Calculate optimal bet size for maximum bankroll growth
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Optimal bet size calculated
Your Edge
+6.67%
Full Kelly %
10.00%
Break-Even
33.3%
Common Kelly scenarios
Monte Carlo simulation with 1,000 iterations
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Your expected advantage
Percentage of bankroll per bet
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Mathematical basis for optimal betting
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.
Important things to know
Common questions about Kelly betting
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.
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 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.
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.
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.
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.