The Kelly criterion is the mathematically optimal strategy for sizing bets when you have a positive edge. Developed by John L. Kelly Jr. at Bell Labs in 1956, it answers the question every bettor faces: not whether to bet, but how much. Unlike flat betting or intuitive sizing, Kelly maximises the long-run growth rate of your bankroll — and does so in a provably optimal way.
Why Kelly beats flat betting in the long run
Flat betting — wagering the same dollar amount every time — ignores two facts: your bankroll changes with each result, and the optimal bet changes with your bankroll. Kelly betting fixes a fraction of your current bankroll rather than a fixed amount, so bets shrink after losses (protecting capital) and grow after wins (exploiting momentum).
The result is a higher geometric growth rate. Because compounding works on percentages rather than absolute dollars, even a small improvement in the per-bet growth rate compounds to a large difference over hundreds of bets. The simulator in the Bankroll Growth tab lets you see this directly: Kelly's curve pulls away from flat betting as the number of bets increases.
Why professionals use fractional Kelly
Full Kelly is theoretically optimal but rests on an assumption rarely met in practice: that your edge estimate is exactly correct. In reality, estimating win probability with precision is hard. If your true edge is lower than you believe, Full Kelly overbets — and overbetting is ruinous. A 2× Kelly bet has the same expected long-run growth as not betting at all, and anything above that destroys bankroll geometrically.
Half Kelly solves this elegantly. It achieves roughly 75% of Full Kelly's growth rate while reducing variance by 50%. For bettors who acknowledge uncertainty in their edge estimates, Half Kelly is the dominant choice: the growth sacrifice is small, the ruin protection is substantial. Quarter Kelly is appropriate when edges are highly uncertain or bankrolls are large relative to the bet market.
Limits of the Kelly criterion
Kelly assumes independent, identically distributed bets and a fixed, known edge. Both assumptions break down in practice. Many bets are correlated (same game, same bettor, same market conditions), and edge estimates carry estimation error that can be larger than the edge itself.
The ruin probability shown here is a continuous approximation — it underestimates true ruin risk in short runs and when bets are large relative to the bankroll. Kelly also does not account for transaction costs, limits, or the time value of money. Use it as a sizing guide rather than a mechanical rule, and always apply a multiplier below 1.0 if you have any doubt about your edge estimate.