a zero-sum game is a game between two players (doesn't matter if it is two single players, two teams, just two participants are allowed.) The possible outcomes are:
player 1 wins, player 2 loses
player 1 loses, player 2 wins
player 1 and player 2 tie (draw, push, etc.)
Handicapping, wagering, etc does not change a thing. non-zero-sum games are games where both sides can win or lose at the same time. I trade you something I don't need for something I do need. You need what I give you, you don't need what you give me. We both win. not zero-sum.
since if the prisoner loses he becomes a captive. If he goes free, he wins. If he is convicted, he is locked up. He wins or loses. The state (the police, the D/A, whatever) has the opposite view. If he goes free, they lose. If he is found guilty, he wins.
If there are more than 2 sides playing, or less than 2 sides playing, zero-sum doesn't apply. It is really only for games with two players, although in many cases an N player game can be reduced to N-1 2 player games and maintain the zero-sum quality. blackjack is a good example since the game is really between the player and the dealer.
with genuine respect, SSR, since you seem to be one of the ones who gets the overall concept, you are using a definition you gave in another posting that appears to come from computer sciences.... In the broader game theory definition of zero sum game, there can be any number of participants in the situation being analyzed. People in this thread have used various tournaments as examples (50 people put in $1 and flip a coin, if you flip heads then you advance, if you flip tails you're out, if everyone flips tails the round is replayed, last person gets all the cash, all the losses equal the win, therefore zero sum). While it's helpful in certain computer programming scenarios to break a problem down to two possible outcomes, it's actually a special, restricted case of a broader, eneral concept.
To quote you: it defines the computer science strategy required to play the game (minimax).
but, if you noticed, one absolute requirement is that for a many-player zero-sum game (and a 21 table fits this perfectly) you must be able to break the game down so that you turn it into multiple 2-player zero-sum games. The bottom line is that the outcome of one player/game does not affect the others, with respect to win/lose/draw outcomes. In the case of 21, we just put in 6x as many tables and only allow heads-up games. Same exact results in that each player win win/lose/push in each round, and it shows that "independence" required when there are multiple players.
The other mentioned quality, that of wins and losses summing to zero always has to be present of course.
As far as that quote, minimax is the epitome of how to handle zero-sum, since anything I do must be either good for me / bad for you, or bad for me / good for you. There are very complex zero-sum games like go, for example. And there are trivial ones like tossing a coin or paper-rock-scissors.
"People in this thread have used various tournaments as examples (50 people put in $1 and flip a coin, if you flip heads then you advance, if you flip tails you're out, if everyone flips tails the round is replayed, last person gets all the cash, all the losses equal the win, therefore zero sum)."
You are describing an exclusive OR function, which is, by defintion, a binary operation.