Markov chain applications in the slot machine industry

Abstract

One of the important sectors within gambling is that of gaming machines. This industry used to favour approaches based on long-run simulations or complete enumerations of all possible outcomes but has now adopted mathematical modelling as the preferred method for calculating the probability distribution of the prizes and deriving the percentage return of the games. The latter is the percentage of the collected money the game will return to the players in the long term. In this context Markov chains are a very important tool for this industry. This paper analyses the different types of slot features modelled as Markov chains, discusses their particular characteristics, illustrates the type of problems that one might encounter in practice and provides suggestions for developing implementations of the models. The cases studied are games that have already been released and are commercially available.