Kelly Criterion Calculator
Estimate how much of your bankroll to risk per bet using the Kelly formula. Enter your win probability and decimal odds.
What Is the Kelly Criterion?
The Kelly Criterion is a bet sizing formula designed to maximize long-term bankroll growth when you have an edge. In plain English: it helps you decide how much to bet, not whether a bet is good in the first place.
It came from information theory and has become popular in sports betting, poker, trading, and portfolio sizing. The core idea is simple: when your edge is bigger, you can risk more; when your edge is smaller, you should risk less.
The Kelly Formula (for Decimal Odds)
For decimal odds, define:
- p = probability of winning (as a decimal, so 55% is 0.55)
- q = probability of losing = 1 - p
- b = net odds = decimal odds - 1
Then Full Kelly fraction is:
f* = (b × p - q) / b
If the result is negative, your estimated edge is not positive and Kelly recommends no bet.
How to Use This Kelly Criterion Calculator
1) Enter your win probability
This is your estimate, not the market’s. If your estimate is poor, your Kelly result will be poor. Good probability modeling matters more than the formula itself.
2) Enter decimal odds
Example: odds of 2.10 mean a $1 stake returns $2.10 total on a win (including stake), so net profit is $1.10.
3) Choose Full or Fractional Kelly
Many people use half-Kelly (0.50) or quarter-Kelly (0.25) to reduce volatility and estimation risk.
4) Add bankroll (optional)
If you enter bankroll, the calculator converts your Kelly percentage into a dollar stake recommendation.
Understanding the Output
- Full Kelly %: The mathematically optimal fraction for maximum long-run growth under perfect assumptions.
- Applied Kelly %: Full Kelly multiplied by your chosen fraction (for safer sizing).
- Expected Value (EV): Estimated profit per $1 staked. Positive EV is required for Kelly to suggest a positive bet.
If Full Kelly is below zero, you likely do not have an edge at the odds you entered.
Why Many Professionals Use Fractional Kelly
Full Kelly can be aggressive, especially when your probability estimate has uncertainty. Fractional Kelly is common because it:
- Reduces drawdown size
- Lowers emotional pressure during losing streaks
- Protects against overconfidence in edge estimates
- Still captures much of the long-term growth benefit
Practical Example
Suppose you estimate a 55% win probability and can bet at decimal odds of 2.10.
- p = 0.55
- q = 0.45
- b = 1.10
Full Kelly = (1.10 × 0.55 - 0.45) / 1.10 = 0.1409, or about 14.09% of bankroll.
Half-Kelly would be roughly 7.05% of bankroll.
Common Mistakes to Avoid
- Confusing odds formats: This calculator uses decimal odds.
- Overestimating win probability: Small probability errors can dramatically change recommended stake.
- Ignoring model uncertainty: Fractional Kelly helps, but humility helps more.
- Using Kelly without edge: No edge means no positive Kelly bet size.
- Going all-in on one estimate: Diversification and risk limits still matter.
Kelly Criterion for Investing vs Betting
In betting, odds are explicit. In investing, “odds” and “probabilities” are inferred, which makes inputs noisier. The Kelly framework is still useful as a risk-sizing mindset: increase position size with stronger expected edge and confidence, and decrease when uncertainty is high.
Final Takeaway
The Kelly Criterion is one of the best-known frameworks for bankroll management and bet sizing. It does not create an edge; it helps you size intelligently if an edge exists. Use conservative assumptions, consider fractional Kelly, and focus heavily on improving your probability estimates.