What is the Kelly Criterion?

zach wick

The Kelly Criterion is a mathematical formula used to determine the optimal amount of money to bet in a given situation, based on the probability of winning and the potential payout of the bet.

The Kelly Criterion is expressed as follows:

f = (bp - q) / b


  • f is the fraction of the bankroll to wager
  • b is the odds received on the bet (in decimal format)
  • p is the probability of winning the bet
  • q is the probability of losing the bet (1 - p)

Using the Kelly Criterion

In sports betting, the Kelly Criterion can be used to determine the optimal amount to bet on a particular game or outcome. For example, if a bettor believes that a team has a 60% chance of winning and the odds for that team to win are 2.00, then the Kelly Criterion formula can be used to calculate the optimal amount to bet:

f = (0.6 x 2.00 - 0.4) / 2.00 = 0.1

In this example, the Kelly Criterion suggests that the bettor should wager 10% of their bankroll on the bet. This is because the expected value of the bet (the potential payout multiplied by the probability of winning) is greater than the expected value of not betting, and the bettor should therefore bet a portion of their bankroll that maximizes their long-term returns.

Interpreting a negative result

Suppose a bettor believes that the New York Knicks have a 40% chance of winning a basketball game, and the sportsbook is offering odds of +150 on the Knicks (which means a bet of $100 would pay out $150 in winnings, plus the original $100 stake returned). Using the Kelly Criterion formula, we can calculate the optimal bet size.

Converting the American odds of +150 to decimal odds, we get:

b = (150 / 100) + 1 = 2.5

Then, plugging in the values:

f = ((0.4 x 2.5) - 0.6) / 2.5 = -0.08

The result is negative, which means that the Kelly Criterion suggests the bettor should not place a bet on this game. This is because the expected value of the bet is negative, and the bettor would be better off not placing a bet.

In general, if the Kelly Criterion calculation produces a negative result, it means that the bettor should not place a bet on that particular outcome, as the expected value is negative.


It is important to note that the Kelly Criterion assumes perfect knowledge of the true probabilities and payouts of each bet, which is often not the case in sports betting. It is also important for bettors to manage their bankroll appropriately, and not bet more than they can afford to lose, even if the Kelly Criterion suggests a larger wager.

If you or someone you know has a gambling problem and wants help, call 1-800-GAMBLER.