Kelly Criterion

The Kelly criterion chooses exposure to maximize expected logarithmic wealth under a specified probability and payoff model. The simple binary formula is (bp - q)/b. It is a growth criterion, not a guarantee against drawdowns or a general minimization of ruin probability.

Kelly sizing maximizes expected logarithmic wealth under a defined probability and payoff model. For a binary wager that loses the stake on failure and pays net odds b on success, the unconstrained fraction is (bp - q)/b, with q = 1 - p. A nonpositive answer means no positive wager when sitting out is permitted.

The difficult input is the edge, not the arithmetic. Probabilities from small or changing samples can be wrong, and simultaneous positions may share a failure. Fractional Kelly reduces exposure relative to an estimate but does not repair that estimate. Liquidity needs, leverage, drawdown tolerance, and a finite horizon may require a different objective.

When to use it

When investment or bet sizing needs to maximize long-term compound growth; when the risk of ruin from over-sizing positions needs to be managed; when positive-expected-value opportunities need to be sized appropriately; when understanding why position sizing matters as much as position selection.

How it can help

Use the criterion to study sizing under an estimated edge. Explicitly consider estimation error, dependence, leverage, liquidity, and whether the objective fits; fractional Kelly is not universally appropriate.