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This paper deals with the application of Approximation Theory type techniquesto study a classical problem in Probability: estimating the parameter of abiased coin. For this purpose, a Minimax Estimation problem is considered andthe characterization of the optimal estimator is shown, together with the weakasymptotics of such optimal choices as the number of coin tosses approachesinfinity; in addition, a number of numerical examples and graphs are displayed.At the same time, the problem is also discussed from the Game Theory viewpoint,as a non-cooperative, two-player game, and a Nash-equilibrium is established.The particular case of n=2 tosses is completely solved.

Probability, Minimax Approximation and Nash-Equilibrium. Estimating the Parameter of a Biased Coin