Kelly Criterion Calculator ā Optimal Bet Size
Calculate the mathematically optimal stake for any bet. Enter your odds and estimated probability to find the Kelly fraction, expected value, and recommended bankroll percentage.
The Kelly Criterion Formula
The Kelly Criterion is a mathematical formula that tells you the optimal percentage of your bankroll to bet on any given outcome. It was developed by John L. Kelly Jr. at Bell Labs in 1956 and has been used by professional bettors, investors, and traders ever since.
Where:
- f* = fraction of bankroll to bet (the Kelly fraction)
- b = net odds (decimal odds ā 1)
- p = your estimated probability of winning
- q = probability of losing (1 ā p)
For decimal odds (most common format), this simplifies to:
Where d is the decimal odds. This is the formula our calculator uses.
How to Use This Calculator
Step 1 ā Enter the odds. Type the decimal odds offered by the bookmaker (e.g. 2.50).
Step 2 ā Enter your probability. This is your estimated probability of winning, not the bookmaker's implied probability. This is the hardest part ā you need to have a model or method for estimating true probabilities.
Step 3 ā Enter your bankroll (optional). If you enter a bankroll amount, the calculator shows the exact stake for each Kelly variant.
Step 4 ā Select a Kelly fraction. We recommend half Kelly (50%) for most bettors. Full Kelly maximizes long-term growth but has extreme short-term variance.
Step 5 ā Click Calculate. The calculator shows your optimal stake, expected value, edge over the bookmaker, and growth rate.
š Example 1: Football Value Bet
You think Liverpool has a 55% chance of winning at odds of 2.00.
| Metric | Calculation | Result |
|---|---|---|
| Net odds (b) | 2.00 ā 1 | 1.00 |
| Kelly fraction | (0.55 Ć 2.00 ā 1) / (2.00 ā 1) | 10% |
| Half Kelly stake | 10% Ć 0.5 | 5% of bankroll |
| EV per unit | 0.55 Ć 1.00 ā 0.45 Ć 1.00 | +ā¬0.10 per ā¬1 staked |
| Edge over book | 55% ā 50% | +5% |
On a ā¬1,000 bankroll, half Kelly recommends a ā¬50 stake on Liverpool at 2.00.
š Example 2: High-E odds Tennis Match
You estimate a 35% chance of an underdog winning at odds of 3.50.
| Metric | Calculation | Result |
|---|---|---|
| Net odds (b) | 3.50 ā 1 | 2.50 |
| Kelly fraction | (0.35 Ć 3.50 ā 1) / (3.50 ā 1) | 8.57% |
| Half Kelly stake | 8.57% Ć 0.5 | 4.29% of bankroll |
| EV per unit | 0.35 Ć 2.50 ā 0.65 Ć 1.00 | +ā¬0.225 per ā¬1 staked |
| Edge over book | 35% ā 28.57% | +6.43% |
On a ā¬1,000 bankroll, half Kelly recommends a ā¬42.90 stake.
š Example 3: Negative EV ā No Bet
You think Team A has a 40% chance at odds of 2.00.
| Metric | Calculation | Result |
|---|---|---|
| Kelly fraction | (0.40 Ć 2.00 ā 1) / (2.00 ā 1) | ā20% (No Bet) |
| EV per unit | 0.40 Ć 1.00 ā 0.60 Ć 1.00 | āā¬0.20 per ā¬1 staked |
The Kelly Criterion returns a negative value ā this means the bet has negative expected value. You should not place this bet. The implied probability (50%) is higher than your estimate (40%), so you're getting bad odds.
Why Half Kelly Is Recommended
Full Kelly maximizes your long-term growth rate, but it comes with extreme short-term volatility. Here's why most professionals prefer half Kelly:
| Kelly Variant | Stake | Bankroll Growth Rate | Max Drawdown Risk | Variance |
|---|---|---|---|---|
| Quarter Kelly | 25% of Kelly | ~37.5% of max | Low (~10-15%) | Low |
| Half Kelly | 50% of Kelly | ~75% of max | Moderate (~15-25%) | Moderate |
| Three-Quarter Kelly | 75% of Kelly | ~93% of max | High (~25-35%) | High |
| Full Kelly | 100% of Kelly | Maximum (100%) | Extreme (~35-50%) | Very High |
Half Kelly gives you 75% of the maximum growth rate while dramatically reducing variance and drawdown risk. It's the sweet spot that most professional sports bettors use.
ā ļø Common Mistakes When Using Kelly
1. Overestimating your edge. The Kelly Criterion is only as good as your probability estimates. If you think an event is 60% likely and it's actually 50%, Kelly will tell you to overbet by a huge margin. Always use conservative estimates.
2. Using Kelly for correlated bets. Kelly assumes each bet is independent. If you're placing multiple bets on the same match or correlated outcomes, the Kelly fraction will overestimate your optimal stake.
3. Ignoring bankroll constraints. Kelly assumes you can bet any fraction of your bankroll. In practice, bookmakers have minimum and maximum stake limits that may prevent you from betting the optimal amount.
4. Betting full Kelly on thin edges. When your edge is small (3-5%), full Kelly still recommends large stakes relative to the edge. Half Kelly or quarter Kelly is safer.
Kelly Criterion in Practice ā 5 Rules
1. Always use fractional Kelly
Unless you're 100% confident in your probability model (you shouldn't be), use half Kelly (50%) as your default. It gives 75% of the growth with a fraction of the variance.
2. Round down, never up
If Kelly says 8.3%, round down to 8%. Being slightly below the optimal stake is always better than being above it ā the penalty for underbetting is small, while the penalty for overbetting grows exponentially.
3. Track your probability estimates
Keep a record of your estimated probabilities alongside actual outcomes. After 100+ bets, compare your calibration. If you predicted events at 60% and they hit 55%, your estimates are slightly optimistic ā adjust down.
4. Don't bet when Kelly is below 2%
Very small Kelly fractions mean the edge is tiny. The transaction cost (time, mental energy, bookmaker margin on future bets) may exceed the expected profit. Set a minimum threshold (2-3% of bankroll) below which you skip the bet.
5. Combine Kelly with value betting
Kelly tells you how much to bet. Our Value Betting Guide teaches you when to bet. Use both together: first identify value bets where your estimated probability exceeds the implied probability, then use Kelly to size them correctly.
Kelly vs Other Staking Methods
| Method | How It Works | Growth Rate | Variance | Risk of Ruin |
|---|---|---|---|---|
| Kelly Criterion | Stake proportional to edge | Maximum | High | Very Low (theoretically 0) |
| Half Kelly | 50% of Kelly stake | 75% of max | Moderate | Extremely Low |
| Flat Staking | Fixed amount per bet | Lower than Kelly | Low | Low |
| Percentage Staking | Fixed % per bet | Lower than Kelly | Low-Moderate | Low |
| Martingale | Double after each loss | Negative (long-term) | Extreme | Very High |
The key advantage of Kelly over flat staking is that Kelly bets more when you have a bigger edge and less when the edge is small. Flat staking treats a 5% edge the same as a 20% edge, which is mathematically suboptimal.
Never use Martingale (doubling after losses). It has negative expected growth and a very high risk of ruin. See our Bankroll Management Guide for more details.