Of course, having a painted game tree, it is very easy to play - the crosses must choose the move leading from the current position to the position with the minimum score zeroes - in a position with the maximum.
What is the theoretical result of chess science is unknown. In the case of tic-tac-toe, this will of course be 0, because the theoretical result of the tic-tac-toe in the optimal game of both players is a draw. In the end, we will raise the estimate to the root. He, in turn, is interested in getting +1, so he will maximize the estimate obtained from the bottom. Thus, he will choose the minimum estimate of those that his have and assign it to this vertex.Ī level above is the turn of. He is interested in obtaining -1, so from several options he will choose the option with the minimum value (-1, if possible, and if not, then at least 0). Imagine that the move now is the crosses. From it leads several branches (exactly one in the tic-tac-toe, but this is not important). We start the “raise” estimate up the tree - consider the vertex immediately standing above the leaf (terminal position). Let the winning of the crosses be -1, the zeros - plus 1, and the draw will be zero. Now we assign to each sheet its assessment.
Of course, for such a sheet of paper there will not be enough all the atoms in the universe, but you can still imagine such a sheet (I, at least, can). Tic-tac-toe is a simple game, its tree should fit on a (large) piece of paper, but you can also imagine a painted tree for chess (there seems to be only 10 ** 50 or so different positions, and the 50-move rule limits the maximum length batches ~ 4000 moves). The resulting structure is called a tree, because (1) it has a root - the starting position, (2) it has leaves - positions from which there are no branches, for one of the players won or a draw happened, and (3) it is remotely like a tree if a sheet of paper is turned over. At the end of each branch we will draw a position that is obtained after this move, and in turn we will draw from it branches - moves that are possible from this position. Since there are 9 moves out of it, we draw 9 lines (branches) out of it. Take a piece of paper and draw the top position from the top. The maximum length of the game is 9 half moves (i.e., the moves of one of the opponents), but it may end quickly if someone wins. For each of them, the opponent has 8 answers, in turn, for each of them - 7 answers for crosses, etc. Here the first player (let it be crosses) has 9 moves (ignore symmetry).
To begin, consider a simpler game, for example, tic-tac-toe on a 3x3 board.
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