Computers and Chess
The current
state-of-the-art in computer chess is fairly intricate, but
all of it involves blind computation that is very simple at
the core.
Let's say you start with a chess board set up for the start
of a game. Each player has 16 pieces. Let's say that white
starts. White has 20 possible moves:
- The white player can move any pawn forward one or two
positions.
- The white player can move either knight in two different
ways.
The white player chooses one of those 20 moves
and makes it.
For the black player, the options are the same: 20 possible
moves. So black chooses a move.
Now white can move again. This next move depends on the
first move that white chose to make, but there are about 20 or
so moves white can make given the current board position, and
then black has 20 or so moves it can make, and so on.
This is how a computer looks at chess. It thinks about it
in a world of "all possible moves," and it makes a big
tree for all of those moves, like this:
|
In this tree, there are 20 possible moves for white. There
are 20 * 20 = 400 possible moves for black, depending on what
white does. Then there are 400 * 20 = 8,000 for white. Then
there are 8,000 * 20 = 160,000 for black, and so on. If you
were to fully develop the entire tree for all possible chess
moves, the total number of board positions is about
1,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,
or 10120, give or take
a few. That's a very big number. For example, there have only
been 1026 nanoseconds since
the Big
Bang. There are thought to be only 1075 atoms
in the entire universe. When you consider that the Milky Way
galaxy contains billions of suns, and there are billions of
galaxies, you can see that that's a whole lot of atoms. That
number is dwarfed by the number of possible chess moves. Chess
is a pretty intricate game!
No computer is ever going to calculate the entire tree.
What a chess computer tries to do is generate the
board-position tree five or 10 or 20 moves into the future.
Assuming that there are about 20 possible moves for any board
position, a five-level tree contains 3,200,000 board
positions. A 10-level tree contains about 10,000,000,000,000
(10 trillion) positions. The depth of the tree that a computer
can calculate is controlled by the speed of the computer
playing the game. The fastest chess computers can generate and
evaluate millions of board positions per second.
Once it generates the tree, then the computer needs to
"evaluate the board positions." That is, the computer has to
look at the pieces on the board and decide whether that
arrangement of pieces is "good" or "bad." The way it does this
is by using an evaluation function. The simplest
possible function might just count the number of pieces each
side has. If the computer is playing white and a certain board
position has 11 white pieces and nine black pieces, the
simplest evaluation function might be:
Obviously, for chess that formula
is way too simple, because some pieces are more
valuable than others. So the formula might apply a weight to
each type of piece. As the programmer thinks about it, he or
she makes the evaluation function more and more complicated by
adding things like board position, control of the center,
vulnerability of the king to check, vulnerability of the
opponent's queen, and tons of other parameters. No matter how
complicated the function gets, however, it is condensed down
to a single number that represents the "goodness" of that
board position.