You are given 3 dice as shown in the figure above where the numbers on the opposite faces of the each of the dice are equal.(For example,the number opposite to 6 in the first dice is also 6.)

Now the game begins like this I choose 1 dice and you choose another one from the remaining and after rolling whichever comes up with larger value wins the game.By choosing which dice are you more likely to win(that is with greater probability) in the following cases:

A.I choose dice A.

B.I choose dice B

C.I choose dice C

## Comments

Sort by:

TopNewestA beats B, B beats C, and C beats A, all with 5/9 probability. Nontransistive dice, i.e, A > B > C > A – Michael Mendrin · 3 years ago

Log in to reply

– Eddie The Head · 3 years ago

Haha....indeed....but rolling twice the case becomes entirely opposite.....but does a pattern hold if we generalize it to k rolls?Log in to reply

I believe non-transitive dice were discovered, if not just made popular, by Dr. James Grime (seen on numberphile)? – Daniel Liu · 3 years ago

Log in to reply

– Eddie The Head · 3 years ago

Yeah...I remember seeing that on numberphile too....Log in to reply

A. I will choose dice C B. I will choose dice A C. I will choose dice B – Venkii Rv · 3 years ago

Log in to reply

I choose c...c<a – Shrevarna Shaji · 2 years, 12 months ago

Log in to reply

A is actually no better than B, and B is no better than C. If u calculate the expected values, they are just the same. This means it will be a fair bet between any chosen pair of dice if u include the rewards for winning a bet as the difference in numbers rolled on the dice. When we choose A to bet with B, for instance, it is possible to get more rewards on B (example: u roll a 9) even when there is a lower probability (4/9) to win. – Cheah Chung Yin · 3 years ago

Log in to reply

Though withoutvan answer its a beautiful question – Muhsin Haneefa · 3 years ago

Log in to reply

non-transitive dice – Eddie The Head · 3 years ago

If you want the answer you may choose to read onLog in to reply