How much should you stake with the Kelly criterion?
Your edge divided by the net odds, as a share of your bankroll: 5.5% for a bettor who wins 55% at −110. Most bettors who use it stake half or a quarter of that, because the full stake swings hard and is too big whenever the real edge is smaller than the estimate.
At −110 with a 55% win rate the Kelly stake is 5.5% of the bankroll. Over 1,000 bets the median simulation turned 1,000 into 3,967 at full Kelly and 2,808 at half Kelly, but 42.2% of the full-Kelly simulations were down to half at some point, against 9.5% at half Kelly.
Run these bets in the simulatorThe house edge of every sports bet
A bettor who wins 55% over 1,000 bets, by Kelly multiple
| Plan | Stake, share of bankroll | Median final bankroll | Down to half at some point | Finished ahead |
|---|---|---|---|---|
| Quarter Kelly | 1.38% | 1,826 | 0.4% | 92.6% |
| Half Kelly | 2.75% | 2,808 | 9.5% | 89.6% |
| Full Kelly | 5.50% | 3,967 | 42.2% | 81.3% |
| Twice Kelly | 11.00% | 981 | 82.7% | 49.1% |
| Full Kelly stake, but the real win rate is 53% | 5.50% | 482 | 78.5% | 34.3% |
Each row is 10,000 simulations of 1,000 bets at −110, starting with 1,000, seed “cgs”. The link above replays the highlighted row. The last row stakes what Kelly gives a 55% bettor while really winning 53%: an estimate two points too high.
Why
Kelly is the stake that makes a bankroll grow fastest over a long run of bets whose edge is known. Stake less and it grows more slowly but more smoothly. Stake more and the swings eat the growth: at about twice Kelly the long-run growth is gone. The catch is the word “known”. The formula takes your win rate as a fact, and a win rate measured over a few hundred bets is not one.