The Kelly criterion explained simply (and why to use fractional Kelly)
You know a bet has value. The odds pay more than the true probability, and you confirmed it with your model. The million-dollar question is no longer whether to bet, but how much. Betting too little wastes your edge; betting too much can burn your bankroll in a bad run even if you're right in the long run.
The Kelly criterion is the mathematical answer to that question. It's not magic nor a system to get you rich: it's a formula that computes the exact percentage of your bankroll that maximizes its long-term growth, given your edge. In this article we explain it simply, with numbers, and tell you why almost no one who knows what they're doing uses full Kelly.
What the Kelly criterion is
Kelly was born in 1956 at Bell Labs, at the hand of John L. Kelly Jr., to optimize signals on telephone lines. Bettors and investors adopted it because it solves a universal problem: how to size a bet when you know your edge.
The core idea: your stake should be proportional to your edge (how much value you have) and inversely proportional to the risk (how much the odds pay). More edge, you bet more. Riskier odds, you adjust.
Kelly doesn't tell you what to bet. It tells you how much, once you already know the bet has value. Without a real edge, Kelly orders you to bet zero.
The formula, no fear
The version for bets with decimal odds is:
f = (b · p − q) / b
Where:
- f = fraction of your bankroll to bet
- b = the net profit per unit (decimal odds − 1)
- p = your estimated probability of winning
- q = probability of losing (1 − p)
Numerical example
Imagine a match. Your model says the home team wins with 55% probability. The bookmaker offers odds of 2.10.
- b = 2.10 − 1 = 1.10
- p = 0.55
- q = 0.45
f = (1.10 × 0.55 − 0.45) / 1.10 = (0.605 − 0.45) / 1.10 = 0.155 / 1.10 = 0.141
Kelly tells you to bet 14.1% of your bankroll. With a bankroll of $10,000, that's $1,410.
If the odds were 1.90 (implied probability ~52.6%) with the same 55% estimate, your edge would be smaller and Kelly would recommend betting less. And if the odds implied a probability higher than your 55%, f would come out negative: there's no value, you don't bet. To understand why the odds hide a probability, check implied probability in the odds.
Why Kelly maximizes growth
What's elegant about Kelly is that it maximizes the geometric growth of the bankroll, not the expected profit of a single bet. The difference matters: your money compounds bet after bet, and maximizing the arithmetic average of one play leads you to bet it all and go bust on the first loss.
Betting the Kelly fraction guarantees, in theory and with infinite bets, the fastest possible growth rate without risk of total ruin. Any percentage above Kelly grows slower and with more volatility: the worst of both worlds.
The danger of full Kelly
Here comes the radical honesty. Kelly is optimal only under two assumptions that almost never hold:
- You know your true probability precisely. In football you don't know it; you estimate it. Your model has error.
- You have infinite bets ahead. You have a finite bankroll and a finite life.
When you overestimate your edge —and you almost always overestimate it—, full Kelly makes you bet too much. The result is brutal variance:
- Drawdowns (declines from your peak) that can exceed 50% of the bankroll even while being profitable.
- Losing streaks that are psychologically unbearable.
- If your estimated edge is inflated, full Kelly can lead you to negative expected loss without your noticing.
Variance in betting is the reason why being right in the long run doesn't save you from suffering in the short term.
Why almost everyone uses fractional Kelly
The solution serious bettors adopt is fractional Kelly: multiply the Kelly fraction by a factor smaller than 1, typically 1/2 (half Kelly) or 1/4 (quarter Kelly).
Back to the 14.1% example:
| Method | Fraction applied | Stake with a $10,000 bankroll |
|---|---|---|
| Full Kelly | 14.1% | $1,410 |
| Half Kelly (1/2) | 7.05% | $705 |
| Quarter Kelly (1/4) | 3.5% | $350 |
Why does it work so well? Because Kelly's growth is a flat curve near the optimum: with half Kelly you keep around 75% of full Kelly's growth, but you cut the variance in half. You trade a little theoretical profitability for a lot more stability and survival. And since your real edge is uncertain, fractional Kelly protects you from your own estimation errors.
Direct recommendation
- If you're starting out or your model isn't validated: quarter Kelly or even a simpler fixed percentage staking.
- If you have a proven track record and you measure your CLV: half Kelly is the gold standard.
- Full Kelly: practically no one, unless your edge is mathematically exact (it isn't).
At EDGE we integrate a Kelly calculator into the flow of every value bet: you take the model's probability, the available odds, and your bankroll, and you get the stake with the fraction you choose. The "measured, no hype" philosophy means that by default we suggest conservative fractions, not the maximum stake that inflates the ego.
The Kelly criterion is the best tool there is for sizing value bets. But use it fractionally, validate your edge with a betting log, and remember that no formula turns a hunch into an edge.
EDGE is an analysis tool, not a bookmaker. Betting carries risk. 18+. Play responsibly.
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