On “Perfect Imbalance”: Memorization and Balance


In their video “Perfect Imbalance” Extra Credits mentions that a problem with balanced games is that there’s often a lot of memorization involved in learning to play them well. They suggest that because Chess is perfectly balanced, players can memorize openings and gain significant advantage from knowing early-game optimal play. By briefly examining why and how players memorize strategies, we can see that balance has nothing to do with memorization being so effective.

“ [Chess is a great game] but it does suffer from the standard problems that perfectly balanced games build up, namely that a collection of fixed strategies end up getting established over time. If you’ve only played casual games of chess at home it’s great. There’s thousands of interesting strategies to discover and try out, and your tactics will evolve over the course of a match. But if you’ve gone a step further and really look at taking your game to the next level you’ll find that there’s a lot of a rote work to do. There are a great number of established strategies and play sequences that you have to memorize before you get to a high enough level of play that you’re really experimenting with anything new again or are once again able to start crafting your own strategies. The set of canonical strategies has built up to such a point that one can spend years if not decades of one’s life studying chess without really getting to create new plays or develop your own stratagems.”

What properties of Chess allow memorizing strategies to be so effective?

In order to use plans that you memorize, you need to recognize that you are in a familiar position. No position is more familiar to a Chess player than the starting board position, since it’s the same every game. It’s an easy and useful starting place for elaborate acts of memorization and recall.

Since you know what the board’s going to look like, you can start thinking about what you’re going to do and what your opponent is going to do in reaction based on this stable foundation. As the game progresses, you’ll be able to know the positions of all the pieces at all times, since Chess is a game of perfect information. All moves in Chess are perfectly reliable, so the only obstacle in the way of predicting a whole game’s moves is your ability to analyse the position and predict play accurately. What makes Chess an interesting game is that its broad possibility space means that it takes practice and a high level of mental skill to hold all of the possible viable moves in your head and think through the different possible outcomes for even the next 5 to 10 moves.

Because of all this reliability and the repetition involved in the opening position, you’ll start memorizing brief runs of play in the early-game that you’ve noticed lead to better positions more often than not. Over hundreds of games you’ll pick out more of these patterns at different common board positions throughout the game and commit them to memory. Broadly, this is not atypical of the learning process required to gain skill in all turn-based strategy games. No matter what game you’re playing, you need to at least memorize enough game rules to be able to imagine what the next few turns might look like in order to determine what you should do this turn. This process of picturing the next few turns and developing short-term strategies gets more efficient and effective with practice, in part because you’re memorizing snippets of strategy and patterns of play that lead to certain outcomes, then reusing them.

The rules of Chess don’t place any obstacles between calculation and memorization. Any time you calculate the right move for a board position, you might as well memorize it and reuse it next time, since there’s no way it could turn out differently–unless your opinion on the right move is actually incorrect! Considering how many people play Chess around the world, and the extensive database of past games logged and commented on by experts, it’s more likely than ever that you’ll find out you’re incorrect without even having to play your way into that realization.

That huge community, and the metagame it creates, makes a sizable contribution to biasing players towards memorization as a way of improving their skill. There are thousands upon thousands of publicly available recorded chess games to review. There are thousands of books about Chess strategy, many of which contain lists of common openings and the patterns of play that seem most effective against them. The depth of available material gives you an almost unlimited number of master-endorsed strategies to memorize if you’d like. This weight of accumulated knowledge can feel oppressive to a new player who wants to get good at game–this is exactly what Extra Credits is talking about when they say that Chess is stale due to memorization.

Notice that I’ve said nothing of balance so far, I’ve only talked about the properties of the system. Balance does nothing to increase the effectiveness of players memorizing strategies as a way to improve their performance. Even if Chess were a battle between armies with asymmetric capabilities, if those sides were used in every Chess match and perfect information were still available, the game would be just as prone to memorization, since asymmetry alone does nothing to change the conditions required to make and re-use extensive plans. If Chess were incredibly unbalanced (say white had all pieces replaced by queens and black had a normal set-up), memorization would be just as prevalent. Memorization would likely be *more effective* in unbalanced chess, because the imbalance would lead to the overpowered player often winning in fewer moves, thus requiring less memorization on average to produce winning results.

In summary, memorization is prevalent in Chess because

  • perfect information is available about the game state, so the players know enough to plan perfectly if they are mentally capable;
  • all moves are perfectly reliable, so that perfect plan will not have to be altered during the course of play;
  • and the game starts from the same state every time, so the perfect plan has a perfectly-reliable starting point.