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How to find solution to a nontransitive dice problem
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The problem is following: given two dice with numbers between 1-6 (but the same number can repeat in the same dice), find a third dice such that the three dice form a nontransitive set of dice, i.e. if the probability for dice B to win dice A in a single dice roll game is more than 0.5, find a third dice so that the probability for the third dice to win dice B is more than 0.5, but the probability to win A is less than 0.5.
When does a solution to this problem exist?
Here's an example (from Wikipedia):
Dice A: 2, 2, 4, 4, 9, 9
Dice B: 1, 1, 6, 6, 8, 8
Dice C: ?, ?, ?, ?, ?, ?
From Wikipedia, I can read that a solution to this is that dice C has numbers 3, 3, 5, 5, 7, 7. But is there an algorithm for finding this solution (other than trying all the combinations) if it's not known?
dice
asked Jul 31 at 13:49
Echows
1446
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The problem is following: given two dice with numbers between 1-6 (but the same number can repeat in the same dice), find a third dice such that the three dice form a nontransitive set of dice, i.e. if the probability for dice B to win dice A in a single dice roll game is more than 0.5, find a third dice so that the probability for the third dice to win dice B is more than 0.5, but the probability to win A is less than 0.5.
When does a solution to this problem exist?
Here's an example (from Wikipedia):
Dice A: 2, 2, 4, 4, 9, 9
Dice B: 1, 1, 6, 6, 8, 8
Dice C: ?, ?, ?, ?, ?, ?
From Wikipedia, I can read that a solution to this is that dice C has numbers 3, 3, 5, 5, 7, 7. But is there an algorithm for finding this solution (other than trying all the combinations) if it's not known?
dice
asked Jul 31 at 13:49
Echows
1446
This doesn't answer your question, but it might give you some ideas how to approach it: math.stackexchange.com/questions/57338.
– joriki
Jul 31 at 13:58
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
The problem is following: given two dice with numbers between 1-6 (but the same number can repeat in the same dice), find a third dice such that the three dice form a nontransitive set of dice, i.e. if the probability for dice B to win dice A in a single dice roll game is more than 0.5, find a third dice so that the probability for the third dice to win dice B is more than 0.5, but the probability to win A is less than 0.5.
When does a solution to this problem exist?
Here's an example (from Wikipedia):
Dice A: 2, 2, 4, 4, 9, 9
Dice B: 1, 1, 6, 6, 8, 8
Dice C: ?, ?, ?, ?, ?, ?
From Wikipedia, I can read that a solution to this is that dice C has numbers 3, 3, 5, 5, 7, 7. But is there an algorithm for finding this solution (other than trying all the combinations) if it's not known?
dice
asked Jul 31 at 13:49
Echows
1446
The problem is following: given two dice with numbers between 1-6 (but the same number can repeat in the same dice), find a third dice such that the three dice form a nontransitive set of dice, i.e. if the probability for dice B to win dice A in a single dice roll game is more than 0.5, find a third dice so that the probability for the third dice to win dice B is more than 0.5, but the probability to win A is less than 0.5.
When does a solution to this problem exist?
Here's an example (from Wikipedia):
Dice A: 2, 2, 4, 4, 9, 9
Dice B: 1, 1, 6, 6, 8, 8
Dice C: ?, ?, ?, ?, ?, ?
From Wikipedia, I can read that a solution to this is that dice C has numbers 3, 3, 5, 5, 7, 7. But is there an algorithm for finding this solution (other than trying all the combinations) if it's not known?
dice
asked Jul 31 at 13:49
Echows
1446
asked Jul 31 at 13:49
Echows
1446
asked Jul 31 at 13:49
Echows
1446
asked Jul 31 at 13:49
Echows
1446
1446
This doesn't answer your question, but it might give you some ideas how to approach it: math.stackexchange.com/questions/57338.
– joriki
Jul 31 at 13:58
add a comment |Â
This doesn't answer your question, but it might give you some ideas how to approach it: math.stackexchange.com/questions/57338.
– joriki
Jul 31 at 13:58
This doesn't answer your question, but it might give you some ideas how to approach it: math.stackexchange.com/questions/57338.
– joriki
Jul 31 at 13:58
This doesn't answer your question, but it might give you some ideas how to approach it: math.stackexchange.com/questions/57338.
– joriki
Jul 31 at 13:58
add a comment |Â
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This doesn't answer your question, but it might give you some ideas how to approach it: math.stackexchange.com/questions/57338.
– joriki
Jul 31 at 13:58