Part of the reason why I love chess is the amazing complexity of the game. As David Shenk explains in his fabulous book The Immortal Game:
After the first round of moves (meaning, white makes its first move and black responds with its first move), there are 400 possible board positions, as white has twenty possible first moves, and black’s response can be either one of twenty moves as well. In the second move, for every one of those 400 positions, there are 27 options that each player has for his or her second move, resulting in a total of 71,852 possible board positions. Talk about geometric progression.
After three moves each for black and white, there are approximately nine million possible board positions. Four moves each brings it to 315 billion possible distinct positions.
So the game has barely started, and already you could have hundreds of billions of possible game sets. So it doesn’t surprise that the total number of unique chess games is near infinite, and obviously beyond human capacity to play through them all. The estimated total is 10 to the power of 120, or a thousand trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion.
That’s a lot of possible games…