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'A Dicey Paradox' printed from http://nrich.maths.org/
Four fair dice are marked on their six faces, using the mathematical constants $e$, $\pi$ and $\phi$ as follows:
A:

4 4 4 4 0 0 

B: 
$\pi \pi \pi \pi \pi \pi$ 
where $\pi$ is approximately 3.142 
C: 
e e e e 7 7 
where e is approximately 2.718 
D: 
5 5 5 $\phi \phi \phi$ 
where $\phi $ is approximately 1.618 
The game is that we each have one die, we throw the dice once and the highest number wins. I invite you to choose first ANY one of the dice. Then I can always choose another one so that I will have a better chance of winning than you. You may think this is unfair and decide you want to play with the die I chose. In that case I can always chose another one so that I still have a better chance
of winning than you. Investigate the probabilities and explain the choices I make in all possible cases.
Does it make any difference if the dice are marked with 3 instead of $\pi$, 2 instead of $e$ and 1 instead of $\phi$?