Chess Openings: To Memorize or Not to Memorize, That is the Question
You might before have asked the question: "Should I memorize chess opening lines?" The answer is not as straightforward, and the reason lies in the game's staggering complexity.
To illustrate, let's take a mind-boggling journey through the mathematics of chess. At move 1 there are 20 moves to pick from, after 3 moves 8,902 chess games. After just 10 half-moves into a game or after move 5, there are approximately 69 trillion possible chess games.1 It is also the number of moves it takes you to arrive at the starting position of the Najdorf.
The number is so vast that it can be hard to really understand it without some kind of mental picture. So imagine each game is a grain of sand (1 grain of sand = 0.1 mm³) the pile of sand would contain nearly 7000 cubic meters of sand. Now imagine you take out a spoon and go over to the sand pile and take a spoonful with you home. The sand you brought with you home could represent a Chessable Life-Time Repertoire with 1000 lines.
You now start to arrange the sand grains in a neatly looking opening tree and you start memorizing the order of the sand grains while you glaze out of your window to watch the huge mountain of sand you left behind.
There are of course a lot of bad sand grains in the pile of sand2, but I hope this picture highlights the challenge chess improvers take on when they attempt to memorize chess openings and responses.
But how often and how deep do normal amateur games go before they face a new position and are “out of their book”?
I decided to take a look into the data and extracted 207 games from the latest Monthly Classical Arena on Lichess. I then made a Python script that looked up the first new position in the players opening explorer.
I decided to look at classical games since I believe people are more likely to play according to theory in a classical tournament compared to a bullet game. The data was then saved to a Google Sheet so I could make some diagrams for you.
The results
The average player had a new position after 5,7 full moves, while the longest game one had in the analyzed games was 20 moves deep. The top of the diagram is around move 5 and then falls after move 6. From a mathematical perspective, it makes sense since after 6 full moves we have hit 62 quadrillion possible chess game variations.
If we look at the games and account for rating and its effect we get the following diagram.
It is pretty clear that there is not a huge correlation between having a high rating and getting deep into known territory. One factor is that lower-rated players might deviate from theory early or maybe it is just normal to be “out-of-book” between moves 5 and 10. However, we can see that when we reach the ratings around 1700-1800 Lichess Classical more games begin to go deeper and beyond move 10.
If we look at the influence of color it looks like Black is sooner arrives at a new position compared to the White side. One explanation could be that chess players are switching more with Black and playing the same with White.
Finally, I took a look at the 20 games that went the longest before deviating from an earlier game they had played vs 20 games where the players had a fresh position after move 1 or 2. The top scored 14/20 points while the bottom scored 8/20 points, so it might be useful to know the position after all.
Final thoughts
I’m well aware that there are many uncertainties and factors that play into the numbers I have presented to you. Mainly it might be that higher-rated players have played more games compared to lower-rated players, which would lead to a higher out-of-book number.
I do however hope that this newsletter has given you something to think about. Is it useful to memorize an opening line vs. learning the ideas in a specific opening? I have at least reevaluated at what depth it is useful to memorize lines.
When you learn ideas you can use them like paths through the desert, while specific lines mostly are useful to remember if the exact position arises in the game. And how often do you really see your opening prep past move 10 or 15 on the board?
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/Martin
For more information about the Shannon number
It seems like I made a math conversion error in the sand grain calculation:
69,352,859,712,417 grains * 0.1 mm³/grain = 6,935,285,971,241.7 mm³.
To convert this to cubic meters, we should divide by 1,000,000,000
6,935,285,971,241.7 mm³ / 1,000,000,000 = 6,935.286 m³.
So the pile is not quite the as massive but only nearly 7000 m3, which is also something.. Sorry about that!
Loved this article, Martin.
I am convinced that the study of openings is to extend our "comfort zone" so to speak. I have often heard that true learning starts at the edge of a person's comfort zone. That's why groan, "Oh no! Not another learning experience!" :-)
So, those positions that arrive when we are out of our preparation are where we can learn the most -- but we prefer to not have our learning happen when the stakes at their highest -- in an OTB tournament game, for example. So I am convinced that the best way to learn an opening from something like chessable is to give a personal look at the end position of what chessable now calls a "priority variation" and make our own conclusions about how we would play those positions -- to try to give yourself a "learning experience" when less is at stake.
It is impractical to memorize a chessable LTR -- but I have lengthy LTRs on chessable -- in fact I am anxiously waiting for Shankland's 3rd part of his Neo-Catalan LTR. I will definitely be looking at the priority variations --- and most importantly, I will be examining the end positions of those priority lines.
BTW, I am +2000 on lichess, around 1800 chess.com ... have been 1799 USCF.