The Kelly Criterion: Optimal Bet Sizing

The Kelly Criterion is a formula developed by John Kelly at Bell Labs in 1956. It calculates the optimal fraction of your bankroll to bet when you have a positive expected value.

The formula is: f* = (bp - q) / b, where b is the decimal odds minus 1, p is your estimated win probability, and q is 1-p.

At GreyhoundAI, we use a fractional Kelly approach (quarter-Kelly by default) to reduce variance while maintaining long-term growth. Our system also caps maximum stakes at 5% of bankroll.

The key insight is that Kelly optimises for long-term geometric growth of your bankroll, not for maximising expected value on any single bet.