Kevin Wampler wrote:
> If you're limited to two players it's a bit trickier, but I think it's 
> still pretty easy to mimic a 1dN roll with the following game:  Both 
> players pick a number between 0 and N-1, then you add the numbers mod N 
> and use the result as the value of the "roll".

Turns out it's easy to extend this to a MdN throw by having each player 
choose a number between 0 and N^M-1, taking the sum mod N^M and then 
using the digits when written in base N as the values for each of the M 
die.  It's also possible to get the same result with somewhat fewer 
moves per player by mapping the result to "bins" in the distribution 
function of the MdN roll.

I think the much more interesting question is weather there's games 
smaller than this which can give the same result.  All the examples I've 
come up with so far rely on the best strategy being uniformly random, 
but if you consider other strategies it might be possible to get a 
simpler game.

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