There's this Minecraft speed-runner called Dream who has been accused of cheating due to his drop luck. A moderator team has calculated that the p-value of the chance you'd get the same drops as Dream just by chance is in the magnitude of 10^-12. So, the moderator team concluded that Dream was cheating, and so did many others. However, isn't this an argument from personal incredulity? There's a nonzero probability that Dream just got lucky and wasn't cheating, even if the probability is very small. This means that people think Dream is cheating just because they can't believe he got that lucky, so isn't that a personal incredulity argument? I also think that it is obvious that Dream is cheating, but I do not know whether this proof is rigorous or not.
Hey there fellow Minecraft lover.
If one is to be rigorous, it is a fallacy by personal incredulity: there is after all a 1 in 1000 billions chance that he did not cheat, so you can't rule out the possibility. One rational way to approach it is to consider how many speed runs of minecraft have been attempted in the whole world so far. If we take a conservative estimate of a billion attemps (10 millions users tried 100 times), the probability of this configuration of drops never happening is (1-10^-12)^(10^9)=0.999, so one chance in a thouthands that it would happen one day. Pretty small but orders of magnitude less improbable. I would require some evidence of the cheating before having a definitive judgement. Part of the decision about cheating is in my opinion due to the mind boggling number of 1/10^-12. If we consider the probability more carefully the number becomes 1/1000 and suddenly it's a lot less clear cut, showing that for the same facts the presentation of the case played a big role in eliciting an emotional response rather than a rational one, exposing the fallacy.
Now, the important thing to take away from this is you don't have to decide now for yourself if he cheated or not. Just be highly doubtful that he managed his performance fairly, along with the recognition of the fact that he was clearly incredibly lucky, which makes the performance less impressive.