Kelly Criterion
Optimal fraction of bankroll to bet for long-run growth.
Formula
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Example
b=1, p=0.6, q=0.4: f* = 0.2 (bet 20%)
How it works
The Kelly Criterion tells you what fraction of your bankroll maximizes the long-run growth rate when you repeatedly face the same type of bet with known odds and win probability. It comes from maximizing the expected value of logarithmic wealth, which automatically balances upside against the danger of betting too much and going broke. If the edge is small or the odds are unfavorable, the formula can give zero or even a negative value, meaning you should not bet at all.
When to use it
Use this when you have a repeated betting or investing situation with measurable probabilities and payoff ratios, such as gambling, trading with an estimated edge, or any decision where bankroll growth over many trials matters. It is especially useful when you want a principled staking rule rather than an arbitrary percentage.
Worked example, step by step
Suppose a wager pays net odds b = 2 if you win, with win probability p = 0.35. Then the loss probability is q = 1 - p = 0.65. Plug into the Kelly formula: f* = (bp - q) / b f* = (2 × 0.35 - 0.65) / 2 f* = (0.70 - 0.65) / 2 f* = 0.05 / 2 f* = 0.025 So the Kelly-optimal stake is 0.025, or 2.5% of your bankroll.
Common mistakes to avoid
- Confusing net odds b with decimal odds or total payout odds
- Using the formula when p is only a rough guess and treating the result as exact
- Betting the full Kelly fraction in high-uncertainty settings without considering risk tolerance or estimation error
Did You Know?
The Kelly criterion, from a 1956 Bell Labs paper, maximises long-run wealth — favoured by pro gamblers and investors alike.
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