Comment by Jtsummers
4 years ago
It's certainly low odds, but it's not impossible nor does it require a trick coin. I've seen people roll a 20 on a d20 10 times in a row, and then not a single 20 the rest of the session on the same die. Shit happens, it's probability and it may be improbable but it isn't impossible.
If you see 60 heads in a row from a coin you’ve been informed is biased to produce heads on average 60% of the time, you'd need a pretty strong bases for trust in your information to not conclude that the most likely explanation is that the bias was underreported. Yes, its possible with the reported bias (or even if the bias was overreported), but that's not the most likely conclusion absent some pretty firm external evidence of the accuracy of the bias estimate you were provided with.
> I’ve seen people roll a 20 on a d20 10 times in a row, and then not a single 20 the rest of the session on the same die.
People rolling dice aren’t, even when they try to be, perfect randomizers, and with a maximally favorable result and an action which demonstrably repeats it, there’s a strong incentive to repeat the action as accurately as possible rather than even trying to be a perfect randomizer.
I don't believe you.
I mean, that's fine, it's an anecdote. If you'd like, take a few dice and set up cameras and an automatic rolling mechanism and see if there are any improbable sequences like alternation between two or three number or a long run of a single number, or a long run without a particular number appearing. Over enough trials you are likely to encounter these kinds of events.
There will always be improbable sequences; with a fair coin, every possible sequence of length N is equally improbable, after all; if you flip a fair coin 64 times, the sequence is guaranteed to be a 1 in 2^64 event.
OTOH, the probability of some other explanation besides a fair coin isn’t consistent among all other possible sequences, so what the actual result does to your estimate of the likelihood of a fair coin depends on the actual sequence, and your basis for believing the coin was fair going in.
Things are only slightly different with, say, a coin you’ve been told has a 60% bias.
EDIT: For instance, if there is a 1:1,000,000 chance that you would be given an underestimate of bias and a 1:1,000,000,000 chance of the outcome you actually receive being true if the coin had only the bias you were informed of, its a lot more likely that you were lied to than that you just got an unusually consistent set of results.
If you had a camera pointing at a thousand coins that flipped once every second since the beginning of the universe, you still would probably not see 60 heads in a row.
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