Playing to Lose: Investigating the Mathematics of Poker Machines

This paper describes an investigation looking at the underlying mathematics of poker machines. The aim of the investigation is for students to get an appreciation of how poker machines are designed to ensure that in the long-term players will inevitably lose when playing. The first part of this paper describes how students can model a simple poker machine game and calculate the probability and payouts for four different winning outcomes. The second part of the paper describes how these calculations can then be used to configure a poker machine simulator written in the Python programming language. The code for the simulator is briefly explained and then results for several trials run in the simulator are presented. A discussion of how the student would be expected to present and interpret these results is then given. The next section of the paper explains how students can model their own more complex poker machine game and in turn how the simulator code can be extended to handle the more complex outcomes. Next, an extension to the investigation is described, in which students investigate how many coins need to be played on average before the player loses all their money. A task sheet, setup instructions, starting code and completed examples for teachers is available for free download on the Tes website at https://www.tes.com/en-au/teaching-resource/blow-up-thepokies-12308352 (Hemer, 2020).