What is the Kelly Criterion
The Kelly criterion is a mathematical formula that calculates the optimal percentage of your bankroll you should bet to maximize long-term growth, given a positive edge.
It was developed by John L. Kelly Jr. in 1956 and is widely used by traders, investors, and professional bettors.
The formula
f* = (bp − q) / b
Where:
- f* = fraction of the bankroll to bet
- b = net profit per unit bet (odds − 1)
- p = estimated probability of winning
- q = estimated probability of losing (1 − p)
Practical example
You have a match with odds 2.50 and estimate the probability of winning as 50%:
- b = 2.50 − 1 = 1.50
- p = 0.50
- q = 0.50
f* = (1.50 × 0.50 − 0.50) / 1.50 = 0.25 / 1.50 = 16.7%
Kelly says you should bet 16.7% of your bankroll.
Why Kelly is the mathematical "optimal"
Kelly maximizes the logarithm of the bankroll, which is equivalent to maximizing the long-term growth rate. It is the only system that guarantees growing the bankroll at the maximum possible rate given a positive edge.
The problem with Kelly: it’s too aggressive
The full Kelly formula can lead to very large bets. A 16.7% bet of your bankroll on a single wager is huge and can cause quick ruin if your probability estimate is slightly off.
That’s why in practice most professionals use fractional Kelly.
Fractional Kelly: the professional standard
Fractional Kelly consists of betting only a fraction of the full Kelly. The most common fractions are:
| Fraction | Bet (in the example) | Aggressiveness |
|---|---|---|
| Full Kelly | 16.7% | Very high |
| 1/2 Kelly | 8.3% | High |
| 1/4 Kelly | 4.2% | Moderate |
| 1/10 Kelly | 1.7% | Conservative |
Most professionals use between 1/4 and 1/2 Kelly.
Fractional Kelly sacrifices some growth speed in exchange for greater protection against estimation errors. It is the practical optimal balance.
How to apply Kelly with Oddfolio
To apply Kelly you need two data points per pick:
- Your estimated probability (p)
- The available odds (which gives b)
Calculate f*, multiply it by the chosen fraction and your current bankroll. That is your stake for that bet.
With Oddfolio record the applied stake and compare results between picks where you used Kelly and where you didn’t. Over time you will see if Kelly improves your performance.
When NOT to use Kelly
- When you don’t have enough confidence in your probability estimate
- When you have fewer than 200 bets recorded (not enough sample)
- When the market is illiquid (the bookmaker may limit or close accounts)
Conclusion
Kelly is the mathematical basis of professional staking. Use it as a guide, not a dogma. Start with 1/4 Kelly or less, record your bets with Oddfolio, and review if your estimated edge is confirmed by real data.