--- "M. Oskar van Deventer" > There are no comparable graphs where any three points can be chosen.
> Is this your conjecture or a mathematical statement? Are you telling me that
> I have been looking for a four-player version in vain, because it cannot
> exist?
I did say that, but now that I understand the problem better, I think I'm
wrong. :) First off, you need a graph where all possible triplets can be
dominated. I think that is possible with a K15 graph.
We extend the game to three players, Eric, you and me. We have a larger
set
of dice. Eric has the first pick, you have the second pick and I pick
last.
Again surprisingly, I'll statistically beat both Eric and you. That is
because I designed a three-player non-transitive set of dice. My
mathpuzzle
to you and your readers: How many dice are there in my set and what are
the
numbers on their faces?
And how about the four-player version? For quite some time, I have been
looking in vain for a four-player non-transitive set of dice. Can you or
your readers find such a set, or prove that it does not exist?