Gambler's Fallacy

The Gambler's Fallacy is a particular type of misuse of statistics, implying that previous independent events are somehow indicative of future results. A common example is that belief that flipping a coin five times in a row, and getting "heads" each time, means that the next time the coin is flipped, it will be more likely to turn up "tails". In fact, the probability of both outcomes is still exactly 50%, assuming an unbiased coin.

One example of this fallacy that is used in Mafia games is to argue that because someone has been Scum in a disproportionate number of their games in the past, they are more likely to be ProTown "this time around". Since roles are assigned randomly each game, previous games will have no effect on the current situation.

It may appear that the town is doing poorly because they make several bad eliminations in a row. While this is undoubtedly worse than eliminating correctly, it does not fall under the Gambler's Fallacy, simply because the odds of hitting a random ProTown player decrease each time, and more information is learned about the players who remain alive.