  This paper deals with the application of Approximation Theory type techniques
to study a classical problem in Probability: estimating the parameter of a
biased coin. For this purpose, a Minimax Estimation problem is considered and
the characterization of the optimal estimator is shown, together with the weak
asymptotics of such optimal choices as the number of coin tosses approaches
infinity; 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.
