How to Use the Kelly Criterion in Betting

The Kelly criterion, developed by John Kelly in the 1950s, gives the bet size that maximises the expected growth rate of a bankroll over many bets, given an edge. It stakes more when the edge is larger and the odds shorter, and nothing when there is no edge. It is a staking rule, not a way to find value.

Kelly needs your estimate of the true probability of winning. That might come from a model, from no-vig prices at a sharp market, or both. This is the hardest step and the one that matters most: if your probability is wrong, Kelly will size bets wrongly.

Use decimal odds. For American odds, positive odds become 1 plus odds divided by 100; negative odds become 1 plus 100 divided by the absolute odds. Then b, the net odds, is decimal odds minus one.

Compute f equals b times p, minus q, all divided by b. For example, at decimal odds of 2.10, b is 1.10. If your probability of winning is 52 percent, q is 48 percent. Then f equals 1.10 times 0.52 minus 0.48, divided by 1.10, which is about 0.084, or 8.4 percent of bankroll at full Kelly.

Full Kelly is aggressive. In practice, most bettors stake a fraction, such as a quarter or half of the Kelly amount. In the example, quarter Kelly would be about 2.1 percent of bankroll. Fractional Kelly gives up some growth in exchange for much smaller drawdowns and protection against overestimated edges.

Kelly stakes are a percentage of current bankroll, so stakes grow after wins and shrink after losses. This automatically reduces risk during losing streaks. Recalculate stakes regularly rather than using a fixed amount.

Full Kelly maximises long-run growth only if your probabilities are exactly right. Overestimating your edge leads to overbetting, which can reduce growth sharply and cause large drawdowns. Even with correct estimates, full Kelly produces volatile results that many bettors find hard to sustain.

The simple formula assumes one bet at a time. When several bets run at once, such as many games on a Sunday, staking full Kelly on each can exceed what the bankroll can bear, especially if outcomes are correlated. Reduce stakes, cap total exposure, or use methods designed for simultaneous bets.

Using the bookmaker's implied probability as your p, which gives zero edge by definition; using inflated model probabilities without calibration; betting full Kelly on small edges with high uncertainty; and forgetting to include the margin when converting prices.

If your bets consistently beat the closing line, your probability estimates are likely better than the market's at the time you bet, which supports using Kelly at a modest fraction. If they do not, your edge may be illusory, and Kelly will simply size losing bets.

Record stake, odds, probability estimate, Kelly fraction, closing price, and result for every bet. Over time, compare predicted and actual win rates to check calibration, and adjust your Kelly fraction accordingly.

A common way to estimate p is to remove the margin from a sharp book's prices. Convert each side's odds to implied probability, sum them, and divide each by the sum. The resulting fair probability can be compared with the price available elsewhere. If the best available price implies a lower probability than the fair estimate, Kelly may suggest a stake.

On betting exchanges, commission is charged on net winnings. Reduce the effective odds by the commission before applying Kelly, otherwise stakes will be too large. The same applies to any fee that reduces payouts.

Even fractional Kelly can suggest large stakes when your model sees a big edge. Large apparent edges are often model errors. Many bettors cap any single stake at a small percentage of bankroll regardless of what Kelly suggests, which protects against the most dangerous mistakes.

This page describes what the Kelly formula does to a stake sequence and is not betting advice.