Edward Lasker, an International Master of chess and eventual co-founder of the American Go Association, once said that "if intelligent life forms exist elsewhere in the universe, they almost certainly play Go." The rules are so natural, so simple, and yet they create a system with almost infinite complexity. The game is so natural yet complex that it becomes like an art, seemingly impossible to totally analyze. For this reason, computers that can soundly beat even the top chess professionals today can be beaten by strong Go amateurs.
For those 3,000 years late to picking up this game, (like I was not too long ago), Go (called Go or Igo in Japanese, Weiqi in Chinese, Baduk in Korean) is an ancient east Asian board game in which two players alternate placing stones on a grid of lines. Stones or groups of stones that are completely surrounded by enemy stones, with no empty spaces in-between, are taken off the board, and usually counted as extra points for the capturer. The overall objective is to surround as much board territory as possible with "alive" groups, ones that cannot be captured by the enemy.
A typical game of Go is played on a 19×19 grid, which makes for 361 spaces on which one can play stones. Given the huge array of potential choices this makes, especially given that stones can be taken and retaken almost ad infinitum, there are more potential games of Go than atoms in the known universe. There are 10,000 trillion different potential games after only fourteen moves. That, more than anything, hinders programmers trying to create a computer that can play the game well. Computers are not powerful enough to come anywhere close to analyzing every board position several moves ahead as they do in chess.
The fine line between building territory and building influence is also very difficult for computers to understand. A human player understands that building a straight line across the second row is a bad idea. It may build secure territory, but only a very small amount, as your opponent is likely sealing up the rest of the board (in a looser fashion, though). The trade-offs between being secure and being efficient are incredibly complicated.
So how well have computers done against human players, exactly? The greatest victory for a computer came in August 2008, when the MoGo program beat Myungwan Kim, a high-ranking professional player, but only with a nine-stone handicap in the computer's favor. Nine stone handicaps are the largest that can typically be given, with the weaker player getting free stones on each star point of the board before the favorite gets a move. Myungwan Kim spent very little time thinking before each move, apparently in an attempt to limit the computer's available time to process the board. He would later beat MoGo twice more with the exact same conditions the next month.
It would probably be short-sighted to say that computer Go programs will never achieve a professional-level understanding of the game, but they certainly face a monumental task. Go represents every way that humans are still superior to artificial intelligence efforts, encapsulated into one simple game system. Complex pattern recognition, very broad image analysis, and incredibly vague trade-offs turn by turn by turn until the game is over. Go is the life's oldest and most natural game, and one of the last that technology will conquer.