Paripesa Id: Guide on Kelly Criterion

The Origins of the Kelly Criterion

This is the second in a series of posts by Paripesa Id discussing the Kelly criterion and how it may be used to make sports bets. Part 1 of this series provides an overview of the Kelly criterion and demonstrates its use. This post provides a straightforward description of how the Kelly criterion was developed, which should help you better grasp the model. Before continuing, please read Part 1 if you haven't previously.

Decimal Betting Odds: Simplified Kelly Criterion Analysis

The proof following employs the decimal betting odds approach. To apply the “b to 1” odds technique, simply changed in the following stages to b + 1. Please keep in mind that this is not definitive proof. Readers should see Kelly's original work for a formal explanation of how the Kelly criterion was developed.

Wn/W0 =(1 + f*(d-1))k(1 – f)(n-k)

This equation tells us how much our cash will have grown after n games. To figure out how much the bankroll grows per game, both sides of the equation need to be raised by a power of 1/n. To show why we do this, let's say you put $100 into an investment that gave you a return of $144 after two times. If you wanted to figure out the rate of growth per time, you would do the following:

144 = 100*(1+growth)2 144/100= (1+growth)2

1.44 = (1 + growth)2

Now, we add 1/n, which is 1/2 in this case, to both sides of the equation. This lets us figure out the rate of growth.

1.441/2 = (1 + growth)2*1/2

1.2 = (1 + growth)

0.2 = growth growth = 20%

So, if the growth rate is 20%, the amount will be $144 after two periods.