2. Philosophy - Stefano Franchi

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C HESS, GAMES, AND FLIES
Let me try to convey a deeper appreciation of Shannon’s program with the help of a
(traditional) tree diagram. Consider the following figure. The ovals, or nodes, represent
possible configurations of the chessboard, and the lines connecting them stand for the ac-
tion performed when a chess piece is moved.
.
Possible move 1
P move 21 P move 22 P move 41
We can consider the initial position of the chessboard as the root of the tree, the first row
as the possible first moves by the white player, the second row as the possible counter-
moves by the black player, the third possible counter-counter-moves by the white player,
etc. It is this tree that has, as Shannon reports, approximately 10120 nodes. Set issues of size
aside for a moment, however, and focus on the structure.
The tree can be created one step (one node, that is) at the time by the recursive appli-
cation of the rules of the game. The complete tree is of course impossible to create, but the
search procedure does not have to rely on a complete tree if it settles for less than optimal
results (Whereas a less-than-complete game theoretic matrix is useless, since maximin
techniques require the whole matrix to operate).
Start
P move 2 P move 3 P move 20
P move 42
The second thing to notice is that the tree does not represent the “perfect” game, or in-
deed any game, but the collection of all possible chess games, from the most trivial to the
grandmaster’s masterpiece. In fact, every complete vertical path of the tree begins with the
initial position and terminates, after a variable number of moves, either with a victory for
white or black or with a draw, and as such stands for a complete game. The tree as a whole
represents the space of “chess” as such. Individual games can be recomprehended as proper
parts of the complete structure (i.e. as complete vertical paths.) The perfect game would be-
come possible after the complete tree is in place, since to play it is necessary to know the
.
White
Black
White