Many of my readers may have already heard about AlphaGo, a computer program developed by Google DeepMind which plays the ancient board game of Go. Developing a program to play Go is not that big of a deal—the first such program was written in 1968—but what is a big deal is how well it plays. In fact, it has just beaten Ke Jie, widely regarded at the moment to be the best human Go player in the world, three games to none in a three-game series.
What is Go?
Go is a very old board game, invented in ancient China over 2500 years ago. Players take turns playing white and black stones on the intersections of a grid, with the goal being to surround more territory than the opponent. The rules themselves are actually quite simple—it takes just a few minutes to learn the basics—but the simple rules have complex emergent properties that make the strategy incredibly deep. Top human players spend their whole lives devoted to studying and improving at the game.
I enjoy playing Go for many of the same reasons that I love math—it is beautiful, deep, often surprising, and rewards patient study. If you want to learn how to play—and I highly recommend that you do—try starting here!
Why is this a big deal?
Ever since IBM’s Deep Blue beat world champion Garry Kasparov in a chess match in 1997, almost 20 years ago, the best chess-playing computer programs have been able to defeat even top human players. Go, on the other hand, is much more difficult for computers to play. There are several reasons for this:
- The number of possible moves is much higher in Go than in chess, and games tend to last much longer (a typical game of Go takes hundreds of moves as opposed to around 40 moves for chess). So it is completely infeasible to just try all possible moves by brute force.
- With chess, it is not too hard to evaluate who is winning in a particular position, by looking at which pieces they have left and where the pieces are on the board; with Go, on the other hand, evaluating who is winning can be extremely difficult.
Up until just a few years ago, the best Go-playing programs could play at the level of a decent amateur player but could not come anywhere close to beating professional-level players. Most people thought that further improvements would be very difficult to achieve and that it would be another decade or two before computer programs could beat top human players. So AlphaGo came as quite a surprise, and is based on recent fundamental advances in machine learning techniques (which are already having lots of other cool applications).
It is particularly interesting that AlphaGo works in a much more “human-like” way than Deep Blue did. Deep Blue was able to win at chess essentially by being really fast at evaluating lots of potential moves—it could analyze hundreds of millions of positions per second—and by consulting giant tables of memorized positions. Chess playing programs are better than us at chess, yes, but as far as I know we haven’t particularly learned anything from them. AlphaGo, on the other hand, “learned” how to play go by studying thousands of human games and then improving by playing itself many, many times. It uses several “neural networks”—a machine learning technique which is ultimately modeled on the structure of the human brain—both to predict promoising moves to study and to evaluate board positions. Of course it also plays out many potential sequences of moves to evaluate them. So it plays using a combination of pattern recognition and speculatively playing out potential sequences of moves—which is exactly how humans play. The amazing thing is that AlphaGo has actually taught us new things about Go—on many occasions it has played moves that humans describe as surprising and beautiful. It has also played moves that the accepted wisdom said were bad moves, but AlphaGo showed how to make them work. One might expect that people in the Go world might feel a sense of loss upon being beaten by a computer program—but the feeling is actually quite the opposite, because of the beatiful way AlphaGo plays and how much it has taught us about the game.