Calculateur du Critère de Kelly

The Kelly Criterion is a mathematical formula that determines the optimal size of a bet as a fraction of your total bankroll. Developed by John L. Kelly Jr. in 1956, it maximizes the expected geometric growth rate of wealth over repeated bets. The formula is f* = (bp − q) / b, where b is the net odds, p is the win probability, and q is the loss probability.

To calculate the Kelly bet size: (1) estimate your probability of winning, (2) determine the odds being offered, (3) plug both into f* = (bp − q) / b, where b = decimal odds − 1 and q = 1 − p. Multiply the resulting fraction by your bankroll to get the dollar amount. For example, with a 55% win probability at even money (2.00 decimal), Kelly says bet 10% of your bankroll.

Half Kelly means betting 50% of the amount the full Kelly formula recommends. It's popular because probability estimates are never perfectly accurate, and even small overestimates of your edge can lead to catastrophic overbetting. Half Kelly sacrifices roughly 25% of the theoretical growth rate but reduces variance by about 50%, giving you a much smoother ride and significant protection against estimation errors.

Yes, the Kelly Criterion works for any repeated bet where you have a positive expected value. In sports betting, your key challenge is accurately estimating the true probability of each outcome. If your probability model is well-calibrated, Kelly sizing will maximize long-term bankroll growth. Most sharp sports bettors use fractional Kelly (25–50%) to account for model uncertainty.

Betting more than the Kelly amount — known as overbetting — actually decreases your expected long-term growth rate despite increasing short-term expected value. In the extreme, consistently betting 2x Kelly leads to expected zero growth. Overbetting increases the probability of large drawdowns and can turn a profitable strategy into a losing one through excessive variance. This is why many professionals prefer fractional Kelly.

The Kelly formula is derived by maximizing the expected value of the logarithm of wealth (geometric mean return) over repeated independent bets. Taking the derivative of E[log(W)] with respect to the bet fraction f and setting it to zero yields f* = (bp − q) / b. This approach is equivalent to maximizing the long-run compounding rate and was originally developed in the context of information theory for optimizing signal transmission.

On a prediction market, the market price of a YES or NO contract is its implied probability — a contract trading at $0.60 implies a 60% chance. To size a position with Kelly, compare your own probability estimate to that implied price: your edge is the gap between them. Enter your estimated win probability and the contract's implied odds into the calculator to get the Kelly fraction. Because your estimate is uncertain, most traders use half or quarter Kelly.

Usually not. Full Kelly assumes your probability estimate is exactly right, which is rarely true on Polymarket or Kalshi where information is noisy. Overestimating your edge leads to overbetting and large drawdowns. Fractional Kelly (half or quarter) sacrifices a little theoretical growth for much lower variance and a smaller chance of ruin — a sensible default for prediction-market position sizing.