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name: s4h-probability description: "Entry point for the probability toolkit. Routes to the right probabilistic thinking skill based on your situation. Use when you say 'probability', 'how likely', 'am I overconfident', 'quantify this', 'what's the base rate', 'expected value', 'scenario weighting', or want probabilistic reasoning applied without knowing which specific tool fits."

Probability

Applies probabilistic thinking to estimates, decisions, and uncertainty. Diagnoses what kind of probability work is needed and applies the right tool.

Which tool fits

You need to...	Tool
Anchor estimates in historical base rates before adjusting	base-rate-anchoring
Test whether stated confidence matches available evidence	confidence-calibration
Calculate expected value to compare options under uncertainty	expected-value-calculation
Assign probabilities to distinct scenarios before deciding	scenario-weighting

Routing Decision

• Estimate feels optimistic — want the outside view → base-rate-anchoring
• Unsure how confident to be, or whether confidence is warranted → confidence-calibration
• Comparing options with different payoffs and probabilities → expected-value-calculation
• Multiple plausible futures and need to think through each → scenario-weighting
• Unclear → confidence-calibration; establishing what confidence is warranted usually determines what other analysis is needed

Framing check: Confirm the specific situation and the type of uncertainty being reasoned about before routing. State what you've identified — the actual subject being estimated or decided, and the core uncertainty — in one sentence, then use AskUserQuestion:

• Question: "I'm reading this as: [your one-sentence framing of the situation and the uncertainty at stake]. 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

Confirm Direction

After diagnosing which tool fits, use the AskUserQuestion tool to confirm direction. Construct the question dynamically to include your diagnosis:

• Question: "My read: [diagnosed tool] — [one sentence on why it fits]. How would you like to proceed?"
• Header: "Direction"
• Options:
  • Yes, run that tool — Execute the diagnosed skill immediately using the context already provided
  • Show all options — List every skill in this category with one-line descriptions
  • Quick version — Run a lighter-weight alternative if one exists for this situation
  • Re-diagnose — Revisit the situation description for a different read

Proceed based on their selection.

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Base Rate Anchoring

Anchors estimates in historical base rates before adjusting for specifics.

Before adjusting for what makes this situation special, establish what usually happens in situations like this one. Find the reference class: what category of event is this? What is the historical base rate for that category? Now adjust: what specific factors make this situation better or worse than the reference class? The adjustment should be modest unless the specific factors are genuinely exceptional; most people underweight the base rate and overweight the specifics.

Output: Reference class identified, base rate established, specific adjustments with justification, and the final calibrated estimate.

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Confidence Calibration

Tests whether stated confidence levels match available evidence.

State the current confidence level. Now audit it: what is the evidence for this belief? How strong is that evidence? What evidence against have you considered? Are you more confident than the evidence warrants (overconfidence — common) or less confident than it warrants (underconfidence — less common but real)? Good calibration means your 80% confident predictions come true about 80% of the time.

Output: Confidence audit — evidence for, evidence against, sources of overconfidence, and a recalibrated confidence level with reasoning.

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Expected Value Calculation

Calculates expected value to compare options under uncertainty.

For each option: list possible outcomes and their probabilities. Estimate the value (positive or negative) of each outcome. Calculate expected value: sum(probability × value) for each outcome. Compare across options. Identify if any option has asymmetric risk — limited downside, large upside — which expected value captures but intuition often misses.

Output: Expected value calculation for each option, comparison table, and interpretation of the asymmetry or risk profile.

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Scenario Weighting

Assigns explicit probabilities to distinct scenarios before making a decision.

Define 3-5 mutually exclusive, collectively exhaustive scenarios for how this situation could unfold. For each scenario: what are the key conditions that make it happen? Assign a probability to each (they must sum to 100%). For each scenario: what decision is optimal? Now aggregate: given the scenario probabilities, what is the best overall decision?

Output: Scenario inventory with probabilities, optimal decision per scenario, and the overall recommendation weighted by scenario probabilities.