How lucky is too lucky?: The Minecraft Speedrunning Dream Controversy Explained

I think the problem is that below 10^-6 there's a pretty broad range of magnitudes that are effectively 'happens to n people every k years (if they try very hard)'. Which makes them rare but not impossible, which is annoying because you can't rule it out but you can't expect to easily reproduce it either. That does tend to be the best way to think about those probabilities. For any probability you can make it happen If you try enough times or with enough people you can try to force it to happen. Below -6 is a pretty wide range of stuff you can just barely make happen if you have enough people, enough tries and enough time. It's only once you get to the 'wouldn't happen to 10^10 people in a million years' that you get to the stuff that you can be fairly sure has never happened. Matt Parker has quite a good video on it [1]. He settles on 10^-19 as something that you can be fairly sure has never happened (deliberately). As for other stuff in the probability rows, maybe include a couple of well known paradoxes like the birthday paradox. And be clear what you're saying, things like getting dealt a royal flush depends a lot on the type of poker game. [1]: ▶ this video

There have been several of these deep dives into manipulated speed runs and they seldom disappoint. Since we are on HN, I'll mention another mathy one that was summarized by Matt Parker: ▶ this video

The key point (in the end) seems to be that the odds for a streak like Niemann had are about 1 in 80k. Statistically speaking, I'd say that's a long shot from a smoking gun. Here's a good rundown of a case where a cheater is considered to have been exposed by statistical evidence, but those odds were on a completely different scale, 10^22: ▶ this video Basically the mistake that is easy to make is that we shouldn't ask: "what is the probability that Hans plays five tournaments like that in a row?", but "what is the probability that someone will play five tournaments like that in a row?". Even if we correct for the fact that there are probably more Minecraft speedruns happening than GM tournaments, odds of 80k just seem a bit too low to call it evidence.

It can still be a fair die. The context implies it's not, but it's only unlikely, not impossible. See ▶ this video It introduces a 10 billion human second century i.e. 3.1 x 10^19. If your chance times it is greater than 1 then it's definitely plausible to be done by someone, somewhere.

Maybe nice to mention that Matt Parker's Stand-up Maths video on the cheating on a MiceCraft speed-run is really very nice [0]. It not only exposes the cheater, it also gives some intuition into negligible probabilities. [0]: ▶ this video

BBC's radio show More or Less did a great piece on this recently. link It is related to Matt Parker's youtube video ▶ this video which has already been mentioned on this post.

The article recommends watching the video by Matt Parker, and so do I. Great refresher on probability (or luck, if you will) For convenience: ▶ this video