Kelly Criterion Calculator

How the Kelly criterion works

John Kelly Jr. derived the formula at Bell Labs in 1956 to maximize the long-term geometric growth rate of capital under repeated favorable bets. Edward Thorp later applied it to blackjack and to portfolio management. The intuition: if you bet too small, you grow slowly; if you bet too big, occasional losses compound and your bankroll goes to zero. There is a unique fraction in between that maximizes long-run growth — that fraction is Kelly.

The formula in plain English

For a discrete bet with two outcomes, f* = p − (1 − p) / b. Here p is your probability of winning, and b is the ratio of average win to average loss. The expression p − (1 − p) / b is your edge per dollar risked, expressed as a fraction.

Concrete example: if you win 55% of the time, with average wins of $150 and average losses of $100, then p = 0.55, b = 1.5, and f* = 0.55 − 0.45 / 1.5 = 0.55 − 0.30 = 0.25. Full Kelly says bet 25% of your bankroll on this opportunity. Half Kelly says 12.5%; quarter Kelly says 6.25%.

Why most professionals use a fraction of Kelly

The full Kelly formula assumes you know your edge exactly. In practice, you estimate it from a sample of past trades, and the estimate is noisy. Overestimating your edge by 20% can cause severe overbetting that destroys the long-run advantage. Half-Kelly captures about 75% of the long-term growth rate with substantially lower volatility and a much lower probability of large drawdowns. Quarter-Kelly is even more conservative — about 50% of full- Kelly growth with a much smoother equity curve. Almost no one runs full Kelly in real money management for this reason.

When Kelly does NOT apply

• Single-shot decisions. Kelly maximizes long-term growth across many bets. For a one-time decision, the right answer depends on your utility function, not on Kelly.
• Multiple correlated bets. Single-bet Kelly assumes one bet at a time. If you have multiple positions running simultaneously, you should size each smaller — divide by the number of independent bets, more if they are correlated.
• Continuous returns. For a strategy that produces a continuous return stream (not discrete win/loss outcomes), use the continuous-Kelly formula: f* = mean(returns) / variance(returns). The QuantOracle API supports this via mode=continuous.
• Non-stationary edge. If your edge changes over time (markets adapt, strategies decay), the static Kelly fraction is wrong. Re-estimate often, and use a smaller fraction than the textbook formula suggests.