Winning Players

[AlanBostick]

[ QUOTE ]
try thinking of it this way;

In a hand of poker 1 person out of nine will win the pot, barring a split. Over the lifetime of the game if the same 9 players play (or 9 million) on average only the percentage that represents 1/9 would show a profit (in a zero sum scenario)

[/ QUOTE ]

This reasoning is completely wrong. Here's a counterexample:

Imagine a nine-handed game where everyone wagers $1 and then a 12-sided die is rolled. If it comes up 10, 11, or 12 it gets rolled again; otherwise, the wagers are awarded to the player in the seat whose number comes up.

After many rolls, the players' wins or losses will be normally distributed around a mean of $0. Half the players will be winners, half will be losers.