Kelly Criterion Calculator

Why bet sizing matters as much as picking winners

Finding bets with a genuine edge is only half the problem professional bettors solve — the other half is deciding how much to stake on each one. Stake too little relative to your edge, and you leave long-run growth on the table even though every individual bet is profitable on average. Stake too much, and normal variance can devastate your bankroll before your edge has a chance to play out over enough bets to show up reliably. The Kelly Criterion, developed by John Kelly at Bell Labs in 1956 for a different problem entirely (signal transmission over noisy telephone lines), turned out to solve exactly this bet-sizing question: it identifies the stake fraction that maximizes the long-run geometric growth rate of a bankroll, given a known edge and payout.

Breaking down the formula

The formula itself — f* = (bp − q) / b — has three inputs. b is the net odds, meaning decimal odds minus 1 (so 3.00 decimal odds gives b = 2, since you profit 2 units per 1 staked). p is your genuinely estimated probability that the bet wins — not the bookmaker’s implied probability, but your own honest assessment, which is where all the real difficulty in using Kelly lives. q is simply 1 − p. The output, f*, is the fraction of your total bankroll the formula recommends staking on this single bet. A f* of 0.05, for example, means 5% of your current bankroll — not 5% of your original starting bankroll, which is an important distinction, since Kelly staking recalculates against your bankroll as it changes.

A worked example: suppose you estimate a 45% chance of winning a bet priced at decimal odds of 2.50 (so b = 1.50). Kelly’s formula gives f* = (1.50 × 0.45 − 0.55) / 1.50 = (0.675 − 0.55) / 1.50 ≈ 0.083, or about 8.3% of your bankroll. If your bankroll is €2,000, full Kelly recommends a stake of roughly €166 on this single bet — a number that can feel uncomfortably large the first time you see it, which is exactly why fractional Kelly exists.

Why almost nobody uses full Kelly in practice

Full Kelly assumes your probability estimate is exactly correct, with zero error. In reality, no bettor’s probability estimate is perfect, and full Kelly is extremely sensitive to that error — overestimating your true edge even slightly leads full Kelly to recommend staking meaningfully more than is actually justified, and the resulting bankroll swings can be severe even when your edge is real. This is why most professional and serious recreational bettors use "fractional Kelly" — commonly half Kelly (staking 50% of what the formula recommends) or quarter Kelly (25%) — deliberately trading away some long-run growth rate in exchange for a much smoother, less volatile bankroll curve. Half Kelly, for instance, gives up about 25% of the theoretical maximum growth rate in exchange for roughly half the variance of full Kelly — a trade most bettors consider well worth it.

Where Kelly staking breaks down

Kelly is only as good as the probability you feed it, and that’s the formula’s single biggest practical weakness. It has no concept of how confident you should be in your own estimate — it treats a carefully researched 45% as equally reliable as a rough guess of 45%, and will size the bet identically either way. It also assumes you can accurately and independently estimate probability for every bet you consider, which is a much harder ongoing task than it sounds, and it says nothing about correlation between bets — staking full Kelly on several correlated outcomes (say, multiple bets tied to the same team’s form) can concentrate risk in a way the formula, applied bet-by-bet, doesn’t account for.

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