Kelly Criterion
A simple formula that tells you the best bet size to use based on your edge and how big your bankroll is.
The Kelly Criterion is a staking formula that John L. Kelly Jr. came up with back in 1956. It works out the mathematically best slice of your bankroll to put on a bet that has positive expected value. The idea is to juggle two goals at once: growing your money as fast as possible while keeping the chance of going broke low. By sizing every bet to match your edge and the odds on offer, Kelly aims to grow a bankroll quicker than any other staking method over time, without ever risking so much on one wager that a single loss wipes you out.
The core formula is: Kelly % = (bp - q) / b, where b is the decimal odds minus 1, p is your chance of winning, and q is your chance of losing (1 - p). The answer is the share of your bankroll to stake. In real life, lots of bettors go with a fractional Kelly, usually staking a quarter or a half of the full amount, to take the edge off the wild swings that aggressive sizing brings. Full Kelly is the best on paper, but it can lead to big ups and downs that most people just don’t enjoy.
Example
Say you reckon a team has a 60% chance of winning, and the book is offering +120 (decimal 2.20). Plug it into Kelly: b = 1.20, p = 0.60, q = 0.40. Kelly % = (1.20 x 0.60 - 0.40) / 1.20 = (0.72 - 0.40) / 1.20 = 0.267, or 26.7% of your bankroll. With a $1,000 bankroll, full Kelly would be $267. Plenty of bettors would instead go half Kelly ($133.50) or quarter Kelly ($66.75) to smooth things out and leave room in case that 60% guess is a little off.
Key Points
- Maximizes long-term growth: Out of all fixed-fraction staking plans, Kelly grows your bankroll the fastest when your probability estimates are spot on.
- Sensitive to probability errors: If your true win-probability guess is even a bit wrong, Kelly can suggest bets that are too big, raising the risk of nasty drawdowns.
- Fractional Kelly is standard practice: Most seasoned bettors use a fraction (commonly 25% to 50%) of full Kelly to cut volatility and build in a cushion against estimation errors.
- Never bets on negative EV: The formula naturally spits out zero or a negative number for bets with no edge, telling you not to stake anything.
- Dynamic sizing: Kelly staking automatically adjusts your bet sizes as the bankroll moves, betting more after wins and less after losses.