Originally posted by wolfgang59
2, Correct - for multiples of 6 the problem is trivial.
1. Not sure of your logic. Maybe I should have been clearer:
All players know the number of players involved.
All players will play to optimize their own winnings.
There is no psychology ... just logic!
Do we opt to choose first or last? what is the tactic/strategy?
I took this to be a game with perfect information, which does place it squarely within the realm of games of logic.
That said, that does not mean there won't be psychology involved as well.
Take the four players example. The last player will see 2 players splitting $3k, 1 player holding $2k, and an umclaimed $1k. Whichever he picks, he will have $1k when he walks away.
Here is where the psychology comes into play. He has to pick one of the tables, and he may use psychology to do that. If he sets as a secondary goal to bring the top player down, he'll pick Table 2. If he decides that it is more important all the money be claimed, he'll pick Table 1.
Now, the first person has this dilemma. Based on where he thinks the last person will go, his best pick could be either Table 2 or Table 3.
If he picks Table 2, and the last person doesn't, then he gets $2000 instead of $1000-$1500. If he is wrong, then he ends up with $1000 where he could have had $1500.
If he believes the last person will choose Table 2, then he can pick Table 3 for $1500 and avoid being left with only $1000. However, if he is wrong, he has cut himself out of $500 he could have had, and may even lose another $500 in addition to this.
On what basis does he choose now? He has no logical reason to believe the last person will or will not choose Table 2, for logic gives it equal status with the other 2 tables.. It must be an assessment of what drives the last player to go, his psychology, unless of course he wishes to give even odds to all 3 possibilities.. That, however, could backfire..