### Gambles with the same Expected return and Kelly bet size

By Elliot Noma, Yu Bai In our previous post we grouped gambles by their optimal bet sizes. Here we consider the subset of these groups in which the gambles share not only an optimal bet size, but also the same expected return. 1. Finding the set of gambles with same expected return and Kelly bet … Continue reading

### The set of gambles with the same Kelly bet size

By Elliot Noma, Yu Bai The Kelly criterion calculates the bet size that maximizes the long run return over repeated gambles. To better understand the relationship between bet size, gamble outcomes and the probability of winning, we explore the space ofÂ gambles having the same optimal leverage. To do this we consider a gamble (p, a, … Continue reading

### Relating the three-outcome and two-outcome Kelly solutions

By Elliot Noma, Yu Bai In our previous article, we derived the general solution for the optimal bet size of a three-outcome gamble. In this article, we will focus on the three outcome gamble whose middle outcome is 0. Adjusting for the probability of the zero-outcome, the optimal bet size for this three-outcome gamble is … Continue reading

### The Kelly criterion for three-outcome gambles

By Elliot Noma, Yu Bai Optimal bet sizing for a three outcome gamble can an be solved using an extensions of the two-outcome analysis for the Kelly criterion. We assume that gambles have three outcomes: a1, a2 and a3 with known probabilities p1, p2 and p3. We want to determine the amount of our portfolio … Continue reading