If you don't play chess, you might wonder: what is it about the game that so compels people, and has done so for thousands of years? Why does it seem more mysterious than other games - so daunting to an outsider?And those who do play have similar questions: Why do I feel so drawn in? And yet, though I know the rules, why does the game seem impenetrable?
Probably because it is.
Before a game begins, chess boards look calm and orderly. Those neat rows of waiting figures are a familiar and even nostalgic sight. But familiarity is quick to shatter when a game gets underway.
There are 400 different options for the way you and your opponent can take your first turns. One move each and you might already be encountering a game you've never played before!
After both players have moved a second time, there are 71,782 possible board configurations. This is many, many times more games of chess than I've played in my life. After three moves apiece there are over 9 million possibilities, and after the fourth pair of moves, 288 billion.
At every turn you and your opponent stake out a path for yourselves through a vast web of choices. After several moves the path you are taking, the chess game you're playing, has never been played before.
Our powers of calculation are surpassed by the number of different games of chess that are possible. One estimate puts it at 10123, a number that has no material existence in the Universe. (For comparison's sake, this is 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000 times more than the number of atoms that exist.)
So why do we love, fear, and play chess? My guess is that it serves as a reminder of the infinite complexity underlying everything - even things that seem black and white.
Chess is a good example of entropy, right?
ReplyDeleteyes, absolutely
ReplyDeleteI used to play chess semi-seriously, so I totally know what you mean here, but have you looked into Go? It swamps chess from the large numbers point of view. Each player has hundreds of options at each point in the game, and the game usually goes on for 200 moves or more.
ReplyDeleteAnd all you have are black stones and white stones (indistinguishable particles and all that), making the complexity even more impressive.
Chess simplifies in the endgame because the number of pieces keeps decreasing. The Japanese version of chess (shogi) allows you to use the pieces you've captured as your own, and there's a variant of chess (crazyhouse) that incorporates this rule. I guess these games could keep going and going...
As the game tree expands rapidly - both in chess and in Go - it might be worthwhile simulating multiple random games at each node (Monte Carlo or Simulated Annealling). I know this has been done for Go (which has no apparent minimax optimisation function); what is the situation with Chess? Is this better than a heuritics and/oe a library of previous games?
ReplyDeleteI've never played Go, Shogi, or Crazyhouse, but now I definitely want to. Something about chess seems perfected to me, but I'm sure that's just another nostalgic bias I have. Eunoia, I actually know nothing about how estimations are done - sounds like you know much more than me, and I'd be interested to learn more about it.
ReplyDeleteI'm glad something beats the whole dark energy (mis-)prediction of QM, which is off by 10^120.
ReplyDelete