What Is the Kelly Criterion?
The Kelly Criterion is a position-sizing formula used to determine how much of your bankroll to risk when you have an edge. Instead of guessing a bet size, Kelly gives a mathematically grounded percentage designed to maximize long-term bankroll growth while avoiding overbetting.
It was originally developed for information theory and later adopted in gambling, investing, and quantitative trading. In practical terms, it answers one key question: “If I believe this bet is favorable, how much should I stake?”
The Formula
For decimal odds, the full Kelly fraction is:
f* = (b × p − q) / b
- f* = fraction of bankroll to wager
- b = net odds (decimal odds − 1)
- p = probability of winning
- q = probability of losing = (1 − p)
If the result is zero or negative, Kelly says you should not place the bet. That usually means your edge is not positive at the offered odds.
How to Use This Kelly Calculator
1) Enter Your Bankroll
Use your current risk capital, not your total net worth. Kelly is built around preserving and compounding a dedicated bankroll.
2) Estimate Win Probability
This is the hardest part. Your probability estimate should come from data, a model, or disciplined analysis—not intuition alone.
3) Enter Decimal Odds
Decimal odds include your stake in the payout. For example, 2.00 means you double your money on a win (stake returned + profit).
4) Choose Fractional Kelly
Full Kelly can be aggressive and volatile. Many people use half Kelly (50%) or quarter Kelly (25%) to reduce drawdowns and model error risk.
Example
Suppose your bankroll is $10,000, your estimated win probability is 55%, and the offered odds are 2.00.
- Net odds b = 2.00 − 1 = 1.00
- p = 0.55, q = 0.45
- Full Kelly: (1.00 × 0.55 − 0.45) / 1.00 = 0.10
Full Kelly suggests staking 10% of bankroll ($1,000). Half Kelly would suggest 5% ($500).
Why Fractional Kelly Is Popular
Kelly assumes your edge estimate is accurate. In reality, probability estimates are noisy and uncertain. Fractional Kelly helps manage that uncertainty.
- Lower volatility
- Smaller drawdowns
- Less sensitivity to model error
- Easier psychologically during losing streaks
Common Mistakes
- Overestimating your edge: the #1 reason Kelly sizing backfires.
- Ignoring bankroll discipline: recalculating from a true bankroll is essential.
- Using full Kelly with uncertain models: often too aggressive.
- Confusing odds formats: make sure you are entering decimal odds correctly.
Final Thoughts
The Kelly Criterion is a powerful tool for rational risk sizing. Used properly, it prevents random bet sizing and supports long-term geometric growth. Used carelessly, it can amplify mistakes in your assumptions.
Treat this calculator as a decision support tool—not a guarantee. Your edge estimate quality matters more than the formula itself.