [Alt X with EV = $Y]
+
+### 4. Sensitivity Analysis
+
+**Key assumptions**:
+- [Assumption 1]: [If this changes by X%, decision flips? Yes/No]
+- [Assumption 2]: [Breakeven value = ?]
+
+**Robustness**: [Is decision robust across scenarios?]
+
+### 5. Risk Adjustment
+
+**Risk profile**: [One-shot or repeated? Risk-averse or neutral?]
+
+**Recommendation**: [Alt X]
+
+**Rationale**: [Why this choice given EV, risk, strategic factors?]
+
+### 6. Action Plan
+
+**Next steps**:
+1. [Immediate action]
+2. [Follow-up in X days/weeks]
+3. [Decision review date]
+
+**Contingencies**: [If Outcome Y occurs, we will...]