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Kelly Criterion calculator

Optimal bet size given win probability, payoff, and bankroll.

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About this calculator

The Kelly Criterion is the mathematically optimal bet size for maximizing long-term geometric growth given a known edge. It was developed by John Kelly Jr. at Bell Labs in 1956 for signal processing and adopted by gamblers, traders, and quants. Used correctly, it maximizes wealth over time. Used carelessly, it leads to massive drawdowns.

The formula

For a single bet: f* = (bp − q) / b, where b is the net odds (win:loss ratio), p is win probability, and q = 1 − p. So with a 55% win rate at 1:1 odds: f* = (1·0.55 − 0.45) / 1 = 10% of bankroll per bet.

Why most pros run fractional Kelly

Full Kelly maximizes long-term growth but creates wild swings — typical drawdowns of 50%+ are mathematically inevitable. Half-Kelly cuts those drawdowns to about 20% while retaining most of the long-term growth. Quarter-Kelly is even safer. Most successful traders run somewhere between 0.25× and 0.5× Kelly because the geometric-growth tradeoff is steep at full Kelly and the inputs (true win rate and odds) are always estimated.

When Kelly breaks

  • Bad inputs — if your "55% win rate" is actually 50%, Kelly tells you to bet zero. If it's 40%, you must not bet. Estimation error is the biggest risk.
  • Correlated bets — Kelly assumes independent outcomes. Betting 20% on each of 5 correlated stocks ≠ betting 20% on one diversified position.
  • Ruin via repeated full-Kelly — even with true positive edge, a bad streak can cripple a full-Kelly account permanently.

Practical use

Sports bettors and poker players use Kelly explicitly. Quant funds use Kelly-derived position sizing inside risk frameworks. Retail traders almost never have well-calibrated edge estimates — the lesson is to size positions much smaller than gut feel says, and to be brutally honest about whether you actually have edge.

Frequently asked questions

What if my edge is negative?
The formula returns a negative percent, which means "don’t bet." If you bet anyway with negative edge, you’re expected to lose money — guaranteed in the long run.
Does Kelly work for stocks?
Yes, but requires you to express stock positions as bets with estimated win probability and payoff. This is much harder than coin flips or poker hands. Pros approximate using expected return / variance ratios.
Why "geometric" growth?
Because returns compound. After a 50% loss, you need a 100% gain to recover. Kelly optimizes for geometric mean return, which accounts for this asymmetry. Simple arithmetic optimization would tell you to lever up to ruin.
Can I use Kelly for options?
Yes — estimate win probability and payoff for each contract, then compute Kelly. Most retail option traders are wildly over-sized because they don’t do this math. Even a "good" 60% win rate at 1:1 odds says bet 20% — most amateurs bet far more.
Kelly Criterion — 55% win rate, 1.00:1 payoff | SuperCalculator