Looking over the Wikipedia page for the Chernoff bound, it's given at the top as $P \geq 1-\mathrm{e}^{- 2n \left( p - \frac{1}{2} \right)^2}$, where $P$ is the probability that a majority of biased random variables $X_1 \ldots X_n$ are $1$.
A little lower on the page, it gives the formula for finding how many trials to establish the biased side as being $n \geq \frac{1}{(p -1/2)^2} \ln \frac{1}{\sqrt{\varepsilon}}.$
I'm having trouble seeing how the second is derived from the first, as I thought that $\varepsilon = 1-P$, and solving the first inequality for $n$ seems to g ive something like $n \geq -\frac{1}{2(p-\frac{1}{2})^2} \ln \varepsilon$. If somebody could show where the second inequality comes from, I would appreciate it.