The game-theoretic approach to setting and solution of statistical problems is considered by the example of confidence interval (CI) estimation problem for parameter θ of the binomial distribution B( n, θ). The confidence probability (CP) and the minimax decision function (MDF) are constructed for any set of CIs. This differs from the classical approach where CI is constructed for a given CP. CPs for fixed width CIs are given in tabulated form. One half of these CIs is shorter than classical CIs for the same CPs. The MDF under consideration enables observation number to be reduced by about 1.5 times from the classical approach for the same reliability and accuracy.