Let q ∈ (0 , 1) and δ ∈ (0 , 1) be real numbers, and let C be a coin that comes up heads with an unknown probability p, such that p ≠ q. We present an algorithm that, on input C, q, and δ , decides, with probability at least 1 − δ , whether p < q or p > q. The expected number of coin flips made by this algorithm is O log log (1 /) + log (1 / δ) 2 , where = | p − q |.