A formula for the bet size that maximizes long-run growth given your win rate and payoff ratio; full Kelly is far too aggressive for most traders.
Kelly fraction = W - (1 - W) / R, where W is win-rate and R is the average win divided by average loss. It gives the theoretically optimal fraction of capital to risk, assuming you know W and R exactly, which you never do.
Because the inputs are estimates and the drawdowns at full Kelly are brutal, practitioners use a quarter or half Kelly at most. Its main value is showing that over-betting is worse than under-betting.
Example: 45% win rate, average win 2x average loss. Kelly = 0.45 - 0.55 / 2 = 0.175, or 17.5% of capital. Half Kelly is 8.75%; most traders would still consider that reckless and use 1% to 2%.
Original diagrams for the ideas on this page. Illustrative, not real market data.
Expectancy: the average trade. Forty trades sorted by outcome: 24 small losses and 16 larger wins. Weighting each side by how often it happens gives the average result per trade, marked here by the dashed line at +$120.
Educational only, not advice. Spotted an error? Post in Site Feedback.