A Monte Carlo Analysis of the Application of the Kelly Criterion on a Finite Time Horizon

Abstract

The Kelly Criterion is a betting strategy that will always outperform other strategies given an infinite numbers of trials. Due to practical limitations, the player is unable to invest in an infinite number of trials. We exam the effectiveness of the Kelly Criterion on even money games on a finite time horizon using the Monte Carlo method and approximate the finite number of trials threshold where if the number of plays , the investor is more likely to end with infinite capital, and where if , the investor is more likely to not end with infinite capital. We also estimate the arbitrarily large number of plays where the marginal gains in wealth between and infinity plays is small enough such that the player is indifferent to realizing these gains. In other words, we estimate as the number of trials needed to almost always see a return of essentially infinite wealth.