What it is
The Kelly criterion, published by John Kelly in 1956, gives the fraction of capital to allocate to a repeated favourable bet in order to maximise the long-run growth rate of wealth. It is the mathematically correct answer to the question of how much, under a specific and rather demanding set of assumptions.
How it works
For a simple binary bet with win probability p, loss probability q = 1 - p and net odds b, the optimal fraction is f* = (b x p - q) / b. For continuously distributed returns the working approximation is f* = mean / variance, which for a strategy is roughly its Sharpe ratio divided by its volatility. The formula maximises expected logarithmic wealth, which is why it dominates any other fixed fraction over a long enough sequence of bets.
How traders use it
Practitioners almost never bet full Kelly. Half-Kelly retains about three quarters of the growth rate with substantially smaller swings, and quarter-Kelly is common in production. The reason is estimation error: the inputs are estimated from limited data, and the penalty for over-betting is severe and asymmetric, while under-betting merely slows compounding.
Where it breaks down
The assumptions are the whole story. Kelly requires a known, stationary edge, independent repeated bets, and the ability to size continuously with no risk of a forced exit. Real strategies have parameter uncertainty, regime change, correlated positions and margin calls. Betting more than f* both raises risk and lowers expected growth, which is the worst of both outcomes, and feeding an overfitted backtest win rate into the formula is the most reliable way to end up there.
Educational reference. This entry describes how a concept is defined and used. It is not investment advice, not a recommendation, and not a signal. Any rule you build from it should be tested with realistic costs before it is traded, and no historical result guarantees a future one.