Kelly Criterion
The Kelly criterion sizes a bet from how big your edge is: bet more when the edge is bigger, less when it is smaller, and nothing when there is none.
The formula
Kelly % = (b × p − q) ÷ b
- p is the chance you think the bet wins.
- q is the chance it loses: 1 − p.
- b is what you win per $1 staked. At -110 that is 100 ÷ 110 = 0.909; at +150 it is 1.5.
Worked examples
A favorite you like at -110You think it wins 57% of the time. The price
implies 52.4%.
(0.909 × 0.57 − 0.43) ÷ 0.909 = 9.7% of your bankroll.
On a $1,000 bankroll: $97.
(0.909 × 0.57 − 0.43) ÷ 0.909 = 9.7% of your bankroll.
On a $1,000 bankroll: $97.
An underdog at +150You think it wins 45% of the time. The price implies 40%.
(1.5 × 0.45 − 0.55) ÷ 1.5 = 8.3%.
(1.5 × 0.45 − 0.55) ÷ 1.5 = 8.3%.
No edgeA coin flip at -110: (0.909 × 0.5 − 0.5) ÷ 0.909 =
−5%. A negative answer means do not bet.
Use half or quarter Kelly
Full Kelly is aggressive: 9.7% of a bankroll on one game is far above the 1-5% rule, and the swings are brutal. Kelly also assumes your 57% is right. If it is really 54%, full Kelly overbets badly. So most bettors stake a fraction:
- Half Kelly: 4.85% in the first example, $48.50 on $1,000.
- Quarter Kelly: 2.4%, about $24.
Key takeaways
- Kelly = (b × p − q) ÷ b, where b is your profit per $1 staked.
- It is only as good as your probability estimate.
- Bet a fraction of it, and skip any bet where it comes out negative.
Use it on the boards
Put it to work
The MC Sports model boards rank every player and game, every game day, and show the numbers behind each score.
See the model boards →