Q: You are required to play a game of skill against opponents A & B. You win if you can win two games in a row. You are presented with two options

Play A first, then B followed by A (option A-B-A)Play B first, then A followed by B (option B-A-B)The probability that you will win against A is \(\frac{1}{3}\) and that against B is \(\frac{1}{2}\). Which option maximizes your chances of winning?

The Probability Tutoring Book: An Intuitive Course for Engineers and Scientists (And Everone Else!)

A: At first brush it appears that option BAB is your best option because you play B more often and your chances of winning against B are higher than against A. However, there is a surprising and counter intuitive twist to the tale. You win only if you win two games in a row. To understand it better, let us enumerate out the cases for the A-B-A option. The options are shown in the table below

Each row enumerates out a possible scenario. The final column is the probability of that scenario playing o…

Play A first, then B followed by A (option A-B-A)Play B first, then A followed by B (option B-A-B)The probability that you will win against A is \(\frac{1}{3}\) and that against B is \(\frac{1}{2}\). Which option maximizes your chances of winning?

The Probability Tutoring Book: An Intuitive Course for Engineers and Scientists (And Everone Else!)

A: At first brush it appears that option BAB is your best option because you play B more often and your chances of winning against B are higher than against A. However, there is a surprising and counter intuitive twist to the tale. You win only if you win two games in a row. To understand it better, let us enumerate out the cases for the A-B-A option. The options are shown in the table below

Each row enumerates out a possible scenario. The final column is the probability of that scenario playing o…