To explain with an example, say I have a claimed to be unbiased coin. There is a chance that when I toss it 20 times, I get heads each time.
Obviously, the more times I toss the coin, the more likely it is that the total times I get heads will be about the same as the number of times I get heads (I believe this is called regression to the mean though I may be wrong with the terminology).
However, what if I get really lucky, and get 100 heads in a row? Though the probability is admittedly very very low (${\frac12}^{100}$) it is still possible. My question is, at what point can you accurately say that the coin is actually biased to give heads, and is not fair as reported? Is there a certain finite limit, or can you only assign it a confidence value? Can I know what the actual bias is with some certainty?
An application could be to know whether one is cheating in a game of roulette, for example.