Bitz & Pizzas: Optimal stopping strategy for a slot machine bonus game
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Bitz & Pizzas: Optimal stopping strategy for a slot machine bonus game Noelia Oses NOF Consulting, Zorroaga pasealekua 23, 20011 Donostia, Euskal Herria, Spain. E-mail: [email protected] Website: http://www.nofcon.com/
Abstract
Slot machine games used to be very simple, often limited to just one spin of the reels, but have evolved to accommodate a variety of features that provide added excitement and the potential for greater wins. They also engage the players more by, quite often, requiring them to make choices. This paper presents one of these games, Bitz & Pizzas. This case study introduces a novel application of Operational Research (OR) and serves as evidence that as slot games, and their corresponding models, are becoming more sophisticated, the role of a well-trained OR professional is becoming more important and necessary in this industry. It also shows that OR practitioners are in touch with the needs of the gambling industry and understand current practices and legislation. OR Insight (2009) 22, 31–44. doi:10.1057/ori.2008.4
Keywords: dynamic programming; gaming; optimal stopping of a finite-horizon Markov chain; slot machines
Introduction Games in the infancy of the slot machine industry were very simple, often limited to just one spin of the reels (Fey, 1994). Since then, they have evolved to accommodate a variety of features. These bonus game routines provide added excitement and the potential for greater wins. Quite often they also engage the players more by requiring them to make choices or decisions. This is a good strategy on the part of the game designers, as research shows that players like feeling that a degree of skill is necessary or that they are, to some & 2009 Operational Research Society Ltd 0953-5543 OR Insight www.palgrave-journals.com/ori/
Vol. 22, 1, 31–44
Oses
extent, in control (Griffiths, 1993). Detailed descriptions of these features with corresponding modelling solutions are presented in Oses and Freeman (2006). The objective of this paper is to illustrate the impact of increased addition of player choices and increased sophistication of slot game features in the modelling of slots. We will discuss how the industry’s needs have evolved regarding the modelling of the games, and it will be shown that Operational Research (OR) practitioners add value to gambling/gaming companies. Mathematical models of slot games are used to calculate the probability distribution of the prizes (‘win distribution’ for short). The most notable result obtained from the win distribution is the ‘percentage return’ of the game, that is, the percentage of the collected money the game will return to the players in the long term. This is the standard measure for the classification of slots. When slot providers purchase a new slot game from a slot manufacturer, they usually also specify the percentage return they want the game to achieve in the long term. A percentage return that is too low might push players to decide against playing the game. On the other hand, if it is too high, the game provider mi
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