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Abstract

The probability distribution of the sum of two fair dice is used to calculate the house advantage of various bets in craps, and is readily available in probability and statistics books and gaming literature. The probability distribution of the sum of A: dice (for k >= 3) is derived in this paper using the method of moment generating function. A recursion formula for deriving the probability distribution of the sum of k dice (for k >= 3) from the probability distribution of the stun of k-1 dice is also given. There are no gaming books or journal articles that demonstrate how a multi-reel slot game is developed. As an application of the probability distribution of the sum of k dice derived in this article, a slot game based on the sum of five dice is presented.