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 $A>B, B>C, C>A$ ?
probability combinatorics
edited Dec 26 '18 at 18:05
gt6989b
34.9k22557
asked Dec 26 '18 at 17:41
Edvards ZakovskisEdvards Zakovskis
354
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add a comment |
$begingroup$
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
edited Dec 26 '18 at 18:05
gt6989b
34.9k22557
asked Dec 26 '18 at 17:41
Edvards ZakovskisEdvards Zakovskis
354
$endgroup$
4
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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"
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– Lorenzo
Dec 26 '18 at 18:05
add a comment |
$begingroup$
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
edited Dec 26 '18 at 18:05
gt6989b
34.9k22557
asked Dec 26 '18 at 17:41
Edvards ZakovskisEdvards Zakovskis
354
$endgroup$
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
probability combinatorics
edited Dec 26 '18 at 18:05
gt6989b
34.9k22557
asked Dec 26 '18 at 17:41
Edvards ZakovskisEdvards Zakovskis
354
edited Dec 26 '18 at 18:05
gt6989b
34.9k22557
asked Dec 26 '18 at 17:41
Edvards ZakovskisEdvards Zakovskis
354
edited Dec 26 '18 at 18:05
gt6989b
34.9k22557
edited Dec 26 '18 at 18:05
gt6989b
34.9k22557
edited Dec 26 '18 at 18:05
gt6989b
34.9k22557
34.9k22557
asked Dec 26 '18 at 17:41
Edvards ZakovskisEdvards Zakovskis
354
asked Dec 26 '18 at 17:41
Edvards ZakovskisEdvards Zakovskis
354
asked Dec 26 '18 at 17:41
Edvards ZakovskisEdvards Zakovskis
354
354
4
$begingroup$
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"
$endgroup$
– Lorenzo
Dec 26 '18 at 18:05
add a comment |
4
$begingroup$
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"
$endgroup$
– Lorenzo
Dec 26 '18 at 18:05
4
4
$begingroup$
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"
$endgroup$
– Lorenzo
Dec 26 '18 at 18:05
$begingroup$
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"
$endgroup$
– Lorenzo
Dec 26 '18 at 18:05
add a comment |
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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"
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– Lorenzo
Dec 26 '18 at 18:05