Probability(is it possible?)












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We are given 3 dice $A,B,C$, with a number from 1 to 6 written on each face. Numbers can repeat, for example $A$ can have the labels $1,1,1,2,3,6$. Let $R_A$ denote a number rolled by a roll of $A$. Define $A>B$ as $mathbb{P}left[R_A > R_Bright] > 1/2$. Is it possible to have 3 dice where $A>B, B>C, C>A$ ?










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    Yes. These are called non-transitive dice. en.wikipedia.org/wiki/Nontransitive_dice Specifically, look at the section "Three-dice set with minimal alterations to standard dice"
    – Lorenzo
    Dec 26 '18 at 18:05
















1














We are given 3 dice $A,B,C$, with a number from 1 to 6 written on each face. Numbers can repeat, for example $A$ can have the labels $1,1,1,2,3,6$. Let $R_A$ denote a number rolled by a roll of $A$. Define $A>B$ as $mathbb{P}left[R_A > R_Bright] > 1/2$. Is it possible to have 3 dice where $A>B, B>C, C>A$ ?










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  • 4




    Yes. These are called non-transitive dice. en.wikipedia.org/wiki/Nontransitive_dice Specifically, look at the section "Three-dice set with minimal alterations to standard dice"
    – Lorenzo
    Dec 26 '18 at 18:05














1












1








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We are given 3 dice $A,B,C$, with a number from 1 to 6 written on each face. Numbers can repeat, for example $A$ can have the labels $1,1,1,2,3,6$. Let $R_A$ denote a number rolled by a roll of $A$. Define $A>B$ as $mathbb{P}left[R_A > R_Bright] > 1/2$. Is it possible to have 3 dice where $A>B, B>C, C>A$ ?










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We are given 3 dice $A,B,C$, with a number from 1 to 6 written on each face. Numbers can repeat, for example $A$ can have the labels $1,1,1,2,3,6$. Let $R_A$ denote a number rolled by a roll of $A$. Define $A>B$ as $mathbb{P}left[R_A > R_Bright] > 1/2$. Is it possible to have 3 dice where $A>B, B>C, C>A$ ?







probability combinatorics






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edited Dec 26 '18 at 18:05









gt6989b

33k22452




33k22452






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asked Dec 26 '18 at 17:41









Edvards Zakovskis

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  • 4




    Yes. These are called non-transitive dice. en.wikipedia.org/wiki/Nontransitive_dice Specifically, look at the section "Three-dice set with minimal alterations to standard dice"
    – Lorenzo
    Dec 26 '18 at 18:05














  • 4




    Yes. These are called non-transitive dice. en.wikipedia.org/wiki/Nontransitive_dice Specifically, look at the section "Three-dice set with minimal alterations to standard dice"
    – Lorenzo
    Dec 26 '18 at 18:05








4




4




Yes. These are called non-transitive dice. en.wikipedia.org/wiki/Nontransitive_dice Specifically, look at the section "Three-dice set with minimal alterations to standard dice"
– Lorenzo
Dec 26 '18 at 18:05




Yes. These are called non-transitive dice. en.wikipedia.org/wiki/Nontransitive_dice Specifically, look at the section "Three-dice set with minimal alterations to standard dice"
– Lorenzo
Dec 26 '18 at 18:05















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