[Question] When Do Unlikely Events Should Be Questioned?

by NSegall 1 min read3rd Nov 20199 comments


Today someone shared a picture on Facebook showing four d20 dies (d20 is a 20-sided die), supposedly all landed on 20. He was saying how cool it was that he and his friends were playing a tabletop role-playing game and they all got a 20 on their spot check at the same time.

My first reaction was "Huh, neat!"

My second reaction was "p = (1/20)^4 = 160,000. In Israel's small role-playing community this seems just very unlikely. This picture is probably a fake."

1st me: "Well, this just happened to be exactly 4 dies. If that happened to be 5 dies, 6 dies, etc ... we would still consider this as an exceptional event with low probability. We have to sum over all the probabilities for all plausible die numbers"

2nd me: "Sure, but every extra die reduces the probability by a factor of 1/20, so it seems likely that we can save ourselves the trouble of summing and just assume that 1/160,000 gives us a fair estimate."

1st me: "But what about if there were only 3 dies? 2 dies? What if they had all shown 1's instead of 20? What if they had shown 17, 18, 19, 20? What if we had encountered that picture on an international role-playing group, much larger than the Israeli one? Where do we draw the line? We need to find a way to estimate the probability of observing a picture on social media of something unlikely that is drawn from a huge set of unlikely possibilities"

At that point me no. 2 usually frowns and forgets about the matter until it emerges again, leaving it unresolved.

So I am now seeking the community's wisdom; let the elders speak. How do you estimate the likelihood of occurrences such as this? Can this problem be easily resolved somehow?