Kelly criterion calculator

The Kelly formula

The Kelly criterion calculates the bet size that maximises the long-run logarithmic growth of your bankroll. For a bet with decimal odds O, your estimated probability p, and complementary probability q = 1 − p:

f* = (b × p − q) / b   where b = O − 1

This is the fraction of your bankroll to wager. If f* is negative, the bet has no edge and you should not bet. If positive, that fraction maximises bankroll growth — but it also produces wild swings.

Why fractional Kelly is standard

Full Kelly assumes you know your probability exactly. Real estimates have error, and Kelly is sensitive to that error in a particularly nasty way: small overestimates of your edge produce large overbets that increase risk of ruin without proportional growth.

Half Kelly (0.5 × f*) gives 75% of the long-run growth with roughly 50% of the volatility. Quarter Kelly (0.25 × f*) gives 56% of growth with 25% volatility. For sports betting, advantage play, or any context with non-trivial probability estimation error, half or quarter Kelly is the practical default.

Worked example

You estimate a tennis match at 55% to favourite. Bookmaker offers decimal odds 1.95 (implied 51.3%). You believe you have a 3.7% edge.

b = 0.95
p = 0.55, q = 0.45
f* = (0.95 × 0.55 − 0.45) / 0.95
f* = (0.5225 − 0.45) / 0.95
f* = 0.0763 = 7.63% of bankroll

Half Kelly = 3.81% of bankroll. On a $5,000 roll, that's $190.50. The expected value of this bet is +$7.05 (3.7% edge × $190.50). Over many such bets, your bankroll grows.

Important caveats

• Garbage in, garbage out. Kelly returns nonsense if your probability estimate is nonsense. Most casual bettors overestimate their edge.
• Casino games are negative EV. Kelly says don't bet — period. Use it for sports, poker, and other games where you might genuinely have edge.
• Bankroll = risk capital, not net worth. Kelly fractions are of money you can afford to lose, not your savings or rent.
• Drawdowns are part of the deal. Even with positive EV, expect 50%+ drawdowns at full Kelly across thousands of bets.

Kelly vs flat betting

Flat betting (always wagering the same dollar amount) ignores bankroll. After a bad run, you're risking a higher percentage of remaining roll on each bet — risk of ruin grows. After a good run, you're risking a lower percentage — growth slows. Kelly auto-adjusts: bet sizes track your bankroll, so percentage risk stays constant. It's the only betting system that mathematically maximises long-run growth — but only when your edge estimate is reliable.