Introduction
The bonus game has become a very important part of the slot machine, as indicated by a large number of patent applications and patents (Bennett, 2000; Slomiany and Grupp, 2000; Vancurra, 2000; Baerlocher et al, 2002; Jaffe et al, 2002; Cannon and Donovan, 2003; Dickerson, 2005). Therefore, probability distributions suitable for developing games are very much in need. In this study, we illustrate how a forgotten discrete probability distribution, viz. the negative hypergeometric distribution, can be used to develop bonus games for slot machines, and also to analyze existing bonus games. The mean and the variance for this distribution were not readily available. However, these measures were recently computed using a new technique (Jones, 2013) and are available at present. The mean of the probability distribution is needed to compute to the house advantage or par of a slot game, and the variance is needed for calculating the variance of the slot game payout distribution. The variance of a slot game significantly impacts the ‘time on device’ that a player gets (Lucas et al, 2007; Lucas and Singh, 2008) from the slot game, and therefore is an important parameter of a slot game
