Finding probability of an unfair coin An unfair coin is tossed giving heads with probability $p$ and tails with probability $1-p$. How many tosses do we have to perform if we want to find $p$ with a desired accuracy?
There is an obvious bound of $N$ tosses for $\lfloor \log_{10}{N} \rfloor$ digits of $p$; is there a better bound?

This is a binomial distribution.  The standard deviation on the number of heads is $\sqrt{Np(1-p)}$, so leaving aside the difference between your measured $p$ and the real $p$ you need $N \gt \frac{p(1-p)}{accuracy^2}$
