The Kelly Criterion: How Much to Bet
Bet too little and your money grows slowly; bet too much and volatility drags you down. The Kelly criterion finds the bet size that grows wealth fastest over the long run.
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Text version · Risk Management & Trading Psychology, lesson 5: “The Kelly Criterion: How Much to Bet”
Bet too little and your money grows slowly; bet too much and volatility drags you down. The Kelly criterion finds the bet size that grows wealth fastest over the long run.
The bet size that grows fastest
Kelly criterion: f* = win rate − loss rate ÷ payoff ratio. As you raise the bet size from 0, long-run growth first rises, then falls; the peak is the Kelly fraction.
Edge ÷ payoff
The Kelly fraction also equals expectancy ÷ payoff ratio. At a 55% win rate and 1:1, the expectancy is 0.1R, so Kelly is 10%. No edge, no bet; overestimate your edge by double and you'll bet double too.
Why traders use half Kelly
Betting the full Kelly fraction brings huge drawdowns, and real win rates and payoff ratios can only be estimated. Betting half Kelly keeps about three quarters of the long-run growth with much smaller drawdowns.
Key takeaways
- Kelly fraction f* = win rate − loss rate ÷ payoff ratio, which also equals expectancy ÷ payoff ratio. A negative result means you shouldn't take the bet.
- Bet more than Kelly and long-run growth actually slows; bet more than twice Kelly and your wealth tends to shrink.
- In practice, "half Kelly" is common: you keep about three-quarters of the growth for a much smaller drawdown, and leave room for estimation errors.
Try it yourself
You can do these exercises in this lesson's interactive simulation:
- Default 55% win rate, 1:1 payoff ratio: what's the Kelly fraction? Drag the bet size there: what's the growth per trade?
- Drag the bet size to 5% (half Kelly): what's the growth per trade now? Roughly what fraction of Kelly's growth is it?
- Drag the bet size to 25% (more than twice Kelly): what does the growth rate become? Where does the orange wealth line go?
- Lower the win rate to 45%: what does the Kelly fraction become? What does the explanation card say?
Quiz and explanations
- 1. A 60% win rate with a 1:1 payoff ratio. What's the Kelly fraction?
- Answer: 20%.0.6 − 0.4 ÷ 1 = 0.2.
- 2. If you bet 3 times the Kelly fraction every time, what's the most likely long-run result?
- Answer: Wealth tends to shrink.When you overbet, the drag from losses outweighs the gains, and the long-run growth rate turns negative.
- 3. A 40% win rate with a 2:1 payoff ratio. What's the Kelly fraction?
- Answer: 10%.0.4 − 0.6 ÷ 2 = 0.1, which is also expectancy 0.2R ÷ payoff ratio 2 = 10%.
Terms in this lesson
- Kelly criterion (Kelly Criterion): The bet size that grows wealth fastest over time: win rate − loss rate ÷ payoff ratio; traders often use half of it to reduce swings.
- risk/reward ratio (Risk : Reward): Money you could lose : money you could make; 1:2 means risking $1 to aim for $2.
- win rate (Win Rate): The share of all trades that made money.