Minimum number of independent trials needed to detect a bias Suppose, I suspect that the probability of occurrence of a particular bit as $0$ is $.558$. Since, it is not $.5$, so this is possibly a bias. Now, my question is:


  What is the minimum number of independent trials I need to confirm my result?


I mean, observing this scenario for, say 100 times, must not be convincing. There should be a theoretical result regarding this. It would be very helpful if someone links such papers while answering.

What I am looking for is: Suppose I suspect a possible bias of $0.5 \pm x$, $x \in (0, .5]$. Then, at least, say $2^{1/x}$ trials are need to confirm my suspicion.

Related: https://stats.stackexchange.com/questions/417981/calculate-the-number-of-trials-needed-to-achieve-certain-number-of-successes-at
I searched the web, and finally (I think) I got:

In page 47, 48 of this thesis, it is mentioned that -


  To detect a bias of $p(1+q)$ (where $p$ is the probability for an Uniform Random event), we need roughly $\dfrac{1}{pq^2}$ samples.