With the advent of computer technology, have we completely and successfully explored the seemingly endless array of positions within a single game of chess? Have we reached the zenith of game theory? Are there any unknown chess mysteries left to solve? Some might simply say no because, after all, computers would have been able to calculate into the dark void of possible positions, so if there was anything unknown it would have been found by the Silicon beast. I say rubbish to that! I firmly believe that there is a vast array of uncharted territory and that territory might lead to some astonishing discoveries that might change the way we play the game. Sorry, my Hyperbaric therapy sessions have thrown my brain into overdrive so I’m stuck dwelling upon such thoughts. To appreciate what I’m getting at, we have to look at the huge number of potential positions that can arise in a single game of chess. The number is so staggering that after first hearing it mentioned, I thought the gentleman rattling off this number was full of…well, you know what I was thinking.
At the start of the game, each player has a choice of 20 first moves. That seems easy enough to digest since each of the eight pawns can move one or two squares on move one (16 possible moves) and each Knight can make one of two moves (4 moves total). As we move forward into the game, the number then jumps to 400 possible positions to be found on the board. So far, this seems reasonable. With another pair of moves made, the number now jumps to197,742. Then the number jumps up to roughly 121,000,000. It only gets worse, large number-wise, from here! The number of ways of playing the first four moves per side in a single game of chess is approximately 318, 979, 564,000. You can look up the theoretical total number of potential positions in a single game of chess online by googling the Shannon Number. Make sure to have a mirror close by so you can watch your jaw drop upon grasping this enormous number.
Rather that get into the Shannon number and the associated mathematics behind these calculations, I want you to think about a number that is far larger than the total number of atoms in your body combined with the number of individual grains of sand on our planet multiplied by a gigantic number and ask yourself, are there still deeper mysteries to explore within the game we love so much, especially considering the huge number of potential positions?
One of the problems that keep us from being able to discover these potential mysteries is that the fact that the very principles that help us to play better, preventing us from taking a side trip into the realm of positional chaos, a place in which principles hold no sway and games are lost. We learn specific game principles that tell us we need to do this or that during a specific phase of the game. Doing otherwise, will lead to a loss and since we’re trying to win more than we lose, we take the path more traveled rather than venture into uncharted waters. It’s slightly ironic that we’re given this vast uncharted territory to explore but can’t take the journey because doing so would lead to positional ruin (and losing games). However, I really believe that there’s something out there in the vast unexplored territories. It’s kind of like believing in UFOs. Mathematical theory tells us the chances of intelligent life elsewhere in the universe is most likely. Yet, a large number of people simply think intelligent life elsewhere (as if we’re actually an intelligent species) is ridiculous. With a number of potential positions in a single game so large my arm would fall off trying to write it out, has the game been fully explored? Theory says no!
Then again, who is going to explore it while trying improve their rating level? Not anyone paying a high entrance fee at their local rated tournaments! It’s the great double edged sword of irony. The question more aptly might be, can we actually explore the unknown in chess?
Because the numbers are so large, we’d need computer assistance. However, you’d have to consider a more specialized program than your high end chess software. After all, it’s designed to come up with the best way to win a game, not take a dip in the dark waters of positional chaos. Chess computers give you the potentially best moves rather than open a portal into the realm of the unknown. A more specialized computer program would be needed. An unconventional path would have to be taken!
I’m going to get together with some mathematicians and computer programmers next month and see if we can seriously look at this problem, finding a way into the rabbit hole (and hopefully a way out). I will be addressing this subject in greater detail in the near future (articles), but wanted to simply throw the idea out for debate. I suspect every chess player has wondered if there was additional life out there on the outer edges of the chess universe. I think it’s a subject worth further study. Until then, here’s a game to enjoy until next week!