This mostly comes up from gaming but you'll obviously see it from gambling and random other stuff. No I'm not talking about the guy who thinks if you roll head 10 times in a row the next one has to be tails. I'm talking about the guys who thinks they know how it works. If I roll head 50 times in a row and ask you what's the chance the next roll is a head, you should ask 'Is the coin fair?' If an inexplicably unlikely event happened, the solution isn't to 'get a bigger sample'. If you just observed an event that has a 1 trillion to 1 chance of happening, you really should question is the odds really what they claim to be. Of course just because something has astronomical odds from happening doesn't mean it can't, but no matter what statistics you use, it doesn't change the fact that it should take about 1 trillion observerances to observe an event that has 1 trillion to 1 chance of happening. If you win the jackpot in lottery twice in a row, someone's definitely going to investigate if there's something wrong because people just don't win lottery twice in a row.
In fact I think it's a passing understanding of statistics that leads to these misconceptions. Something that has 1000 to 1 chance of happening can be explained by luck. Something that has 1 trillion in 1 chance of happening cannot be explained by luck. You should almost always question whether the underyling odds are correct if such an event happened, and no amount of fancy statistical tools can possibly make it reasonable for you to observe this event.
In fact I think it's a passing understanding of statistics that leads to these misconceptions. Something that has 1000 to 1 chance of happening can be explained by luck. Something that has 1 trillion in 1 chance of happening cannot be explained by luck. You should almost always question whether the underyling odds are correct if such an event happened, and no amount of fancy statistical tools can possibly make it reasonable for you to observe this event.
