The method of successive approximation value of the game. In the study of game situations may often happen that there is no need to obtain an exact solution of the game or because of any reason to find the exact value of the price game and the optimal mixed strategy is impossible or very difficult. Then we can use approximate methods for solving matrix games. We describe one such method - the method of successive approximation value of the game. Number of calculations using this method increases approximately in proportion to the number of rows and columns of winning. Essentially, the method of successive approximation rates is as follows: mental game is carried out many times, ie sequentially, in each batch of the game, each player chooses the strategy that gives him the greatest total (cumulative) payoff. In other words, in a thought of the game, each player chooses a sequence of their pure strategies, which provides the first player to the maximum average gain, and the second-minimum average loss.

After this realization several parties calculate the average value of winning the first player to lose the second player, and their average taken as the approximate value of the price game. Moreover, this method allows you to find the approximate value of optimal mixed strategies for both players: it is necessary to calculate the frequency of each pure strategy and adopt it for the approximate value of the probability of the use of a pure strategy in an optimal mixed strategy corresponding to the player. We can prove that with an unlimited increase in the number of lost games (in the above sense) the average gain of the first player and average loss of the second player will be unrestricted approach (seek) to the price of the game, and the approximate values of mixed strategies in the case where the solution of the game only, will seek to the optimal mixed strategies for each player. Generally speaking, the desire to approximate values of these quantities to the true values is slow. However, this process is easy to mechanize and thus help to obtain solution of the game with the required degree of accuracy even with relatively large gains matrices of order