منابع مشابه
Dice games and Arrows theorem
We observe that non-transitivity is not the most general way that Arrows impossibility theorem is reected in dice games. Non-transitivity in dice games is a well-known phenomenon. It was described in several Scienti c American columns in the 1970s, beginning with [3], and has since become a popular topic, discussed in articles like [4, 5] and textbooks on elementary mathematics and probabilit...
متن کاملOptimal strategies for equal-sum dice games
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...
متن کاملCharacterising Score Distributions in Dice Games
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...
متن کاملDice-Rolls in Role-Playing Games
Most RPGs (role-playing games) use some sort of randomizer when resolving actions. Most often dice are used for this, but a few games use cards, rock-paper-scissors or other means of randomization. There are dozens of different ways dice have been used in RPGs, and we are likely to see many more in the future. This is not an evolution from bad methods to better methods – there is no such thing ...
متن کاملTied dice
A generalized die is a list (x1; :::; xn) of integers. For integers n 1, a b and s let D(n; a; b; s) be the set of all dice with a x1 ::: xn b and P xi = s. Two dice X and Y are tied if the number of pairs (i; j) with xi < yj equals the number of pairs (i; j) with xi > yj . We prove the following: with one exception (unique up to isomorphism), if X 6= Y 2 D(n; a; b; s) are tied dice neither of ...
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ژورنال
عنوان ژورنال: Statistical Science
سال: 2018
ISSN: 0883-4237
DOI: 10.1214/17-sts640