What Is the Kelly Criterion?
The Kelly Criterion is a mathematical formula developed by scientist John L. Kelly Jr. in 1956. Originally designed for signal transmission theory, it was quickly adopted by gamblers and investors as a method for determining the optimal proportion of a bankroll to risk on a given bet. The goal is to maximise the long-term growth rate of your bankroll while avoiding ruin.
The Formula
The standard Kelly formula is:
f* = (bp – q) / b
Where:
- f* = the fraction of your bankroll to stake
- b = the net odds received (decimal odds minus 1)
- p = your estimated probability of winning
- q = your estimated probability of losing (1 – p)
A Worked Example
Suppose you believe a team has a 55% chance of winning (p = 0.55), and the decimal odds available are 2.10 (b = 1.10).
- f* = (1.10 × 0.55 – 0.45) / 1.10
- f* = (0.605 – 0.45) / 1.10
- f* = 0.155 / 1.10
- f* ≈ 0.141 or 14.1% of your bankroll
If the formula returns a negative number, there is no value in the bet and you should not stake anything.
Why Full Kelly Is Rarely Recommended
While mathematically optimal, full Kelly staking leads to extreme volatility in practice. A 14% stake is aggressive, and even a short losing run can be psychologically devastating. Most experienced bettors use a fractional Kelly approach — typically staking 25–50% of the Kelly-suggested amount. This sacrifices some long-term growth rate in exchange for dramatically reduced variance.
| Kelly Fraction | Growth Rate Trade-off | Volatility |
|---|---|---|
| Full Kelly (100%) | Maximum theoretical growth | Very High |
| Half Kelly (50%) | ~75% of full Kelly growth | Moderate |
| Quarter Kelly (25%) | ~56% of full Kelly growth | Low |
The Critical Dependency: Accurate Probability Estimates
The Kelly Criterion is only as good as the probability estimates you feed into it. Overestimating your edge leads to over-staking, which is damaging. The formula assumes your estimated probability is accurate — in reality, even skilled bettors work with uncertain estimates, which is another reason to err toward fractional Kelly.
Practical Steps to Apply Kelly Staking
- Before looking at odds, independently estimate the probability of each outcome you're considering.
- Convert the available odds to implied probability and confirm your edge is positive.
- Apply the Kelly formula to find the suggested stake fraction.
- Multiply by your chosen Kelly fraction (e.g. 0.5 for half Kelly).
- Calculate the actual stake: fraction × current bankroll.
- Record the bet and result in your tracking system.
Is Kelly Right for Every Bettor?
The Kelly Criterion is best suited to bettors who have a demonstrable, calibrated edge and who track their results rigorously. For beginners or recreational bettors, flat staking (a fixed percentage of bankroll per bet) is simpler and just as protective. Kelly becomes increasingly powerful as your ability to estimate probabilities accurately improves over time.
Final Takeaway
The Kelly Criterion is a powerful tool, not a magic solution. Used correctly with fractional application and honest probability estimates, it provides a rational, mathematically grounded approach to bet sizing that can meaningfully improve long-term outcomes.