An Analysis of Probability Through the Medium of Games

Abstract

By looking at the board game Rack-O, it is apparent that chance plays a large part in possibly winning the game. The work of this thesis is to derive probabilities of winning according to the game rules quickly and easily, and understanding why the likelihood of winning without strategy is what it is. Additionally, the probability of winning and gaining extra points in the game is analyzed using Mathematica to provide computational data for this problem. Simplifying the aspects of the game and redefining them in mathematical terms, such as referring to the number on the card as a value and a hand as a set of ten values, allows for a simpler understanding of how the rules function mathematically. The necessity exists to find the probability of receiving a winning hand regardless of extra points due to the rules of the game, but otherwise the rest of the analysis is not dependent on the game, and while based on the game, is not necessarily specific to it. Once this probability is found, it is then possible to determine, using programming, a general idea of the probability of receiving bonus points in the simplest and fastest way within the game, while simultaneously allowing for the general probability of selecting consecutive numbers to be determined.