Page 219 - Probability Demystified

208 CHAPTER 11 Game Theory

10. When Player B uses his optimal strategy, the value of the game will be

1
a. 3
6
2
b. 5
3

5
c. 2
6
1
d. 4
8

Probability Sidelight

COMPUTERS AND GAME THEORY

Computers have been used to analyze games, most notably the game of
chess. Experts have written programs enabling computers to play humans.
Matches between chess champion Garry Kasparov and the computer named
Deep Blue, as well as his matches against the newer computer X3D Fritz,
have received universal notoriety.
Computers cannot think, but they can make billions of calculations per
second. What the computer does when it is its turn to make a chess move is to
generate a tree of moves. Each player has about 20 choices of a move per
turn. Based on these choices, the computer calculates the possible moves of
its human opponent; then it moves based on the human’s possible moves.
With each move, the computer evaluates the position of the chess pieces on
the board at that time. Each chess piece is assigned a value based on its
importance. For example, a pawn is worth one point, a knight is worth three
points, a rook is worth five points, and a queen is worth nine points. The
computer then works backwards, assuming its human opponent will make
his best move. This process is repeated after each human move. It is not pos-
sible for the computer to make trees for an entire game since it has been
estimated that there are 10 1050 possible chess moves. By looking ahead several
moves, the computer can play a fairly decent game. Some programs can
beat almost all human opponents. (Chess champions excluded, of course!)