What is the Kelly criterion?

The Kelly criterion is a mathematical staking formula that calculates the optimal fraction of your bankroll to place on each bet in order to maximise long-run bankroll growth.

Developed by physicist John L. Kelly Jr. in 1956, the formula has since become a cornerstone of disciplined bankroll management in sports betting, poker, and financial trading. Where flat staking ignores edge and variance, Kelly accounts for both — sizing stakes up when your edge is large and pulling them back when risk is high.

The Formula Explained

The core equation is:

f = (bp − q) / b

Where:

• f = fraction of bankroll to stake
• b = decimal odds minus 1 (the net odds received)
• p = your estimated probability of winning
• q = probability of losing (1 − p)

This simplifies to f = edge / odds, which tells you everything: the bet size is determined entirely by how much edge you have relative to the price on offer.

Worked Example

Suppose a bookmaker offers decimal odds of 2.50 on a coin-flip market, but you assess the true probability of winning at 55% (0.55).

• b = 2.50 − 1 = 1.50
• p = 0.55
• q = 0.45
• f = (1.50 × 0.55 − 0.45) / 1.50 = (0.825 − 0.45) / 1.50 = 0.375 / 1.50 = 0.25

Kelly says to stake 25% of your bankroll on this bet. If your edge shrinks — say your true probability is only 52% — the recommended stake drops to roughly 5.3%. The formula self-adjusts automatically.

Use WeeBet's Kelly calculator tool to run these numbers without manual arithmetic.

Full Kelly vs Fractional Kelly

Most professional bettors do not use full Kelly. The formula is exquisitely sensitive to the accuracy of your probability estimate, and even a small overestimate of edge can produce dangerously large stakes.

Half-Kelly — staking 50% of the calculated fraction — sacrifices roughly 25% of the theoretical growth rate in exchange for substantially lower variance. Most practitioners consider this trade-off worthwhile.

Why Over-Betting Kelly Causes Ruin

Kelly's mathematical guarantee is asymmetric: it maximises the geometric growth rate, which means overbetting destroys it. Stake more than Kelly recommends and your expected bankroll growth turns negative, even if the bet itself has a positive expected value. At double Kelly, expected growth drops to zero. Beyond that, ruin becomes probable over a long enough series of bets.

This is why an accurate probability estimate is non-negotiable. If you believe you have a 60% edge but your true edge is 52%, you will overbet — and the formula will quietly work against you.

Please bet responsibly. Set deposit limits and stake only what you can afford to lose.

Frequently Asked Questions

Does Kelly work for sports betting?

Yes, though it requires an honest, well-calibrated probability model — not a gut feeling. Applied to sports betting, Kelly is most useful for bettors who track their historical accuracy and can genuinely estimate true probabilities with some confidence.

What is fractional Kelly and why do most bettors use it?

Fractional Kelly means staking a fixed proportion — most commonly 50% — of the full Kelly recommendation. It reduces the wild bankroll swings that full Kelly produces without abandoning the underlying logic of edge-proportional staking.

Can Kelly criterion guarantee profit?

No. Kelly maximises the growth rate over a long sequence of bets, but it cannot manufacture edge where none exists. If your probability estimates are wrong or you have no real edge, Kelly will size your losing bets with the same mathematical rigour it applies to winning ones.

Is Kelly used outside of betting?

Yes. Traders and portfolio managers apply Kelly to position sizing in equities and options markets. Warren Buffett's partner Charlie Munger has cited Kelly-style thinking as central to concentrated portfolio decisions, though institutional constraints usually force practitioners toward fractional versions.