Calculate mathematically optimal stake sizing and bankroll growth based on your estimated win probability and edge.
What is the Kelly Criterion?
Formulated by mathematician John L. Kelly Jr. in 1956, the Kelly Criterion calculates the mathematically optimal percentage of your bankroll to allocate to an investment or bet with positive expected value (+EV). It balances rapid bankroll growth against the risk of ruin.
The formula:f* = (p × b - 1) / (b - 1), where p is the true probability of winning and b is the decimal odds.
Fractional Kelly: Full Kelly staking can experience intense volatility and large drawdowns during bad variance runs. In practice, professional sports bettors use Half Kelly (0.5x) or Quarter Kelly (0.25x) to dramatically reduce variance and protect bankroll capital against estimation errors.
Worked example
Staking Calculation
With a £1,000 bankroll, offered odds of 2.50, and an estimated true win probability of 45% (fair odds 2.22, giving an edge of +12.5%):
• Full Kelly (1.0x): 8.33% bankroll allocation (£83.33 stake)
• Half Kelly (0.5x): 4.17% bankroll allocation (£41.67 stake)
• Quarter Kelly (0.25x): 2.08% bankroll allocation (£20.83 stake)