That's not how it works. For a geometric distribution with p=1/80 the mean or expected value is indeed 80. https://en.wikipedia.org/wiki/Geometric_distribution

That's not how it works. For a geometric distribution with p=1/80 the mean or expected value is indeed 80. https://en.wikipedia.org/wiki/Geometric_distribution https://en.wikipedia.org/wiki/Geometric_distribution Your gun example has a uniform distribution between 1 and 80 with an expected value of roughly 40 if you don't spin the chamber each time between pulling the trigger. If you spin it each time, then it's again the geometric distribution and the expected value is 80. If you don't spin the chamber between each time, then each time you pull the trigger the probability of dying at that round is not 1/80, the probability goes up and up at each round, it's only 1/80 on the first round.