Kelly Criterion Calculator
Calculate optimal bet size for maximum bankroll growth
Bet Parameters
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Kelly Fraction
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Kelly Results
Optimal bet size calculated
Kelly Breakdown
Your Edge
+6.67%
Full Kelly %
10.00%
Break-Even
33.3%
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Common Kelly scenarios
Kelly Bankroll Simulator
Monte Carlo simulation with 1,000 iterations
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Kelly Criterion Formula
Mathematical basis for optimal betting
Quick Answer
TL;DR summary
The Kelly Criterion formula is f^* = \frac{bp - q}{b}, where b = decimal odds - 1, p = win probability, q = loss probability. For +200 odds (b=2) with 40% win probability: f^* = \frac{2 \times 0.4 - 0.6}{2} = 10\%. Bet 10% of bankroll. Most bettors use Half Kelly (5%) to reduce variance.
Key Facts About Kelly Criterion
Important things to know
- Kelly Criterion maximizes long-term bankroll growth mathematically
- Full Kelly is aggressive and can lead to large swings (50%+ drawdowns)
- Half Kelly provides ~75% of the growth with significantly less variance
- Quarter Kelly is conservative, ideal for uncertain edge estimates
- Negative Kelly means don't bet - you have negative expected value
- Kelly assumes you know your true edge precisely (you usually don't)
- Professional bettors typically cap single bets at 2-5% of bankroll regardless of Kelly
Frequently Asked Questions
Common questions about Kelly betting
What is the Kelly Criterion?
The Kelly Criterion is a mathematical formula for determining optimal bet size to maximize long-term bankroll growth. Developed by John Kelly at Bell Labs in 1956, it balances risk and reward by betting proportionally to your edge. Larger edges warrant larger bets; smaller edges warrant smaller bets.
Why use Half Kelly instead of Full Kelly?
Full Kelly betting is mathematically optimal for growth but causes extreme variance. Half Kelly achieves about 75% of full Kelly's growth rate with much smoother results. Since we never know our true edge precisely, fractional Kelly protects against overestimating our edge, which is common.
When does Kelly say not to bet?
When Kelly outputs zero or negative, it means you have no edge or negative expected value. The formula will never suggest betting more than 100% of bankroll or on -EV propositions. A Kelly of 0% means the break-even point - your estimated win rate exactly equals the implied probability.
What about multiple simultaneous bets?
Simultaneous Kelly is more complex. For uncorrelated bets, you can sum individual Kelly fractions, but this increases variance. Many bettors use a "Kelly cap" (e.g., max 25% total exposure) or reduce each bet proportionally. For correlated bets, the math becomes significantly more complex.
What's the risk of ruin with Kelly betting?
True Kelly betting has 0% risk of ruin theoretically - it never bets everything and scales down as bankroll shrinks. However, real-world factors (estimation errors, minimum bet sizes, correlated bets) can cause ruin. Half Kelly dramatically reduces ruin risk in practice.
Should I ever bet more than Kelly suggests?
No. Betting more than Kelly ("over-betting") reduces long-term growth and increases variance exponentially. At 2x Kelly, your expected growth rate equals 0 - you're gambling with no mathematical edge despite having one. At 3x Kelly, you expect to lose money long-term.