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Kelly Criterion Calculator

Find the mathematically optimal fraction of your bankroll to stake on a favorable bet, f* = p − q/b, given your win probability and the odds.

Full Kelly stake
10%
Recommended stake (100% Kelly)
10%
Recommended stake amount
$100.00
Expected value per $1 staked
$0.10
Breakeven win probability implied by these odds
50%

How it works

The Kelly criterion is the bankroll fraction f that maximizes the long-run expected growth rate of wealth when a favorable bet is repeated many times. For a bet with win probability p (losing with probability q = 1 − p) that pays net odds b per $1 staked on a win, maximizing the expected logarithm of wealth gives the closed form f* = p − q/b — equivalently (bp − q)/b. Net odds b is decimal odds minus 1, since decimal odds already include the returned stake and Kelly's formula only cares about the profit.

A positive f* means the bet has a genuine edge at these odds and Kelly recommends staking that fraction of your bankroll; a zero or negative f* means there's no edge (or a losing one), and the correct move is simply not to bet at all, not to bet a negative amount. The calculator also reports the fraction scaled by a chosen 'Kelly fraction' — betting a fraction of the full Kelly amount (commonly half) is a standard way to trade some long-run growth for materially lower bankroll swings, since full Kelly's growth-maximizing property comes with substantial volatility.

Expected value per $1 staked (p·b − q) and the odds' own breakeven win probability (1 ÷ decimal odds, the probability at which this bet has exactly zero edge) are shown alongside the Kelly fraction as separate reference figures — they answer 'is this bet worth taking at all' and 'what would make it even', which is a different question from 'how much of my bankroll should I risk.'

FAQ

Why does the calculator ask for my own probability estimate instead of using the odds?

Kelly betting only works when you have a genuine edge — a probability estimate of your own that differs from what the odds imply. If you just used the odds' own implied probability, every bet would compute to exactly zero edge, since bookmakers and exchanges price odds close to their own best estimate. The whole premise of Kelly staking is that you (or your model) believe the true probability is different from the market's, which is a fact only you can supply — this calculator can't estimate it for you.

Why would I ever bet less than full Kelly?

Full Kelly maximizes long-run growth, but it does so with very large short-run swings — a string of losses can draw a full-Kelly bankroll down by 50% or more even when the underlying edge is real, and any error in your probability estimate is amplified. Fractional Kelly (commonly half) gives up some growth rate in exchange for meaningfully smaller drawdowns, which is why many practitioners treat full Kelly as an upper bound rather than a target.

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