Kelly Criterion

The Kelly Criterion answers a question most bettors never formalise: not “should I bet this?” but “how much of my bankroll should I risk on it?” It was developed by the Bell Labs scientist John Kelly in 1956 for a completely different problem — signal noise in telephone lines — but the maths translates directly to any wager with a known edge and known odds. Instead of staking flat amounts or picking numbers that feel right, Kelly derives the stake that grows your bankroll fastest over many bets while avoiding the ruin that comes from overstaking a string of losers.

The formula needs two inputs you must supply yourself: the decimal odds on offer, and your own honest estimate of the true probability that the bet wins. From those it calculates your edge and converts that edge into a percentage of bankroll to stake. Bet less than Kelly and you’re leaving growth on the table; bet more and the maths shows your bankroll’s long-run growth rate actually falls, because the extra variance eats into compounding — a subtlety that surprises people who assume “more edge, more stake” scales in a straight line.

The formula itself, in decimal-odds terms, is:

f* = (bp − q) / b

where f* is the fraction of bankroll to stake, b is the decimal odds minus 1 (the net odds), p is your estimated win probability, and q is 1 − p (the estimated lose probability). If bp − q comes out negative, Kelly tells you plainly: there’s no edge here, don’t bet.

Example

Say you follow Villarreal closely and think the market has them wrong to face Real Betis. The book prices Villarreal to win at 2.40 (fractional 7/5), which implies a 41.7% chance (1 ÷ 2.40). From your own model — recent form, home advantage, a couple of Betis injuries the market seems slow to price in — you land on a true win probability of 48%.

• b = 2.40 − 1 = 1.40
• p = 0.48, q = 0.52
• f* = (1.40 × 0.48 − 0.52) / 1.40 = (0.672 − 0.52) / 1.40 = 0.152 / 1.40 = 0.1086, or 10.9% of bankroll

With a €4,000 bankroll, full Kelly says stake €434 on Villarreal at 2.40. That number looks aggressive to most bettors, and it should — full Kelly assumes your 48% is exactly right, with zero estimation error, which real handicapping never delivers. In practice, most disciplined bettors stake “half Kelly” or “quarter Kelly” — literally halving or quartering the recommended fraction — to cushion against the fact that their probability estimate is a guess, not a certainty. Half Kelly here means €217, roughly 5.4% of bankroll, giving up some theoretical growth for a much smoother equity curve and far less damage if your 48% was really closer to 43%.

Key Points

• The edge has to be real before the formula matters: Kelly only sizes a bet correctly if your probability estimate is genuinely better than the market’s. Plugging in a hopeful number rather than a researched one just produces a confidently-wrong stake — garbage in, garbage out.
• Fractional Kelly is the practical default: Because nobody’s win-probability estimate is perfectly calibrated, staking half or a quarter of the full Kelly figure is standard practice among serious bettors. It sacrifices some theoretical growth rate for a much lower risk of a bad drawdown when your edge estimate turns out optimistic.
• Kelly explains why odds shopping matters so much: In the Villarreal example, if you’d found 2.55 instead of 2.40 at another bookmaker for the same 48% view, b rises to 1.55 and the recommended stake jumps to roughly 15% of bankroll — a meaningfully bigger edge from a small price difference, which is the whole case for comparing prices before betting.
• Recalculate stake for every bet, never reuse a number: Kelly stakes move with both the odds and your probability estimate, so a fixed “my Kelly bet is always €400” habit defeats the purpose. A short-priced favourite and a rangy underdog with the same edge in expected-value terms can call for very different fractions of bankroll.
• It says nothing about whether to bet, only how much: Kelly is a staking tool, not a selection tool. It will happily tell you to stake 15% of your bankroll on a bad estimate — the formula trusts your inputs completely, so the discipline has to come from how rigorously you built p in the first place.
• A run of Kelly losses is expected, not a sign the method is broken: Because stakes shrink automatically as your bankroll shrinks, Kelly is mathematically built to survive a bad streak — but it can still feel uncomfortable watching stakes drop after a run of losers. That’s the system working as designed, not a reason to abandon it mid-streak.