Enter your odds or return assumptions to see the Kelly bet size, how growth changes with the fraction you bet, the payoff of each outcome, and a simulation of how different bet sizes play out over time.
A bet you either win or lose. Kelly: f = p − (1 − p) ÷ b
Annual figures. Kelly: f = (μ − r) ÷ σ²
Possible outcomes for one holding period. Kelly maximises Σ p × ln(1 + f × return).
| Probability % | Return % |
|---|
Compare any fraction against the Kelly multiples.
Random paths, same luck for every bet size.
Typical compounded growth per bet. The peak is the Kelly fraction; past about 2× Kelly growth turns negative.
Change in your bankroll from one bet, for each outcome.
Log scale.
| Bet size | Fraction | Typical growth | Unlucky (10th) | Median | Lucky (90th) | Chance of halving | Chance of losing money |
|---|
“Typical growth” is the compounded (geometric) rate, exp(E[ln(1 + return)]) − 1. “Chance of halving” is the share of simulated paths that fell to half the starting bankroll or less at any point. The investing model uses monthly steps with normally distributed returns. Educational tool only, not financial advice.