An Instance-Based Algorithm for Deciding the Bias of a Coin

11/11/2020

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by   Luís Fernando Schultz Xavier da Silveira, et al.

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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 ( loglog(1/ε) + log(1/δ)/ε^2), where ε = |p-q|.