A model of a two-automata zero-sum game is described. The game consists of a repeated number of plays; each play is spanned over three moves. The automata participating in the game have no prior information about it and play in a manner similar to that in which human beings, who do not know the game matrix, would play the game. Hence, each automaton is informed of the actions of his adversaries in the previous move and uses this information to make his move. At the end of each play a referee informs the automata who won and who lost. Conditions on the payoff functions, sufficient for the automata to obtain the value of the game with an arbitrarily high probability, are derived from the semimartingale equations describing the behavior of the model.