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From skills-for-humanity
Calculates expected value to compare options under uncertainty. Guides through framing, outcome listing, value assignment, and catastrophic downside checks.
How this skill is triggered — by the user, by Claude, or both
Slash command
/skills-for-humanity:s4h-probability-expected-value-calculationThe summary Claude sees in its skill listing — used to decide when to auto-load this skill
Expected value is the correct framework for comparing options under uncertainty. It multiplies each outcome's value by its probability and sums across all outcomes, producing a single number that accounts for the full distribution rather than just the most likely case. EV analysis forces explicitness about both probabilities and values — and it exposes asymmetric risk that intuition misses. One...
Expected value is the correct framework for comparing options under uncertainty. It multiplies each outcome's value by its probability and sums across all outcomes, producing a single number that accounts for the full distribution rather than just the most likely case. EV analysis forces explicitness about both probabilities and values — and it exposes asymmetric risk that intuition misses. One important constraint: EV math is overridden when any outcome is catastrophic enough to be unacceptable regardless of probability.
Step 1: Define the Options List the options being compared. Include "do nothing" or "wait" as explicit options — they have EVs too.
Framing check: Confirm the specific decision and its options before continuing. State what you've identified — the actual choice being evaluated, the options in play, and the unit of value — in one sentence, then use AskUserQuestion:
Step 2: List Outcomes for Each Option For each option: what are the possible outcomes? Use scenario-weighting to assign probabilities if this has not already been done. Outcomes must be mutually exclusive and exhaustive per option.
Step 3: Assign Values Assign a value to each outcome in a consistent unit (revenue, cost savings, time, abstract utility). The same unit must apply across all options for comparison to be valid. Negative values for bad outcomes.
Step 4: Calculate EV For each option: EV = sum of (probability × value) across all outcomes. Show the calculation.
Step 5: Compare EVs Identify the highest-EV option. Note whether any option has higher EV but worse downside — this is the asymmetric risk check.
Step 6: Check for Catastrophic Downside Is any outcome bad enough that it would be unacceptable regardless of its probability and regardless of EV? Ruin, existential harm, irreversible loss. If yes: that outcome overrides the EV comparison. Flag it explicitly.
Before proceeding, use the AskUserQuestion tool. State your interpretation of the situation in 1–2 sentences — what is being analyzed and what the core question is — then ask:
Proceed based on their selection. If the user reframes, incorporate the correction before running any analysis.
EV Table
| Option | Outcome | Probability | Value | P × V |
|---|---|---|---|---|
| Option A | Outcome 1 | |||
| Outcome 2 | ||||
| EV | = | |||
| Option B | Outcome 1 | |||
| EV | = |
Recommended Option: [highest EV + rationale]
Catastrophic Downside Flag: [Y/N — if yes: which outcome, why it overrides EV, revised recommendation]
Asymmetric Risk Note: [if any option has high upside but fat downside tail that EV smooths over]
EV assumes outcomes are fungible and the decision will be made many times — neither is always true. For one-shot decisions with irreversible outcomes, weight catastrophic downside beyond what probability × value captures.
After delivering this output, use AskUserQuestion to offer the next move:
/s4h-decision-criteria-weighting — Use expected values in the decision matrix/s4h-resource-allocation-analysis — Allocate resources proportional to expected value/s4h-decision-premortem-analysis — Stress-test the highest-EV optionnpx claudepluginhub human-avatar/skills-for-humanityCalculates probability-weighted averages of outcomes for rational decision-making under uncertainty. Covers scenario identification, probability estimation, payoff quantification, and risk-adjusted interpretation.
Routes probabilistic thinking to the right skill: base-rate anchoring, confidence calibration, expected value, or scenario weighting. Activates on queries about probability, likelihood, and uncertainty.
Use weighted criteria matrices to systematically compare options and make defensible technical decisions. Use when evaluating competing approaches or vendors.