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Message: <blockquote data-quote="Gorgon Zee" data-source="post: 8963718" data-attributes="member: 75787">OK. Puts professional hat on.The original statement was "I rolled a 20 around 6 times in a row, each one a confirmed crit."So there is initial uncertainty about how many times the dice were rolled. People are not great at this sort of recollection, and while it's not impossible that the actual N was as low as 3, 4-5 seems more likely, so let's take it from this evidence that he rolled 4 or 5 times.Next up, the dice. My upfront belief is that there is an unknown prior distribution of how unfair a dice is, but that distribution is likely to contain dice that roll given numbers more times as often as expected. Given the evidence that it did do so, the Bayesian in me says that I must update my prior (that the dice is a bit biased in an unknown direction) to say that the dice is biased to roll d20s. More precisely it was biased. Further testing is needed to see if it is currently biased. Maybe that side was slightly tacky or the other sides slippery for some reason.I'll go with 2x as biased because people who test this do see that level of bias often enough, and because this result is so unusual I'm goin with the high end. So we have a dice being thrown 4-5 times, each time with a 0.1 chance of a 20, for odds of one in 10,000 to 100,000. Let's take the middle 1:50000However, since we are observing an event and noting its unusual nature after it has occurred, we have to ask "what other events would have been equally noteworthy?" As a player, I'd think you'd notice a similar sequence of 1s, so if either are considered notable, we're at 1:25000 odds.So that's the odds if exactly one sequence had been attempted. But how many sequences were attempted that evening but that one player? Maybe 10 might be a good number (exact calculation is hard as we have overlapping sequences. I'm sort of guessing about 50 rolls an evening and ignoring the overlap odds completely to say 10 independent sequences), dropping the odds to 1:2500. And we have 5 players, each of whom could have done the same, so now it's down to 1:500Take away: When you are presented with an observation that seems incredible, remember that it was only one of a very, very huge number of possible observations that could have seemed incredible. Also, if something yields an extreme result, consider that the input distributions may be extremely biased. For additional reading: Look up legal cases where the jury were told that DNA evidence showed that the odds of the accused not being guilty were millions to one against, but in fact they were quite reasonable.(e.g. <a href="https://slate.com/technology/2013/06/dna-math-if-police-find-a-genetic-match-that-doesnt-mean-they-have-the-right-suspect.html" target="_blank">If Police Find a DNA “Match,” That Doesn’t Mean They Have the Right Suspect</a>)</blockquote>

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