★

Kelly Criterion Calculator

Find the mathematically optimal bet size for any edge

Formula

The Kelly Formula

f* = (b · p − q) / b

f* = fraction of bankroll to wager  |  b = net odds (payout-to-1)  |  p = win probability  |  q = 1 − p

Calculator

Calculate Optimal Bet Size

Enter your win probability, the payout odds, and your total bankroll.

Frequently Asked Questions

What is the Kelly Criterion?
The Kelly Criterion is a formula developed by John Kelly at Bell Labs in 1956. It calculates the optimal percentage of your bankroll to bet when you have an edge, maximizing long-term compound growth rate while managing risk.
What is fractional Kelly?
Fractional Kelly means wagering a fraction (typically half or quarter) of the full Kelly recommendation. This dramatically reduces variance and risk of ruin with only a modest reduction in growth rate. Most professionals use half-Kelly or less.
What happens if I bet more than Kelly?
Betting more than the Kelly amount actually reduces your long-term growth rate and increases your risk of ruin. At exactly double Kelly, your expected growth rate drops to zero. Beyond that, you're expected to lose money over time despite having a positive edge.
Can I use this for sports betting?
Yes. Convert the bookmaker's decimal or American odds to "payout to 1" format, estimate your true win probability, and the calculator will tell you the optimal stake. The hard part is accurately estimating the true probability — if your estimate is wrong, Kelly can lead to over-betting.
What if Kelly says to bet 0% or negative?
A Kelly percentage of zero or less means the bet has no edge or negative expected value. The optimal strategy is to not bet at all. Kelly only applies to situations where you have a genuine mathematical advantage.

Kelly Criterion: Optimal Bet Sizing Calculator

The Kelly Criterion is the gold standard of bankroll management in advantage gambling, sports betting, and investing. This free calculator computes the optimal wager size based on your edge and the offered odds.

Why Kelly Works

Kelly maximizes the geometric growth rate of your bankroll. Over many bets, it produces a higher bankroll than any other fixed-fraction strategy. It's used by professional gamblers, hedge funds, and anyone who needs to allocate capital under uncertainty.

The Practical Approach

In practice, most advantage players use half-Kelly or quarter-Kelly because the full Kelly amount assumes your probability estimates are perfectly accurate. Fractional Kelly provides a buffer against estimation errors while still capturing most of the growth.