I am given the task to check if a coin is biased to land on heads. The bias must exceed a certain threshold i.e. $p > 0.5 + \epsilon$ for some given $\epsilon$. I would like to know how the number of flips affects the certainty of the conclusion that the coin is biased according to this definition.
Concretely, if I am allowed to flip the coin $n$ times, what is the probability of a false positive (coin is not biased but I claim that it is) and a false negative (coin is biased but I fail to spot it) as a function of $n$ and $\epsilon$?