The Kelly Criterion: How Much to Actually Stake on a +EV Bet
A positive EV number tells you a bet is worth making. It says nothing about how much to bet. Here's the Kelly criterion formula, a worked example, and why most bettors should use a fraction of it.
Finding a bet with positive expected value tells you the bet is worth making. It tells you nothing about how much of your bankroll to put on it. Bet too little and a real edge takes forever to show up in your results. Bet too much and normal variance — not bad luck, just ordinary variance — can wipe you out even with a genuine edge. The Kelly criterion is the standard formula for closing that gap.
The formula
f = (bp - q) / b
Where:
f= fraction of your bankroll to stakeb= the net odds received, as a decimal (e.g.+150pays 1.5 units of profit per unit staked, sob = 1.5)p= your estimated probability of winningq= probability of losing, or1 - p
The formula is really just a ratio: your edge (bp - q, the same quantity behind the EV calculation) divided by the payout odds. A bigger edge argues for a bigger stake; longer odds argue for a smaller one, because a single loss costs more relative to bankroll.
A worked example
Take a bet at +150 (b = 1.5) where your model gives a 48% win probability (p = 0.48, q = 0.52):
f = (1.5 × 0.48 − 0.52) / 1.5
f = (0.72 − 0.52) / 1.5
f = 0.20 / 1.5
f ≈ 0.133
Full Kelly says stake about 13.3% of your bankroll on this single bet. For almost anyone, that number should immediately look too aggressive — and that instinct is correct.
Why full Kelly is rarely used in practice
Kelly is mathematically optimal for maximizing long-run bankroll growth if your probability estimate is exactly correct. That "if" is the entire problem. Every model probability is an estimate, not a certainty, and Kelly's stake size is extremely sensitive to overestimating your edge. A model that thinks it has a 5% edge but actually has a 1% edge — a very easy mistake to make — gets full-Kelly-sized into bets far larger than the real edge justifies, and the resulting swings can be brutal even when the model is directionally right.
The standard fix is fractional Kelly: stake some fraction — commonly a half or a quarter — of what the formula recommends.
half-Kelly stake = f / 2
In the example above, half-Kelly is about 6.6% of bankroll instead of 13.3%. You give up some long-run growth rate in exchange for a meaningfully smoother ride and much more protection against a model that's more confident than it should be.
| Approach | Stake (example above) | Trade-off |
|---|---|---|
| Full Kelly | ~13.3% | Fastest theoretical growth, highest variance, most exposed to model error |
| Half Kelly | ~6.6% | Common professional default — most of the growth, far less swing |
| Quarter Kelly | ~3.3% | Conservative, appropriate when confidence in the model is lower |
What this doesn't solve
Kelly sizing doesn't make a bad probability estimate good — it just sizes whatever estimate you feed it. Garbage in still produces a confidently-sized garbage stake out. It also assumes each bet is independent and that you're willing to size relative to your current bankroll after each result, which is a discipline most bettors don't actually follow.
The honest takeaway
A positive EV number answers "is this worth betting." Kelly — almost always some fraction of it — answers "how much." Treat both as inputs to a process, not guarantees: the formulas are only as good as the probability estimate underneath them, which is exactly the caveat we give every number in our EV calculator.
This piece is educational and reflects general statistical concepts — not a recommendation to place any specific bet.