The mathematical formula for optimal bet sizing. Why it works, why it'll wreck you in practice, and the conservative version professional bettors actually use.
There's a single formula that, applied correctly, theoretically maximises long-run growth of a betting bankroll. It's called the Kelly Criterion. Professional bettors use it. Hedge funds use it. It's been written about in dense academic papers since 1956.
The full Kelly formula is also a financial wrecking ball if you apply it the way the textbook suggests. Most professionals use a fractional version — typically a quarter of what the formula recommends — because the textbook version assumes you know things you don't actually know.
This post is about what Kelly is, why it's mathematically beautiful, why the textbook version is dangerous, and what the disciplined version actually looks like.
Imagine you find a bet you think has positive expected value. The bookmaker is offering odds that imply the favourite will win 70% of the time. You think the favourite will win 75% of the time. You're confident enough to act.
How much do you bet?
The naive answer is "a lot, because you have an edge." This is wrong. Bet too much and a single loss wipes out a meaningful chunk of your bankroll. The bigger question is: how much should you bet, given the size of your edge and the odds being offered?
That's what Kelly answers.
For a bet with two outcomes (win or lose):
$$f = \frac{bp - q}{b}$$
Where:
Worked example. Bookmaker offers 2.50 (decimal odds) on a team. You think the team has a 50% chance of winning.
Kelly says:
$f = (1.50 × 0.50 - 0.50) / 1.50 = 0.25 / 1.50 = 0.167$
Stake 16.7% of your bankroll.
Worked example 2. Same odds (2.50), but you think the team has a 60% chance of winning (a much bigger edge).
Stake 33.3% of your bankroll on a single bet.
You see the issue. Kelly's recommended stakes are aggressive. Even a moderate edge produces stakes that feel large.
Kelly is the bet size that maximises the logarithmic growth of your bankroll over many bets.
The intuition: if you double your bankroll, that's worth the same to you (proportionally) whether you started with £100 or £100,000. Logarithmic utility captures this — you care about percentage growth, not absolute pounds. Kelly is the formula that grows your bankroll at the highest expected logarithmic rate over time.
Importantly, Kelly is not the bet size that maximises expected return on a single bet. That would be "bet everything every time you have an edge" — which works for one bet and ruins you on the next. Kelly is the bet size that wins the long game.
Mathematically, Kelly is provably optimal under specific conditions. Bet less than Kelly, and you grow slower. Bet more than Kelly, and your long-run growth slows or even goes negative — you can lose money over time even with positive-EV bets if you're staking too aggressively.
The math is correct under specific conditions. The conditions are roughly:
In practice, these conditions are nearly always violated.
Condition 1 fails because you don't know your edge. When your model says 60%, your actual probability might be 55% or 65%. The headline number is your best estimate, but it has uncertainty around it. Kelly assumes you have the true probability. You don't — you have a noisy estimate.
If your true edge is smaller than you think, full Kelly stakes you at multiples of optimal. The result is bankroll volatility that can be ruinous.
Condition 3 fails because Kelly is volatile. Even when applied perfectly, full Kelly can produce 50% drawdowns. The math says you'll recover and grow long-run, but most people can't psychologically tolerate watching their bankroll halve. They abandon the strategy, often at exactly the wrong time.
This is why every serious bettor talks about fractional Kelly.
Fractional Kelly is exactly what it sounds like: stake a fraction of what full Kelly recommends.
Most professional bettors use somewhere between quarter Kelly and half Kelly. The math is roughly: you sacrifice some long-run growth in exchange for dramatic reduction in ruin risk and emotional sustainability.
Our model recommends quarter-Kelly stakes on bets it identifies as having edge. We chose this for two reasons:
Worked example: same edge as before, but with quarter Kelly.
Full Kelly: stake 16.7%. Quarter Kelly: stake 4.2%.
On a £1,000 bankroll, that's £42 instead of £167. The bet is still positive EV. The growth rate over many bets is slower, but the variance is dramatically lower. You're not going to lose 50% of your bankroll in a bad week.
This is the actual recommendation for serious bettors. Forget what the textbook says about full Kelly. Use quarter Kelly. Adjust if you have specific reasons (very high confidence in your edge, very tolerant of variance, very small bankroll where capping the loss matters less).
Kelly assumes specific conditions. Some situations break the assumptions:
1. When you can't estimate your edge reliably.
If your "edge" is just intuition or vague analysis, Kelly is meaningless because the formula needs your probability estimate to be roughly accurate. Most casual bettors fall here. Their estimated probabilities are unrelated to actual probabilities, so the optimal stake size is zero (or fixed-percentage flat-stake amounts that don't pretend to be Kelly).
2. When you're betting non-independent events.
Multi-bet parlays, Asian handicap with correlated lines, simultaneous bets on related markets — these violate the Kelly assumption that bets are independent. Kelly understates risk in correlated bet structures.
3. When you have a small bankroll.
Kelly assumes proportional thinking — losing 10% of your bankroll feels the same regardless of starting amount. For small bankrolls, fixed minimum stake amounts force you to deviate from Kelly. If a bookmaker's minimum stake is £5 and your Kelly says £3, you have to either skip the bet or overstake.
Three rules for thinking about stake sizing:
1. Don't bet without an edge. Most football matches are priced efficiently. Acting without a measurable edge is just paying the bookmaker margin. Kelly tells you how to size a bet given you have edge — it doesn't tell you to bet on everything.
2. Use quarter Kelly or half Kelly. Not full. The math is correct but the assumptions don't hold in practice. Quarter Kelly is the sustainable version.
3. Cap your single-bet stakes. Even with quarter Kelly, big-edge spots can recommend uncomfortable stake sizes. Cap any single bet at a percentage you can emotionally sustain (typically 5-10% of bankroll). This caps your variance even when Kelly thinks you should stake more.
A final, uncomfortable truth: Kelly only applies if you're producing your own probability estimates. If you're acting on bookmaker odds plus intuition, you have no edge to size, and the right answer is "flat stakes a small fraction of bankroll on bets you choose carefully."
Most casual bettors think they have edge when they don't. Kelly is irrelevant to them, and the math is mostly an academic curiosity. The bigger question is whether they're betting at all, and whether the bets are positive EV in the first place.
If you have a model — any kind, even a simple one — Kelly becomes useful. If you're acting on tips, narrative, or vibes, the formula doesn't help. The formula isn't a get-rich tool. It's a stake-sizing tool for people who already have an edge.
The Kelly Criterion is one of the most beautiful pieces of math in betting. It's also one of the most misused. Use the conservative version, respect your bankroll, and remember the formula assumes things about your edge that probably aren't true.
That's the actual lesson.
OddsIQ provides AI analysis, not financial or betting advice. Past performance does not guarantee future results. Gamble responsibly: BeGambleAware, GamCare, GamStop.