Even a biased coin will flip independently, which is all you need for it to be a fallacy. If you flip a coin a thousand times that you aren't sure is biased an

Even a biased coin will flip independently, which is all you need for it to be a fallacy. If you flip a coin a thousand times that you aren't sure is biased and it comes out heads each time, you might reasonably decide it is probably a two-headed coin and update your expectation to a ~100% chance of heads. But that's the opposite of the gambler's fallacy, which would think that after a thousand heads it's practically guaranteed to come up tails the next time. So which is it- is the string of heads evidence of bias (you should expect more heads) or is the gambler's fallacy true (you should expect more tails)?