How can a computer play chess? For many people that is an important question. Chess seems like a distinctly human activity requiring intelligence and thought, so how can a computer possibly play chess?

In this edition of How Stuff Works we will take a look at this question. What you will find is that computers don't really "play" chess like people do. A computer playing chess is not "thinking". Instead it is calculating through a set of formulas that cause the computer to make good moves. As computers have gotten faster and faster, the quality of these calculated moves has gotten better and better. Computers chess calculators are now the best chess players on the planet, even though they do it totally blindly!

People and chess
If you have ever watched a child first learning to play chess (or if you can remember back to your own first games), you know that a human chess player starts with very limited abilities. Once a player understands the basic rules that control each piece, he or she can "play" chess. However, the new player is not very good. Each early defeat comes as something of a surprise - "oh, I didn't think about that!" or "I didn't see that coming!" are common exclamations. The human mind absorbs these experiences, stores away different board configurations, discovers certain tricks and ploys, and generally absorbs the nuances of the game one move at a time. As the level of skill develops, the player will often read books to discover patterns of play used by the best players. Strategies and tactics develop to guide the player through each game.

For a human being, therefore, the game of chess involves a great deal of high-level abstract thought. It uses visual pattern matching to recall board positions, rules and guidelines, conscious thought and even psychology!

Computers do none of this...

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.

For the black player the options are the same - 20 possible moves. So black chooses a move.

Now white can move again. It depends on what white chose to do in the first move, 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 only thought to be 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's a lot of atoms - 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 5 or 10 or 20 moves into the future. Assuming that there are about 20 possible moves for any board position, a 5-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 simply count the number of pieces each side has. If the computer is playing white and a certain board position has 11 white pieces and 9 black pieces, the simplest evaluation function might be:

11 - 9 = 2

The following diagram shows a 3-level tree that looks three moves ahead and has evaluated the value of the final board positions:

The computer is playing as the white player. The black player has moved and left the board position at the top of the tree. In this tree, white can make 3 possible moves. From each of those 3 possible moves black can make 3 possible moves. From each of those 9 board positions white can make two possible moves (in real life the total number of moves from any position is 20 or so, but that would be hard to draw...).

To decide what to do, the computer looks at this tree and it works up from the bottom. Its calculations are set up so that it finds the best board positions from each of the possible positions black will take (it takes the maximum):

One level up, it assumes that black will choose the worst possible position for white (it takes the minimum):

Finally, it takes the maximum of the top 3 numbers - 7. That is the move the computer will make. Once Black makes its move the computer goes through this whole process again, generating a new tree and evaluating all of the board positions to figure out its next move.

This approach is called the minimax algorithm because it alternates between the maximums and minimums as it moves up the tree. By applying a technique called alpha beta pruning, the algorithm can run about twice as fast and takes a lot less memory. As you can see, this process is completely mechanical and involves no thought. It is simply a brute force calculation that applies an evaluation function to all possible board positions in a tree of a certain depth.

What is interesting is that this sort of technique works pretty well. On a fast enough computer, the algorithm can look far enough ahead to play a very good game. If you add in learning techniques that modify the evaluation function based on past games, the machine can even improve over time.

The key thing to keep in mind, however, is that this is nothing like human thought. When we learn how human thinking works and create a computer that uses those techniques to play chess, we will really be onto something...

Links

• Kasparov vs. Deep Blue - IBM's web site for its Deep Blue chess computer
• Kasparov vs. the World - Innovative chess game on the Internet where the world votes on the next move to make against Kasparov. The game started on June 21, 1999.
• Computer chess references
• Game playing
• Yahoo Chess Links