── ── Startups
Expected Value and the Kelly Criterion
Two questions decide most repeated bets: is this bet good (expected value), and how big should it be (Kelly)? EV = p·W − q·L; if EV ≤ 0, don't bet. The Kelly criterion f* = (bp − q)/b sizes the bet to maximize long-run compound growth. Most professional ruin comes not from bad bets but from positive-EV bets sized too large.
Run Expected Value and the Kelly Criterion on a real problem
Bring something you're actually deciding — free, in the browser.
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
Bill Benter and Computer-Model Horse Betting in Hong Kong (1985 → 2001)
A worked example in a domain far from a card table: pari-mutuel horse racing, where the odds are set by the crowd's own money and your bet moves the payout against you. Primary-source documented in Benter's own 1994 technical paper.
Install this skill (free, MIT)
npx skills add deciqAI/knowledge-skillsUseful? Star the repo — stars help other builders find it.
FAQ
What is the Kelly criterion in plain terms?
A formula for how much of your bankroll to stake on a favorable bet: f* = (bp − q)/b, where b is the payout odds, p the win probability, and q = 1 − p. It maximizes long-term compound growth — bet more than Kelly and volatility destroys you even with the odds in your favor.
Why do positive expected-value bets still ruin people?
Because EV describes the average across parallel universes while you live one sequential path. Oversized bets create drawdowns you can't recover from — a 50% loss needs a 100% gain to break even. Sizing, not selection, is where most professional gamblers and traders die.
Why use fractional Kelly instead of full Kelly?
Full Kelly assumes you know p and b exactly — casino conditions. In business and markets your probabilities are estimates, and overestimating p makes full Kelly systematically overbet. Half-Kelly gives up about a quarter of the growth rate for roughly half the volatility, a trade practitioners almost always take.
Related mental models
A system has a feedback loop when its output circles back as input to the next cycle.
Before product-market fit, the founder must run sales personally — not because it scales, but because it's the fastest, highest-fidelity discovery loop and the only way…
Herzberg's 1959 Pittsburgh study found satisfaction and dissatisfaction are two independent axes.
The most common strategic error is applying the wrong growth mode to a goal.