The formula that maximises long-term bankroll growth rate, derived from information theory and adopted by professional gamblers and investors alike.
f* = (bp − q) ÷ b
f* = fraction of bankroll to stake
b = decimal odds − 1 (the net odds)
p = your estimated win probability
q = 1 − p (probability of losing)
Decimal odds of 2.50 (so b = 1.50). You estimate true win probability at 45% (p = 0.45, q = 0.55).
With a $1,000 bankroll, Kelly suggests staking $83 on this single bet.
Kelly staking maximises the expected logarithmic growth rate of your bankroll over the long run — mathematically the optimal balance between growing your bankroll aggressively and avoiding ruin. Staking more than Kelly increases variance and long-term ruin risk without improving the growth rate; staking less simply grows your bankroll more slowly than optimal.
Kelly is only as good as your probability estimate p. Overestimate your edge even slightly, and full Kelly staking becomes dangerously aggressive. This is the single biggest practical problem with the formula — most bettors' probability estimates carry real uncertainty.
Most professional bettors use a fraction of full Kelly — commonly half-Kelly (50%) or quarter-Kelly (25%) — to dramatically reduce variance and protect against estimation error, at the cost of somewhat slower theoretical growth.
| Kelly Fraction | Stake (from example) | Risk Level |
|---|---|---|
| Full Kelly (100%) | 8.3% | High variance, max theoretical growth |
| Half Kelly (50%) | 4.15% | Moderate variance, ~75% of growth rate |
| Quarter Kelly (25%) | 2.08% | Low variance, safer for uncertain edges |
If you can't confidently estimate your win probability — which is most casual bettors, most of the time — Kelly will likely do more harm than good. In that case, simple fixed or proportional staking is more robust and forgiving of estimation error.
Enter your odds, probability estimate, and bankroll into our free Kelly calculator to get full, half, and quarter Kelly stake recommendations instantly.