Kelly Criterion Calculator

Calculate the mathematically optimal bet size based on your edge and bankroll. Maximize long-term growth while managing risk.

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Understanding the Kelly Criterion

What is the Kelly Criterion?

The Kelly Criterion is a formula developed by John Kelly in 1956 to determine the optimal size of a series of bets. It maximizes the expected logarithm of wealth, which translates to maximum long-term growth rate. The formula balances the tradeoff between betting too much (risking ruin) and betting too little (leaving money on the table).

The Formula

f* = (bp - q) / b

f* = fraction of bankroll to bet

b = decimal odds - 1 (net odds)

p = probability of winning

q = probability of losing (1 - p)

Why Use Fractional Kelly?

Full Kelly betting is mathematically optimal but assumes you know your exact edge—which you rarely do. Estimation errors can lead to overbetting. Most professional bettors use fractional Kelly (typically half or quarter) to account for uncertainty and reduce variance. Half Kelly achieves 75% of the growth rate with significantly less volatility.

Important Considerations

  • Kelly assumes you can accurately estimate your win probability
  • It maximizes long-term growth, not short-term profits
  • Overbetting (betting more than Kelly suggests) reduces long-term growth
  • The formula assumes bets are independent and you have unlimited opportunities
  • Real-world factors like bet limits and bankroll constraints matter

Kelly Fraction Comparison

Fraction Growth Rate Volatility Best For
Full Kelly (100%) Maximum Very High Theoretical only
Half Kelly (50%) ~75% of max Moderate Recommended for most
Quarter Kelly (25%) ~50% of max Low Conservative bettors
Eighth Kelly (12.5%) ~25% of max Very Low Risk-averse / uncertain edge