| name | s4h-probability-expected-value-calculation |
| description | Calculates expected value to compare options under uncertainty. Use when asked about 'expected value', 'is this risk worth taking', 'EV calculation', 'compare these options', 'worth the risk', or 'asymmetric risk'. |
Probability Expected Value Calculation
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.
Your Process
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:
- Question: "I'm reading this as: [your one-sentence framing of the decision, its options, and what success/failure looks like]. Is that right?"
- Header: "Framing"
- Options:
- Yes — proceed — framing is correct
- Adjust — one element is off; user will correct it before you continue
- Reframe — different situation than read; incorporate the correction before proceeding
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.
Human Check-in
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:
- Question: "My read: [your 1–2 sentence interpretation]. How do you want to proceed?"
- Header: "Scope"
- Options:
- Full analysis — Complete all steps, reasoning shown throughout
- Key findings only — Bottom-line output, skip step-by-step detail
- EV comparison table only — Final expected values per option, skip the step-by-step breakdown
- Reframe — The read is off; correct it and the analysis will follow the corrected framing
Proceed based on their selection. If the user reframes, incorporate the correction before running any analysis.
Output Format
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]
Notes
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.
What's Next
After delivering this output, use AskUserQuestion to offer the next move:
- Question: "Expected values calculated. What's next?"
- Header: "Next"
- Options:
/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 option- Done — Wrap up and synthesise what we have so far
