Size the optimal bet.

What the Kelly fraction optimises

Kelly answers a specific question: what fraction of capital, bet repeatedly, maximises the long-run growth rate of wealth? The answer is f* = W − (1 − W) ÷ R, where W is win probability and R is the ratio of average win to average loss. Bet more than f* and growth slows despite the larger stake; bet enough more and expected wealth goes to zero.

It optimises geometric growth, not comfort and not expected value. That distinction matters — the fraction that maximises expected dollars is usually far larger than Kelly, and following it reliably ends in ruin because it ignores the path.

A worked example

A strategy wins 55% of the time with a win/loss ratio of 1.5. Full Kelly is 0.55 − (0.45 ÷ 1.5) = 0.55 − 0.30 = 0.25, or 25% of capital per trade.

Almost nobody should trade that. Quarter-Kelly puts it at 6.25%, still aggressive by most standards, and half-Kelly at 12.5% would produce drawdowns beyond what most traders tolerate. Fractional Kelly gives up a modest amount of theoretical growth for a very large reduction in volatility — usually a trade worth making.

Where this calculator misleads you

Kelly assumes you know W and R exactly. You do not — you have estimates from a finite sample, and the formula is acutely sensitive to error in them. Overestimating your win rate by a few points produces a fraction well above true optimum, and betting above optimal Kelly is worse than betting well below it. The asymmetry of that error is the entire argument for fractional Kelly.

It also assumes outcomes are independent and identically distributed. Trading outcomes are neither: edges cluster, losing streaks correlate with regime changes, and the win rate that held last year may not hold now. Every one of those violations pushes the safe fraction downward.

Full Kelly on an estimated trading edge is the textbook route to a blown account. Treat the output as an upper bound that reality argues against, not a target.

Terms on this page

Kelly fraction (f*)

Fraction of capital per bet that maximises long-run geometric growth: W − (1 − W) ÷ R.

Fractional Kelly

Betting a fixed portion of f* — commonly a half or a quarter — to cut volatility at modest cost to growth.

Geometric growth

Compounded growth rate of wealth. What Kelly maximises, as distinct from expected value.

Over-betting

Staking above f*. Reduces growth and, far enough past it, guarantees eventual ruin.