At face value chess is very easy to learn. You can pick up the rules and moves in a day’s work or sometimes two at the most. So, why is it that this game which is so easy to get started with feels so complex when you start to play more often? What is it that drives the undeniable complexity of chess and is it something that we can learn to adapt to in order to improve our game?
Why is chess so complicated? Chess is so complicated because there are 6 different pieces replicated in various amounts to make 32 in total, and they are allowed to move on a board of 64 squares. This makes billions of possible positions and an infinite number strategies that can make use of them. Chess being complicated is a good thing too: It means that no one can learn all the possible outcomes so playing chess will always be interesting.
It really is a matter of geometry and mathematics. That might not sound very exciting but it actually is (no, really!)
The Geometric Complications Of Chess
There are 6 pieces in chess which are replicated in various numbers to put 32 (2 x 16) pieces in total on to a board of 64 squares (8 x 8). None of these numbers are particularly big, are they? Yet, this handful of squares and pieces can lead to some incredible mathematical outcomes.
A Greedy Man: A Cautionary Tale
Many people will have heard the story of the greedy man who when asked by a king for a reward of his choosing, asked for a single grain of rice to be placed on the first square of a chessboard and for the king to double for each square until the king had covered the whole chessboard.
The king soon realized his mistake when he discovered that he would place 1 grain on the first square, 2 on the second, but by the 64th square he would need 264 grains of rice and there aren’t that many grains of rice in the whole world. (That number has 20 digits, and it’s exactly 18,446,744,073,709,551,616.)
Unfortunately, being a king, he rectified his error by having the greedy man’s head chopped off. Oops.
Rice Vs. Positions In Chess
So, we’ve determined that 264 is a lot of rice. In fact, rather more rice than there is in the whole world but how many moves are there in chess and what about positions that could arise on the board?
Well, the player begins with the ability to make 16 x pawn moves (any pawn may move 1 or 2 squares) or 4 x knight moves (the knight may move to either side in front of the pawns) and so does his opponent. So, when both players have made their moves there are 20 (total possible first moves) x 20 (total possible first moves for the other player) or 202 combinations available and that makes 400 potential board positions at the end of the first move!
Things don’t slow down, and you’re going to have to trust us on the math here as it starts to get complicate – but after just 2 moves, there are potentially 72,000 different positions that could have been created on the board!
After 3, well you’re at 9 million! And once you hit 4 there are 288 billion!
There Are A Huge Number Of Positions In Chess
It doesn’t stop going up rapidly from there. In fact, according to mathematicians much cleverer than I am, there are about 1080 possible moves on a chess board and this results in 10120 possible positions!
That’s a whole lot of moves. In fact, it’s rather more moves than there were grains of rice on the planet and there are even more positions.
This means that it is impossible for even the smartest human being to work through all the moves and positions that are in front of them on the board.
However, it gets worse. Even if our human player were to enroll a computer which was as powerful as is theoretically possible (e.g. far more powerful than the computers we can make today) and set it on the problem, that computer would not finish evaluating everything before the universe had ended.
Yes, there are so many moves and positions in chess that a computer operating at, quite literally, light speeds couldn’t analyze them all without running out of time.
The Complexity Of Chess Means It Can’t Be “Solved”
Solving a game means that a solution is created where if two players were to play perfectly against each other, a player should either be able to force a win (because there is an inherent advantage in the game – say, starting with the white pieces, for example) or at the very least always draw the game.
A full solution means that this is true from any position on the board, a weak one means that the game has been solved for its starting position, only.
Checkers has been weakly solved. In fact, it was solved more than a decade ago, though a complete solution may need to wait a while longer.
Chess because of the complexity described above, will never be solved, not even weakly. This is good news because it means there will never be a day when you can memorize a series of moves and be certain of winning (or at least, not losing).
Visualization And Complexity
The best human players in the world, can come to terms with some of this complexity and they can visualize potential variations of a game based on the board in front of them and looking forward at the most promising moves and their potential outcomes further on in time.
In order to make this process manageable (no chess player is visualizing 288 billion moves, for example) they will discard moves that are obviously bad and this allows them to increase their “reach into the future”.
Chess Grandmasters See Farther Into The Future
Thus, a grandmaster or a world champion chess player may look 10 or more moves into the future, though not much more than that. There is a limit to the human capability to visualize complex solutions and it seems likely that if chess players haven’t hit this limit that they have come very close to it.
A weaker player will visualize much less. A beginner may not visualize at all and a decent player in a general tournament may only look 4 or 5 moves ahead which is enough to give them a big advantage over a beginner but probably ensures a thrashing from a grandmaster.
Computers, on the other hand, can look 20 or more moves ahead and they can check all variations. This is the reason that a grandmaster cannot beat a computer without the computer assuming some sort of handicap (the current handicap appears to be the computer has to give up at least a knight before the grandmaster has a chance of winning).
Thus, if you want to improve your chess game despite the complexity of the game, you should work on your visualization skills. The further ahead you can plan your game, the stronger you will become.
So why is chess so complicated? It’s because there are 1080 potential moves and 10120 potential positions on the board. That’s the reason why chess is so complicated in a nutshell. Even if you had the best brain on earth, there is a limit to the number of moves you can “see ahead” because human beings are not computers, and there is no computer (now or ever) that can see all these potential outcomes, either. Chess’s complexity is defined by geometry.
In terms of the complexity of chess between players, however, much of the challenge in chess is not memorization but rather being able to visualize potential future states of the board. We can use certain models to cut down on the number of positions that we map (some moves are obviously terrible or even suicidal and can be simply discounted in our projections) but there is a limit to this. The superior player is usually the one that find this less complicated than the other.