Recently played Among Us with some friends. There were five of us in all. I ended up being the imposter three times and by the third time, I suspected some of us were unaware of the Gambler's/Monte Carlo Fallacy After the third time being picked, I leveraged this and honestly, they did the work for me. Fresh in my mind from relistening to Sean Carroll's Mindscape podcast.
The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the incorrect belief that, if a particular event occurs more frequently than normal during the past, it is less likely to happen in the future (or vice versa), when it has otherwise been established that the probability of such events does not depend on what has happened in the past. Such events, having the quality of historical independence, are referred to as statistically independent.
In every new game, the probability of being picked doesn't change. One out of five (1:5) gives us a 20% of being picked each time assuming the impostor picked at random. No matter how many games we play. Since the selection of the impostor is not based on history. The perceived probability of getting picked as an imposter 3 successive times is 1/5 * 1/5 * 1/5 = 1/125, but the actual probability is actually 1/5. There is some Baysian intuition that plays a role in this fallacy.
It's analogous to a coin flip where each flip is 50% for a consistently weighted (fair) coin.
In contrast with games like Blackjack/21, the probabilities always change due to cards being discarded (memory).
This is one application of being aware of this, but it is useful in stock investment and any situation where random evenly distributed events with occur.
