The Algorithm

Philidor once said that the pawns are the soul of the game. That could actually be a very modern understanding of an economy. Pawns are the currency of chess after all. I prefer Botvinnik’s statement, that the real soul of chess is the trade. Playing well means making good trades. In Chess, material, time and space all have specific values which can be measured in pawn-units. That’s what computers have told us (after we taught it to them). Computers evaluate candidates and just play the move with the highest evaluation.

Computers don’t even need a plan, they just make “good” moves. A sequence of good moves may look like a plan in hindsight, but that is just a coincidence. Lasker was wrong, when he said that a bad plan is better than no plan. Countless games have been lost because of bad plans, where just making good moves with no deeper purpose whatsoever would have been sufficient.

The question is how to find “good” moves. At this point I am going to show you a game of Rubinstein that I find to be very instructive. Just play through the moves and ignore the obvious fact that Schlechter wasn’t up to the task, or didn’t feel well that day, whatever. Later on, I will go through the game again, but this time with comments.

This game is not unusual for Rubinstein and pretty much all of his games play out in a similar fashion. The reason is that he probably had something like an algorithm, a method of play. The question is: What was it and can we develop such a method too?

My first theory is, that a move-search-algorithm should be the exact copy of the positional-evaluation-function. For instance, if you look at a position and determine that one side has an advantage, then you need concrete reasons to justify this claim. Evaluating a position correctly is a skill. If you are searching for the best move, you need the very same skill again.

The second theory – which can be found in Dorfman’s “The Method in Chess” – states, that there is a hierarchy of factors when it comes to evaluating a position. Stop! Can’t we can translate everything in chess into pawn-values and isn’t a pawn is a pawn after all? Well, it seems that some pawns are more equal than others. In other words, there are hidden values in chess.

What am I talking about? Ok, here we go:

We all know that king-safety is the most important factor in chess, because if you lose your king, the game is over and nobody cares how much you got in return. The king has an infinite value that cannot be expressed in pawn-units, like you can’t put a price tag on your life. Therefore king-safety is the number one factor in the hierarchy of chess values. The practical problem is of course how to determine if the king is safe or not. Here it helps to just add the value of the attacking units and to subtract the value of the defending units. The higher the difference is, the more reason you should have for concern. Since there are positions where a single pawn can give mate, this is all very relative of course.

To explain what comes second in the hierarchy I need to deviate a bit. The biggest problem in chess is the search-horizon. Since we can’t calculate that one candidate move leads to mate in 75 moves, while the other leads to a draw in 120 moves, we need to operate with lesser goals. Botvinnik came up with such a goal for his chess-engine PIONEER: Winning material. Once you won “enough” material, mate will follow automatically, unless your opponent can build up some sort of fortress or bail out to a theoretically drawn ending. Having a material advantage doesn’t not just mean owning an extra piece of wood. It can also be the bishop pair, or Q+N > Q+B and R+B > R+N (Capablanca Rules), or just B vs. N in certain positions. Since winning material is our default goal in chess, we can put it into second place in our hierarchy.

The third factor in the hierarchy is the pawn structure, since pawns – like a skeleton – give the game it’s shape. Note: Pawns can’t move backwards, so not every move that looks appealing will turn out to be an improvement after all.

The fourth and final factor in the hierarchy of positional factors should be the placement of the pieces. Pieces – like blood – inject life into the position. Here Makagonov’s Rule comes in handy: If you don’t know what to do, improve the position of your worst piece!

Here are the questions that you should ask yourself in this order:
1. Are the kings safe?
2. Can I win material?
3. Can I improve my pawn structure or can I spoil my opponent’s pawn structure?
4. Can I improve my pieces or restrict my opponent’s pieces?

Believe it or not, but this “algorithm” produces rankings that are very similar to computer candidate moves.

Now let’s look at Rubinstein’s game again, this time with comments!

As you can see, there is a method to the madness, or at least it looks like one. My personal feeling is that Rubinstein didn’t even bother with trying to understand Schlechter’s moves. In fact, there is not much point in it, since they are pretty bad anyways. It seems that Gligoric was right: Ignore your opponent, just play the pieces!

Here are a few more pointers to shape your thinking process:

  • Don’t start a wild attack, but worry a lot if your opponent does
  • Winning material should be your default-mode
  • Pawns can’t move backwards, so don’t overcommit
  • Improve your pieces or restrict the pieces of your opponent

Shortcut: Grab their bishops! If you don’t see a way to win material, just improve your worst piece!

One final reminder: While it is nice to have some sort of algorithm to approach the position, you shouldn’t go overboard and ignore the fact that chess is a very concrete game. Even the very best abstract concepts can fail to concrete tactics and unfortunately this happens quite often. That is the main reason for decisive results after all.

Play it safe!