S4h Probability Expected Value Calculation

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

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