Final answer:
A gamble with an expected value of zero is termed a fair game, indicating that over time, no party is expected to make a profit or suffer a loss. This term is used in probability and statistics to describe a scenario where wins and losses are perfectly balanced.
Step-by-step explanation:
If a gamble has an expected value of zero, then it is termed a fair game. The expected value is a statistical measure used to determine the average outcome of a gamble or situation when that outcome is uncertain. A fair game means that over time, neither the player nor the house is expected to gain or lose money, as the wins and losses will balance out. In contrast, in an unfair game, one party has an advantage over the other, resulting in an expected value that is not zero. A risky game may have a high potential for gain or loss, but not necessarily an expected value of zero. Finally, a safe game implies low risk, but again, does not relate to the expected value directly.
Applying this concept to different gambling scenarios, we may find that games of chance can have varying expected values based on their rules and payouts. For example, a card game or a die game with fair rules and equal payouts for wins and losses would be considered a fair game. However, if the rules are skewed in favor of the house or another player, making the expected value negative or positive, then the game would be considered unfair. It is important for those engaging in such games to understand these concepts to make informed decisions.