The Kelly Criterion: How Much to Stake (and Why Fractional)

Once you've found an edge, the Kelly criterion tells you how much of your bankroll to stake to grow it fastest over the long run. It's elegant and optimal in theory. Used at full strength on a mis-estimated edge, it will wreck you.

The Kelly formula

For a bet with win probability p, loss probability q = 1 − p, and decimal profit b per dollar, the Kelly fraction is f* = (b · p − q) / b. That fraction of your bankroll is the stake that maximizes the expected growth rate of your money. Bet more and growth falls off and volatility explodes; bet less and you leave growth on the table.

Why full Kelly is dangerous

Kelly is optimal only if your p is exactly right. It never is, because edge estimates are noisy. And Kelly is asymmetric: overestimating your edge and overbetting is far more punishing than underbetting by the same amount. A full-Kelly stake on an edge you've overestimated leads to deep drawdowns and, often, ruin.

Fractional Kelly

The standard fix is to bet a fixed fraction of the Kelly stake, a quarter or a half. Fractional Kelly keeps most of the long-run growth while sharply cutting volatility and drawdown, and it builds in a buffer against your own estimation error. Quarter-Kelly is a common default for exactly this reason.

For several bets at once, naive per-bet Kelly overallocates, especially for correlated outcomes in the same game. Size them jointly instead.