Chess – Design Oriented Blog

In response to my article On “Perfect Imbalance”, Travis Clark wrote in with his insightful perspective on balance and memorization in Chess.

POV: PLAYER. DIFFICULTY 4. LEVEL 1 – 2

As for the state of balance in Chess, Travis makes a great point about the subtle nature of the imbalances present in what appears to be a symmetrical system:

“It is almost symmetrical, and visually tricks people into to thinking so with the optical-illusion of black and white squares and the pieces in front of you line up with pieces in-front of your opponent. Fold the board in half along its supposed line of symmetry and you will find every black square folds on top of a white square. The board itself isn’t meant to be symmetrical. Its a very small difference but bishops are assigned to move along a specific color square so the board itself creates some very slight but uneven gameplay. Now take a close look at the pieces. Things look a little different if you are playing black versus playing white. If you are playing as white your king is on the fourth square from the right. If you are playing black, you must look from black’s perspective, your king is on the fifth square from the right. The situation for the queens are similar. I believe it is this way because it is aesthetically pleasing. However, every opening strategy is hinged on this very slightly imbalanced set-up.” ~Travis

In the original article, I had considered making a comment on the fact that Chess is not a symmetrical game, primarily because of White’s first-turn advantage, but Travis brings up a good further point about how the aesthetically-pleasing apparently-symmetrical setup is hiding some one-square positioning differences that rest at the core of the strategy-space of the game. He later also mentioned the importance of first-turn advantage as well:

“The most drastic way chess is imbalanced is the fact that white always goes first. You may wonder how much of a difference white’s privilege actually makes. …Because of the small differences in starting positions and the advantage white has in time there is a Chess theory which states that if two perfect computers were to play each-other, with all the Chess databases known to man for reference material the best outcome black could hope for would be a draw in every game.” ~Travis

Travis pointed out a memorization-free style of learning chess that worked well for him:

“Josh Waitzkin is one of my chess heroes. He wrote an excellent book called The Art of Learning that I highly recommend, and in partnership with Chessmaster(Ubisoft) created a fantastic chess course. The reason why I was drawn in to chess so deeply and find it fascinating are his annotated games. His style of play and teaching didn’t revolve around the learning of specific patterns or memorizing databases. In place of the rote portion he would explain the theory of why certain opening patterns developed and what the Grandmaster’s that used them were trying to accomplish what they gave up and got in return and how it suited their style of play. I never once had been one to memorize openings. Using his training I could look at a completely unfamiliar opening, that my opponent may have memorized, and look at its goal and strengths and weaknesses and choose a move based on that.” ~Travis

And he went on to talk about the mind-games that can be involved in Chess:

“But the heart of chess is this competitive spirit. Connecting with someone through competition is the key. Memorization is a piece of the puzzle but I argue that it is a much smaller piece than the current image of chess projects. Raw calculation is indeed a factor along with pattern recognition, logic, strategy, poise and other mental talents; however, I believe the biggest portion is the psychology of competition. You have to be in tune with what you opponent is thinking and find a move that counters, disrupts, or solidifies your opponent’s thought process while fitting the current position on the board. The correct move isn’t always the mathematical best move, rather it is the move that will beat the opponent in right in-front of you in that moment with their current state of mind. As annotated by Josh, this psychological warfare happens on the grandmaster level, the beginner level and everything in-between. That is why I argue that it is the heart of this slightly imbalanced non-symmetrical game.” ~Travis

It’s a great point, and one that I think is too often thrown by the wayside when we try to talk about design in the abstract. People are playing these games, and seldom can they near the mathematical precision of a computer, in terms of memory and applying algorithms and valuation strategies effectively and consistently. Even though Chess is a perfectly deterministic game involving no hidden information that would affect objectively optimal play, a degree of psychologically-hidden information exists because of the limitations of the human mind’s ability to apprehend the many branches of the decisions tree. Even at the highest levels, says Travis, players benefit from exploiting the limitations of the wetware of their opponent while trying to avoid being exploited themselves. Memorization might be an “ideal” solution to chess, but as the metagame stands now, there’s plenty of room for human limitations to be exploited by using the mind and emotions of the opponent as a weapon.

Thanks for the great email, Travis!

POV: DESIGNER. DIFFICULTY 3. LEVEL 1 – 1

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.

Tag: Chess

Reader Response: “On Perfect Imbalance”

On “Perfect Imbalance”: Memorization and Balance