What is the Kelly criterion in betting?
The Kelly criterion is a staking formula that tells you what percentage of your bankroll to bet, based on the odds and your estimated edge, in order to maximise long-term bankroll growth.
Most staking plans ignore how good the bet is. Kelly doesn’t. Big edge, bigger stake. Small edge, smaller stake. No edge, no bet. It was worked out by John Kelly at Bell Labs in 1956 and later adopted by gamblers and investors. It’s used the same way on both sides of the Atlantic.
Example
The formula:
Stake % = (b × p − q) ÷ b
- b = decimal odds minus 1
- p = your estimated chance of winning
- q = chance of losing (1 − p)
You have a $1,000 bankroll. The odds are 2.50, so b = 1.5. You rate the chance at 45%, so p = 0.45 and q = 0.55.
- (1.5 × 0.45 − 0.55) ÷ 1.5
- (0.675 − 0.55) ÷ 1.5
- 0.125 ÷ 1.5 = 8.3%
Full Kelly says stake $83. Now drop your estimate to 40%, which is exactly what the odds imply: (1.5 × 0.40 − 0.60) ÷ 1.5 = 0. Kelly says don’t bet. Below 40% the answer goes negative, which also means don’t bet.
Watch out
Kelly assumes you know the true probability. You don’t. Nobody does. And the formula punishes overconfidence hard: feed it a 45% that’s really 41% and it tells you to bet far too much on a bet with almost no edge.
Full Kelly is also a wild ride even with perfect inputs. Deep drops in your bankroll are part of the package.
That’s why almost everyone who uses it bets a fraction:
- Half Kelly: about $42 in the example above.
- Quarter Kelly: about $21.
You give up some growth and get a much smoother ride. If you’re newer to this, flat stakes of 1–2% are simpler and safer. My bankroll management guide compares the options.