Any
game in which a number of
players must play for portions of a
fixed amount of
material, i.e.
chips,
money,
xp,
energy,
etc. The meaning of this is that whenever one player increases their
score, the score of the rest of the
group must
decrease by the same amount.
Poker is the best example of a zero sum game.
Blackjack and other
house games are also zero-sum games, but for all
practical purposes they are not, as you will be
thrown out of the
casino long before the house lets you make any
significant dent in their
cage.
A common logical fallacy is to compare a complex issue in economics to a zero-sum game. This is most frequent when you hear about how, say, the United States has one quarter the population of India, yet consumes three times the world's resources. This may be indicative of an inequality, but the statement erroneously implies that if we Americans were to limit our consumption, this would somehow encourage the GDP of India to rise. In all likelihood, the opposite would be true, as the decrease in consumption would include a decrease in consumption of Indian goods, which would depress the nation even more. Another reason this argument is bad is because some of the goods consumed are not static resources, such as grain, which (these days) is grown according to demand.
You may also find that some noders complain about how other people's writeups get voted on and cooled more than theirs, as though voting was a zero-sum game. Although there is indeed a limited number of votes available per day, this is fallacious because it implies that all votes are used every day, and that if other nodes didn't get voted on, their nodes would get voted up.