The Kelly Criterion is a math formula that tells you what fraction of your bankroll to wager on a given bet to attain the most rapid possible growth of your bankroll.  It was developed in 1956 by physicist and Bell Labs research scientist John L. Kelly. 

The formula is quite simple from a math standpoint:

f = (bp-q)/b

where

• f is the portion of the current bankroll to wager
• b is the ratio of profit to amount risked on the bet when you win
• p is the probability of winning the bet
• q is the probability of losing the bet (1-p)

If the bet size is 0 or negative,  you should not take the bet.

You will be losing money in the long run. 

A simple illustration of this would be a situation where you are rolling a single die.  If the number rolled in a 6, you win 7 times the amount wagered.  If the number rolled is 1,2,3, or 5, you lose your bet.  What is the optimal amount to bet on this game?

• b = 7
• p = .1667
• q = .8333

f = [(7)(.1667) - .8333]/7

f = 0.0477

Your Optimum bet size in this situation would be 4.77% of your bankroll.

As your bankroll grows the dollar amount you bet would also grow. 

The 4.77% would remain constant.

This formula can be applied to sports betting with great effect, but only if the bettor can accurately estimate the probability that his bet will win.  This tends to be very difficult, so as a precaution against over betting many bettors will bet half the Kelly recommended amount.  This Half Kelly method produces about 75% of the rate of return of full Kelly, while also muting volatility and preventing inadvertent over betting from win probability estimates that are too high.