Game Theory & Decision

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Kelly Criterion

Optimal fraction of bankroll to bet for long-run growth.

Formula

f^* = \frac{bp - q}{b}

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Variables

f*Fraction to bet

bNet odds received

pWin probability

qLoss probability 1-p

Example

b=1, p=0.6, q=0.4: f* = 0.2 (bet 20%)

Did You Know?

The Kelly criterion, from a 1956 Bell Labs paper, maximises long-run wealth — favoured by pro gamblers and investors alike.

game theory kelly betting

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