Odds Format
Bankroll ($)
Odds
Win Probability (%)
Kelly Fraction
Results
Enter bankroll, odds and win probability to see results.
What Is It?
The Kelly Criterion is a formula developed by John Kelly Jr. at Bell Labs in 1956. It determines the optimal percentage of your bankroll to wager on a bet where you have an edge. Betting too much risks ruin; betting too little leaves profit on the table. Kelly finds the sweet spot.
The calculator takes your total bankroll, the odds, and your estimated win probability, then outputs the recommended stake as both a percentage of bankroll and a dollar amount. It also shows your edge and the implied probability of the odds.
Many professional bettors and investors use fractional Kelly (half or quarter) to reduce variance while still capturing most of the growth benefit. The calculator supports Full, Half, and Quarter Kelly modes.
How to Use
Formulas & Data Sources
Where: b = Decimal Odds – 1 (the net profit per $1 if you win), p = probability of winning (your estimate, as decimal), q = 1 – p (probability of losing).
If Kelly% is 0 or less, the bet has no edge ā don’t bet.
The win probability is user-supplied. The Kelly formula assumes your probability estimate is accurate ā overestimating your edge leads to overbetting.
Real-World Scenarios
Bankroll: $1,000. Odds: 2.50 (b = 1.50). Your probability: 45%. Kelly% = (1.50 x 0.45 – 0.55) / 1.50 = 8.33%.
This is aggressive ā many would use Half Kelly ($41.65) for safety.
Odds: 1.80 (b = 0.80). Your probability: 50%. Kelly% = (0.80 x 0.50 – 0.50) / 0.80 = -12.5%.
You have a $5,000 bankroll and plan to make 200 bets this season. For a bet at 2.00 with 55% true probability: Full Kelly = 10%.
This approach protects against losing streaks while still growing your bankroll.
Frequently Asked Questions
QWhy not just bet a fixed amount?
Fixed staking ignores edge size. Kelly stakes more on bigger edges and less on smaller ones, maximizing long-term bankroll growth. It’s mathematically optimal for compounding.
QWhy use Half or Quarter Kelly instead of Full?
Full Kelly is very aggressive and assumes your probability estimates are perfect. In practice, estimates have errors. Half Kelly achieves ~75% of the growth rate with much lower variance and risk of ruin.
QWhat if Kelly says to bet 30% of my bankroll?
An unusually high Kelly% usually means your probability estimate is too aggressive or the odds are exceptionally good. Double-check your inputs. Most experienced bettors cap their stake at 5% of bankroll regardless of what Kelly suggests.
QCan Kelly be used for accumulators?
Kelly can be applied to any bet with known odds and an estimated edge. For accumulators, calculate the combined odds and your estimated combined probability, then run Kelly on those values.
