Mathematical Games of Dice - A Research Based Calculations Using Computer Algebra Systems

Authors

  • Ryohei Miyadera, Akira Murakami, Nazuki Terakawa, Keito Tanemura, Mao Fujino and Hisayoshi Sakahira

Abstract

In this paper, a game in which each player throws several dice is examined. The winner is the
player whose sum of the dice he/she throws is higher than that of any other player. This rule makes it a
straightforward game, but certain facts on the probability of winning are discovered. First, a variation of
the game in which players use three standard (6-faced) dice or a 20-faced die is studied. It is found that if
player ? with three standard dice plays against player ? with a 20-faced die in a two-player game, the
probability of winning is the same for each. Conversely, the player with the 20-faced die has a better chance
of winning when the number of players participating in the game is greater than two. The game is also
studied using different dice, which leads to the discovery of a sufficient condition of dice combinations for a
player to increase the likelihood of winning against more than one other player. These mathematical facts
are described via the computer algebra system Mathematica. There does not appear to be a game with the
same mathematical structure as the game treated in this article, although it is natural to select a person out
of many people by random methods. Furthermore, it is essential to know the advantages and disadvantages
of the selection process of a person in such a process. Thus, the topic treated in this article is worth
studying.

Published

2020-01-31

Issue

Section

Articles