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Poker is a zero sum game because the Poker room rake counts as a player...
5 players sit down to play...at the end of the night...
As + Bs + Cs + Ds + Es = Ae + Be + Ce + De + Ee + Rake
s=starting $
e=ending $
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Note that one can more easily analyse a zero-sum game; and it turns out that
one can transform any game into a zero-sum game by adding an additional dummy player (often called "the board"), whose losses compensate the players' net winnings.
Link.
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