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The study of positional play brings great benefit to the visually-graphic specific positional game in the form of so-called game tree. Positional game tree is called a plane figure consisting of nodes and a finite number of upward-directed line segments connecting these nodes, each node is denoted by the numeral corresponding to the number of the player makes a move, and depicts the course of this player, so each course has a set of nodes on one a certain level. At the lowest level there is only one node - the base of the tree, each node is connected only with one node at a lower level, each line segment indicates the choice made by a player on this course, and is denoted by the number corresponding to the choice made. If the game uses a turn, a player is not implemented, and a random mechanism, typically a node, corresponding to the move, given the number 0 (zero). Vertices of the tree is the end of the line segments emanating from the nodes of the last level. Branch of a tree called a broken line consisting of rectilinear segments of the tree that starts at the lowest node, and goes up sequentially through appropriate nodes to the top of the tree. Each branch of the tree shows the game play. For images necessary information about the choice made by certain passages of players on the game tree dot so-called information sets of nodes specific player. At each information set contains only indistinguishable for the player units, ie, only those nodes for each pair of which corresponds to a player can not specify exactly where in the tree, he is making this move. For example, a graphical representation of positional play, as set out shown in Fig.1.

Since the first course of doing the first player, then the lowest node corresponds to the move the first player and designated numeral I. From this node are based on two segments (branches), corresponding to the choice of 1 or 2, which are designated respectively by the numbers 1 and 2. The second course of doing a second player, so the nodes in the second level marked the numeral 2. Since the second player to know the choice of the first player on the first course, then he, making his move, he knows where in the tree (on which branch of the tree) is located. If the first player chosen in the first course of the number 1, then the second player is on the left branch of the tree, and if the first player chosen in the first course number 2, the second is on the right branch of the tree.

Thus, the left node with the digit 2 forms a separate set of information Further, since the first player known to choose the second player, he knows exactly where in the tree itself is making a choice on the third course. Therefore, each node of the third level forms a single information set. Each party games appear on the tree as a separate branch that goes from the lowest node in one node of each level and ends with one of the top point. There can be eight possible parties (by the uppermost points). Any party game characterized by the point whose coordinates correspond to the choice of a particular player.

There can be 5 points (1, 1, 0), (1, 1, 2) (1, 2, 1), (1, 2, 2) (2, 1, 1), (2,1, 2), (2, 2, 1 ), (2, 2, 2). Each point corresponds to the first player to win according to the functions M (x, y, z). Most of the top point of each affix