### Using game simulations to shed insight into common gaming behaviours

#### Abstract

Gambling and probably theory have a long intertwined history, with early publications dating to the 17th century. Fair games of chance, such as Blackjack or Baccarat, are exact: because the relevant elements of randomness within these games are known, probability theory can be applied to deduce outcomes, notably the house advantage. Application of probability theory can, however, prove unwieldy for computing the outcome of everyday gambling behaviours, such as using betting systems, like the Martingale, or enacting gambling biases such as the Gambler? Fallacy or its converse? Allow the Herd Mentality’s Simulation is one proven way to assess possible outcomes in such situations. Within this presentation we share insights from two gaming simulations we have created. The first simulates the behaviour of Optimal blackjack players, all of whom intend to play approximately two hours, or one hundred hands. This simulation shows the effect of setting monetary loss/win limits. As should be expected, regardless of the width of the limit or the limit’s symmetry, the house advantage does not change; however, the length of play does, which in turn affects the cumulative losses and the handle, a relevant insight for gaming establishments. Asymmetrical betting limits, such as? Leave if I lose $500, but stay until I win $1000 increases the number of players who finish with losses relative to players with symmetrical bet limits, which could affect player psychology. A second simulation explores the effect of the herd mentality when applied to Baccarat (i.e., contrary to the gambler? fallacy bets escalate on to the winning side of a streak). The able differential is the difference between total banker bets to total player bets or vice versa, thereby limiting the casino’s exposure to loss. Intuitively, as the differential increases, so does the collective player handle, hence house winnings, thus suggesting that high differentials are beneficial for the house? Regardless of differential, the house advantage does not change; but the greater the differential, the greater the number of shoes that end with players losing and the more extreme are the spikes in the positive domain for players (the house paying out for a hand of play). This simulation is therefore intended to help casino managers set betting limits that maximize total winnings while bearing in mind both the probability and magnitude of negative outcomes of increased differentials.