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). #ALGORITHM FOR CHESS PROGRAM DOWNLOAD PLUS#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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