An instance-based algorithm for deciding the bias of a coin

Let q is an element of (0, 1) and delta is an element of (0, 1) be real numbers, and let C be a coin that comes up heads with an unknown probability p, such that p not equal q. We present an algorithm that, on input C, q, and delta, decides, with probability at least 1 - delta, whether p < q or p > q. The expected number of coin flips made by this algorithm is O(loglog(1/epsilon) + log 91/delta)/epsilon(2)), where epsilon = |p - q|.