# Daily Fantasy Sports Risk Management – Use the Kelly Criterion to determine bet size

Selecting the optimal bet size for a Daily Fantasy Sports game is key to managing the risk associated with the game. If you bet your entire balance in one game, one loss means you are out of the game until you redeposit. On the other hand, making a small bet means your balance will grow slowly.

Did you know that there is a large body of research supporting the use of the Kelly Criterion to select the optimal bet size based on two factors (1) prior knowledge of the payout and (2) the probability of success? Both factors can be determined by the Daily Fantasy Sports player and the optimal fraction of your account balance to wager can be determined.

The standard Daily Fantasy 50/50 games has two outcomes (1) lose the entire amount bet or (2) win the total pool bet minus 10% rake divided by all players, which works out to 1.8 times your bet. That is, playing a $10 “50/50 game” will mean you win nothing or you win $18.

All Daily Fantasy Players should be tracking their win and loss record. The total number of Wins divided by the total games played will determine your past probability of success. As an example, suppose your record is 15 Wins and 9 Losses. Your past probability of success is 15 / ( 15 + 9 ) = 15/24 = 62.5 %.

The Kelly Criterion can now be used to determine the optimal size of the bet.

F = (( P * ( b + 1 )) – 1 ) / b

Where

F is the fraction of the account balance to wager

b is the amount received on the wager, which is 0.8 as detailed above

p is the probability of winning

So if your past probability of success is 0.625, the Kelly Criterion suggests the optimal bet size to be:

F = (( 0.625 * ( 0.8 + 1 )) – 1 ) / 0.8 = (1.125 – 1 ) / 0.8 = 0.1563

This means that at this point in time, selecting 15.63% of your account balance is the optimal amount to wager. If your probability of success improves, the fraction will grow larger.

For 50/50 games, the formula can be simplified to just:

F = (2.25 * p) – 1.25

Example: Probability is 0.625

Kelly Criterion Fraction F = (2.25 * 0.625) – 1.25 = 0.1563

The attached graphic provides a handy guide to the Kelly Criterion for 50/50 games.

In the above example, we used the performance of the past 24 games played to determine the probability of winning. If your playing strategy changed in that period you may want to consider using a shorter number of games to get a more representative number of your skill. And, as always, you never want to wager more then you would be comfortable losing. Use of the Kelly Criterion can be helpful in setting an upper limit to your wager.

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