In this paper we consider a non-cooperative two-person zero-sum matrix game, called dice game. In an (n, σ) dice game, two players can independently choose a dice from a collection of hypothetical dice having n faces and with a total of σ eyes distributed over these faces. They independently roll their dice and the player showing the highest number of eyes wins (in case of a tie, none of the pl...

There are multiple proposed interpretations of probability theory: one such interpretation is true-false logic under uncertainty. Cox’s Theorem is a representation theorem that states, under a certain set of axioms describing the meaning of uncertainty, that every truefalse logic under uncertainty is isomorphic to conditional probability theory. This result was used by Jaynes to develop a philo...

We analyse a variety of ways that comparing dice values can be used to simulate battles in games, measuring the ‘win bias’, ‘tie percentage’, and ‘closeness’ of each variant, to provide game designers with quantitative measurements of how small rule changes can significantly affect game balance. Closeness, a metric we introduce, is related to the inverse of the second moment, and measures how c...

1.1. Example: A Dice-Rolling Problem. In board games like Monopoly, Clue, Parcheesi, and so on, players take turns rolling a pair of dice and then moving tokens on a board according to rules that depend on the dice rolls. The rules of these games are all somewhat complicated, but in most of the games, in most circumstances, the number of spaces a player moves his/her token is the sum of the num...

Dice Coefficient is the techniques to find similarity of an object and widely used in digital library, sciences and other fields. Thus, this project is the first attempts to employed Dice Coefficient for selecting paper in conference management system. An experimental result with limited test cases indicates Dice Coefficient is potentially to be used in the broad spectrum of respective applicat...

The subject of Sicherman dice began with a question posed and answered by Colonel George Sicherman which was originally reported in the February 1978 issue of Scientific American. Sicherman wanted to determine if there was another way to label a pair of sixsided dice, using only positive integers such that the probabilities of the sums would be the same as a standard dice. Sicherman discovered ...