A scenario where the risks and rewards are offset by the probabilities of their realization, resulting in a net gain/loss of exactly 0 after the appropriate amount of occurrences.
For example, assume you risk 3 coins to make 1 coin. In a zero-sum game, your odds of success should be 3:1 or 75%. This means that for every 4 (3 + 1) games played, you can expect to win 3 times, making 1 coin for each occurence, and lose once costing you 3 coins. The final ratio after all 4 occurrences is exactly 0, thus you have a zero-sum game.