1 A Monte Carlo Analysis of Hypothetical Multi-Line Slot Machine Play GRAHAM D.I. BARR 1 and IAN N. DURBACH 1 1 Department of Statistical Sciences, University of Cape Town Abstract: Behavioural research into slot machine gambling tends to focus on charac- teristics of the gambler or on qualitative aspects of the slot machine such as audiovisual displays and bonus features. In this paper we take a different approach by using Monte Carlo simulation to relate hypothetical slot machine gambling behaviour to the statistical characteristics of the slot machines themselves. The measures we use – expected mone- tary win, volatility of payouts, and the probability that any single play returns a winning result – have the advantage that they are mathematically precise and can be linked to psy- chological risk and return criteria that people may look to as they decide both whether to gamble or not and how to play. Introduction Slot machines represent an enormously popular and profitable industry 1 . Yet despite their popularity and status as money-spinners there has been relatively little attempt outside of the gambling industry itself to investigate the statistical characteristics of slot machines, or to relate these statistical characteristics to the behaviour and preferences of those play- ing the slot machines. Thus, behavioural research into the roots of persistent slot machine play has tended to focus more on the characteristics of the gambler (e.g. Ladouceur et al., 2003; Rodgers, 1997) or on the qualitative aspects of the slot machine such as audiovisual displays (Loba et al., 2001) and bonus features (Moodie and Finnigan, 2005), than on the statistical characteristics of the slot machines themselves. Our main aim in this paper is to use a Monte Carlo simulation approach to evaluate slot machine performance in terms of three fundamental measures of risk and return. The three measures we use are the expected monetary value of any payouts, the volatility or uncertainty around those payouts, and the excitement or entertainment value of play, as operationalised by the probability that a single play results in a payout being won. For a given slot machine, these three measures vary as a function of various aspects of game play that must be selected by the player – specifically, the number of lines played and the amount bet pet line. Each variety of slot machine can therefore be depicted by a three-dimensional risk-return curve representing the various trade-offs between risk and return that are presented to a player through his or her selection of a number of lines to play and a total amount to bet. Different slot machine varieties can be depicted by a set of three-dimensional risk-return curves, which allows a casino to describe various forms of hypothetical gambling behaviour that they are catering for with their portfolio of machines. It is also possible to use the risk-return framework to investigate different types of gambling behaviour that might theoretically occur. The modelling of the slot machines themselves has also become increasingly complex as the slot machine has evolved from a mechanical device – the classic spinning reels