{"title":"Possible Probability and Irreducibility of Balanced Nontransitive Dice","authors":"Injo Hur, Yeansu Kim","doi":"10.1155/2021/6648248","DOIUrl":null,"url":null,"abstract":"We construct irreducible balanced non-transitive sets of n-sided dice for any positive integer n. We also study so-called a fair set of dice, which is one main tool in the construction of irreducible balanced non-transitive sets of dice. Furthermore, we study possible probabilities of non-transitive sets of dice.","PeriodicalId":8470,"journal":{"name":"arXiv: Probability","volume":"74 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/2021/6648248","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
We construct irreducible balanced non-transitive sets of n-sided dice for any positive integer n. We also study so-called a fair set of dice, which is one main tool in the construction of irreducible balanced non-transitive sets of dice. Furthermore, we study possible probabilities of non-transitive sets of dice.
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