Kelly Criterion Calculator
Compute the theoretically optimal bet size that maximizes long-term log-growth of your bankroll. Includes a growth-curve simulation showing why fractional Kelly is usually safer.
Inputs
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Result
Growth simulation
Log-scale bankroll over time. Full Kelly grows fastest but has highest drawdown. Half-Kelly often gives ~75% of the growth with much less variance.
What Kelly actually says
For a bet that wins with probability p and pays b:1, the Kelly fraction is:
f* = (bp − q) / b, where q = 1 − p
Betting f* maximizes the long-term growth rate of your log-bankroll, which is equivalent to minimizing the time to reach a target. Kelly is provably optimal in the limit but assumes you know p and b exactly. Real-world estimates are noisy, so most serious practitioners use "fractional Kelly" (½ or ¼ Kelly).
Who uses it
- Sports bettors sizing wagers against sharp lines.
- Traders position-sizing individual bets.
- Information theorists gambling on Huffman codes and similar.
Limitations
- If you overestimate p, full Kelly can blow up — the chart shows this dramatically.
- Kelly says nothing about utility curves. A risk-averse bettor should use a smaller fraction.
- Negative Kelly (when f* < 0) means: don't make this bet at all. The tool will warn.