── ── Startups
Expected Value and the Kelly Criterion
Two questions decide most repeated bets: is this bet good? (EV) and how big? (Kelly). Most professional ruin comes from positive-EV bets sized wrong. EV = p · W − q · L. If EV ≤ 0, do not bet. Kelly f\ = (bp − q) / b** maximizes long-term geometric growth (Kelly, Bell Labs, 1956). Full Kelly requires casino-grade…
How it works
Run the EV-Kelly Sizing (EV → Kelly → fractional Kelly → stop trigger):
1. Confirm the decision is repeated. If "once," stop → use regret-minimization. 2. Map the bet. Win prob p, loss prob q = 1−p, payoff on win W, loss L, odds b = W/L. 3. Compute EV. EV = Σ(pᵢ · payoffᵢ). State per unit staked. 4. Edge gate. EV > 0? If no, stop — do not bet. 5. Estimate input uncertainty. Are p and W measured or estimated? Write 80% CI on edge. 6. Compute Kelly fraction. f\ = (bp − q) / b. For continuous: f\ ≈ μ/σ². 7. Apply fractional Kelly. Half-Kelly under modest uncertainty; quarter-Kelly under serious uncertainty. 8. Set stop trigger. "I will re-estimate if: (a) drawdown > X%, (b) outcomes diverge N σ over Y trials, (c) regime change invalidates edge model."
When to use it
- user asks 'how much should I bet/invest on this?', 'what's the expected value here?', 'Kelly criterion', 'optimal bet size', 'fractional Kelly', 'how big a position should I take?', or is allocating capital across repeated decisions (ad spend by segment, VC portfolio construction, position sizing, A/B test ramp)
When not to use it
When the decision is routine and reversible, applying a formal method costs more than it returns.
Worked example
Ed Thorp, Blackjack, and Princeton-Newport (1961 → 1988)
A worked example. Not a casino fable — primary-source documented, including the Bell Labs origin.
Install this skill (free, MIT)
npx skills add deciqAI/knowledge-skills