The current puzzle at The Grey Labrynth is an amusing math puzzle.

http://www.greylabyrinth.com/puzzles/puzzle.php?puzzle_id=206

Hmm, if I were in this situation (ok, maybe I could not play infinite rounds), I would try to deterministically play 3,2,1, 3,2,1, 3... If player 2 and player 3 adapt to this (playing 2,1,3,2,1,3, and 1,3,2,1,3,2,..., resp.) then we all would get the maximum (symmetric) result: 0, at the same time avoiding any collision. At the beginning there will be probably a phase in which it is not clear who plays 1 and 2 when I play 3. This could be resolved by selecting at random before the "sync" has happened. At the moment I cannot see how the 2 other guys (and myself) could have a better strategy than this... Choosing random numbers all the time has two disadvantages: first, all 3 should have the same distribution (which is not possible, since the interval to choose from is not defined), second, you have collisions that reduce your expectation value... [On the other hand, all 3 could communicate by choosing a very obvious code, e.g. 1=a, 2=b,... (all 3 must speak the same language) and deal out how to play. Since you play afterwards infinite rounds this communication would not reduce your expectation value.] Christoph

I'll give it a try (spoiler sketch, perhaps): If there is an optimal strategy S w/o communication and collusion, it should have the property that when two players play S, they are each guaranteed to win at least 1/3 of the time, while the third player can win AT MOST 1/3 of the time. We can assume the 3rd player, wlog, is playing a pure strategy. One strategy that satisfies the properties above is, "Pick number i with probability 1/2^i." On 1/12/07, Dave Dyer <ddyer@real-me.net> wrote:

The current puzzle at The Grey Labrynth is an amusing math puzzle.

http://www.greylabyrinth.com/puzzles/puzzle.php?puzzle_id=206

_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun