The Problem With Memorization
Starting the game with perfect computer moves seems like it should help you win. Why doesn't it?
In one round of my last over-the-board tournament, my opponent played a line of the London I wasn’t ready for. I immediately messed up and played an inferior move. But four moves later, I had a strong attack.
In another round as White I got a variation of the Catalan that I had studied closely with a friend. I played 13 moves of preparation, including several counterintuitive moves that I would never find over the board, but that the computer said were best. Soon after the end of my preparation I started to go astray and lost the game.
Why does this seem to happen so often? As James Altucher said in a comment to a previous post, “I would think if you are playing like a computer for the first 23 moves that would be good for your game.” You would think so, wouldn’t you! And yet it doesn’t always seem to help. Why not?
The Math of Exponents
The first reason is just math. Because of how exponentials work, it’s very rare that you would get any long, specific line in a particular game.
In a typical middlegame position each side has 30-40 legal moves. These add up quickly. Or rather, multiply up, because that’s the mathematical operation that describes the branching paths of a chess game. If each side has 40 legal moves, after a single move by each side, there are 40 * 40 = 1600 possible sequences. After just one move!
Many of these legal moves are garbage and can be safely ignored, but not all of them. It’s not uncommon for there to be six decent moves in a typical opening position. Even small numbers get big very quickly when you start multiplying them together. When I made my opening explorer, I had to limit it to four moves, because with any more the graph became too cluttered to see.
There’s a famous story relating exponential growth and chess. It involves a man making a deal with a king for a commodity grain using a chessboard. In some versions the man is the inventor of chess, in others just a con man; in some versions the grain is rice, in others wheat; but the deal is the same.
On the first square of the chessboard the king will give the man one grain of, let’s say, wheat. Then for every subsequent square he will double the amount: two on the second square, four on the third square, and so on. In the story, the king agrees to the deal, but soon finds out that this will amount to more wheat than is in his entire treasury.
Intuitively it’s hard to imagine that the number will grow so quickly, but it does. The total number of grains turns out to be 18,446,744,073,709,551,615, or eighteen quintillion, four hundred forty-six quadrillion, seven hundred forty-four trillion, seventy-three billion, seven hundred nine million, five hundred fifty-one thousand, six hundred and fifteen.
And keep in mind that the branching factor in the story is only two - the count doubles on each square - not six, or 40, as in a real chess game. The number of possibilities in a chess game is much, much bigger than the grains of wheat in the story.
There’s something I’ve always found odd about this story. It involves a chessboard and exponentiation, but the arrangement has nothing to do with chess. The chessboard is just an incidental prop.
But as we’ve seen, exponents are intimately related to the rules of chess. They’re why, no matter how many variations you memorize, you will only know an infinitesimal fraction of all the paths a chess game can take.
Playing the Game
So there’s a math reason why you’re unlikely to get any specific line. The other issue with memorization is that there’s still the small matter of playing the rest of the game.
Long, prepared variations tend to follow the best moves for both sides, which means the game should stay relatively balanced. If all goes well, you might get an advantage of 0.5 in the computer evaluation - half a pawn. If you and your opponent regularly make serious mistakes, such an advantage isn’t very relevant.
Additionally, the punishment for your opponent if they veer from the line might not be as much as you think. Unless they make an outright blunder, you’ll probably only get an advantage in the range of 0.5-1.0, far from a winning position. The game will still be decided by who plays better in the middlegame.
Does it then follow, as some people say, that you shouldn’t study the opening?
No, I don’t think so. Every game starts with the opening. In fact, every game starts with the exact same position. (You can’t find these hard-hitting insights anywhere else!) It would be really strange if the right strategy was to never study this phase of the game.
Rather, it’s about how you study the opening. Sam Shankland has said, "The most valuable aspect of opening work is that it guides our understanding of resulting middlegame positions." Typical plans, pawn breaks, where to put your pieces, which exchanges benefit you - these are the things you really need to know. By focusing on these, you address the two big problems of memorizing specific lines:
You almost never get the line you memorized. Plans and ideas are valuable even if your opponent doesn’t follow the exact line you remember.
At some point the line ends and you have to play chess. In this case, you also need to know the plans and ideas of the position.
The tricky part is that every opening is different. It would be great if you could develop universal skills that would let you play well in any position. To some extent you can - skills like calculation and visualization are relevant in almost every position. But in practice, chess is more like a collection of distinct subgames, each with their own strategic rules.
Grandmasters are always saying things like, “Everyone knows that in the King’s Indian, when White plays exf5, it’s better to recapture with the pawn than the bishop.” But of course, not everyone knows this. Only grandmasters know it. It’s what makes them grandmasters.
As a FIDE master who’s not primarily focused on chess competition, one of my main issues is that my subgame knowledge is uneven. In “my” positions I can compete on a grandmaster level, but in other kinds of positions I’m apt to lose like a beginner.
As you start building up your subgame knowledge, at the end of every opening line you learn, ask yourself, “Would I be happy playing this position in a tournament game?” If the answer is no, your opening preparation probably isn’t doing you much good.
The last number is 6 not 5 in the grain problem
Great post. Is the best way to become familiar with a given opening's resulting middlegame positions - aside from amassing a large volume of games played - to play through a bunch of master games in that opening? If not, what else?