Kelly Criterion Calculator
Calculate mathematically optimal bet sizing. Advanced tool with important caveats.
Advanced Tool Warning
The Kelly Criterion is a mathematical formula, not a betting strategy. It requires accurate probability estimates, something extremely difficult to achieve. Using Kelly with incorrect probability estimates will lose money faster than flat betting. Most recreational bettors should use simpler bankroll management (1-2% stakes).
Kelly Calculation
Understanding Kelly Criterion
The Formula
Kelly % = (bp - q) / b
Where: b = decimal odds - 1, p = probability of winning, q = probability of losing (1 - p)
What It Does
Kelly calculates the stake size that maximizes long-term bankroll growth, given your edge. It's mathematically optimal for capital growth, but only if your probability estimates are accurate.
Why It's Dangerous
Full Kelly is extremely aggressive. A 10% edge might suggest betting 20% of your bankroll. Losing streaks happen, and Kelly can result in massive drawdowns even when you have an edge.
More critically: if your probability estimate is wrong, Kelly will accelerate your losses. Most bettors overestimate their edge, making Kelly counterproductive.
Practical Advice
If you must use Kelly: use half or quarter Kelly to reduce variance. Better yet: stick to flat 1-2% stakes unless you have verified, long-term profitable betting results that prove your edge is real.
The Kelly Criterion Explained
The Kelly Criterion is a mathematical formula for optimal bet sizing. It maximizes long-term bankroll growth while accounting for both your edge and the risk of ruin. Developed by John Kelly at Bell Labs in 1956, it has become fundamental to professional gambling and investing.
When to Use Kelly
Kelly only works when you have positive expected value. If your edge is zero or negative, Kelly recommends betting nothing. The formula assumes you can accurately assess your win probability, overestimating your edge leads to over-betting and potential ruin.
Fractional Kelly
Most professionals use fractional Kelly, typically betting one-quarter to one-half of the suggested stake. This reduces variance significantly while still capturing most of the growth benefit. Full Kelly is mathematically optimal but emotionally brutal due to large swings.
Practical Limitations
Kelly assumes unlimited betting opportunities and perfect probability assessment. Real-world constraints like maximum bet limits, bankroll access, and estimation errors mean Kelly should be a guide rather than a rule. Conservative sizing outperforms aggressive sizing for most bettors.