Sunday, December 12, 2010

Option Principle

A worthwhile yet neglected contribution to chess literature is the Option Principle. The Option Principle was first enunciated by Weaver Adams. In his book, White to Play and Win (1939), Adams wrote:
A third characteristic of a good move has to do with the conservation of valuable options, as follows: If a piece appear to have two or more equally attractive moves in a given position, this usually may be taken as a sign that a move of this particular piece is incorrect at the moment, or, in other words, that the best square for this piece is not as yet determinable. Necessarily, however, the best square for the correct piece to move to is determinable (otherwise the move would be incorrect). And because of this fact, the correct piece to move can usually be seen to have but one attractive square to move to. … "In practice it is easy to overlook an optional square for a piece, especially if this is one which at the moment is impossible due to obstruction, or undesirable because attacked by enemy pieces. Any one of these squares represents an important and valuable option in proportion as it can be foreseen that the game might take a course which would render these squares available and/or desirable at some future time (p.15).  

Sixty years later the Option Principle was reintroduced into chess literature by Dr. Hans Berliner. In 1999, Dr. Berliner published his book, The System, which incorporated the Option Principle as a central pillar of his system. According to Berliner:
The Option Principle states: make the move (develop the piece) which does the least to reduce your options to make other important moves. When there are several pieces that can be developed, move the one for which the Optimal Placement is most clear. This is a generalization of Lasker’s rule ‘knights before bishops’. Usually a bishop has more good locations to choose from than a knight, so develop the knight first. However, the System options principle is much more general. It frequently encourages the non-movement of a piece that is already well placed on the back rank. It may also discourage castling, if the rook is well placed for an attack. … The Option Principle also prohibits making a move that blocks a friendly piece from reaching its optimal location. … there is always at least one move that is crying out to be played before other moves. (p.36-37).
In 2008, the Option Principle again found its way into print with the publication of The Final Theory of Chess and in 2009 it found a home on the World Wide Web with the Final Theory of Chess Open Encyclopedia of Chess Openings.

In addition to the three aforementioned books, the Option Principle is hinted at with varying degrees of vagueness by several other chess writers.
  • Philidor warned against obstructing one’s own pawns. He advocated 2…d6 (after 1.e4 e5 2.Nf3) in order to avoid losing the option of advancing Black’s c-pawn.
  • The second World Champion, Emanual Lasker, applied the Option Principle to the range of plans in which multiple pieces could cooperate. He wrote: “or, to use another term, say flexibility, or adaptability or elasticity. The main idea of this co-operation is to increase the range of possible plans to follow, without specifying too early which road you would prefer to travel. By co-operation you aim to keep the position plastic, alive; by lack of co-operation you take the life out of your position, and to infuse it with new life you will need outside aid” (Lasker, Emanual. Lasker's Manual of Chess, p.231).
  • Nimzowitsch emphasized the reduction in options entailed when the central pawns are advanced early. In his notes to the game Nimzowitsch-Rubinstein (Berliner Tageblatt Tournament, Berlin 1928) he wrote of 1.Nf3: “Certainly the most solid move, whereas moves such as 1.e4 and 1.d4 are both ‘committal’ and ‘compromising’.”
  • A final example comes from the classic book, The Art of Attack, by Vladimir Vuković. Parsimoniously, Vukovic states the Option Principle with a single phrase:  “moves entailing fewer obligations should be carried out before those which are more strongly binding” (Vuković, Vladimir, The Art of Attack, p.12).

Please feel free to comment on this post to share further examples (either implicit or explicit) of the Option Principle appearing in chess literature.

Wednesday, December 1, 2010

Epistemology of the Chess Advantage

What does it mean when we speak of an "advantage" in the game of chess? Furthermore, what does it mean when a computer program evaluates a position at, for example, -0.38?

The chess analyst must always look upon computer analysis with suspicion because the computer evaluation of a position is most likely incorrect. The measure of "advantage" that you and I deal with regularly (i.e. centipawns) sits upon a questionable epistemological foundation. In any given position, there are only three “true” evaluations. These are:  1) 0.00 2) infinity 3) - infinity. Stated differently, assuming perfect play, a position must be a draw, a win for White, or a win for Black. Therefore, any evaluation which is not 0.00 or an announced mate in # is by definition wrong.

To illustrate this, take an endgame position with only a Black king, a White king and a White bishop. White cannot be said to have a 300 centipawn advantage. In such a situation, being “up a bishop” is meaningless. Since the computer recognizes such a position to be a draw, it will give us the correct evaluation of 0.00. In other less recognizable but perfectly drawn positions, the computer will insist that one side or another has an advantage of (insert number) of centipawns. The same is often true in positions where a forced win can, after more exhaustive analysis, be demonstrated.

If there was no move horizon beyond which the computer can not see then the computer would be able to see all possible forced results in any position (win, loss, or draw). If there was no move horizon then the only evaluations of any given position would be positive infinity, 0.00, negative infinity. Any evaluation which is not one of these three values is by definition incorrect. It is a product of the chess engine programming which is designed to compensate for imperfect information (i.e. move horizon).

Arithmetic evaluations of chess positions are useful but ultimately fictitious. 

This brings up the notion of ‘arithmeticism’ in chess. Especially with the appearance of chess-playing computers which update a numerical assessment of the position on every half-move, there are players who tend to think in terms of arithmetic advantages, e.g., ‘White is better by 0.33 pawns’. This has its uses, but can lead to a rather artificial view of the game. What happens when both sides make a few moves which are the best ones, and suddenly the 0.33 pawns is down to 0.00, or full equality? The defender of this point of view will say: ‘Well, I didn’t see far enough ahead. If I had, I would have accurately assessed the original position as 0.00. The only problem with this point of view is that chess is a draw, and all kinds of clear advantages (in the sense of having a good probability of winning a position in a practical game) are insufficient to force a win against perfect defense. So most positions would be assessed as 0.00, which is not very helpful. In the extreme, we have the same problem when we claim, for example, that 1.Nf3 is ‘better’ than 1.e4, or 1.d4 is better than 1.c4. These are rather meaningless statements, unless we put them in the context of ‘better against opponent X’ or ‘better from the standpoint of achieving good results with the least study’ or some such. As for the objective claim of superiority, what would be our criterion? I would suggest that only if a given first move consistently performs better than others against all levels of competition might we designate it as ‘better’ in a practical sense. Since all reasonable first moves lead to a draw with perfect play, a claim of ultimate theoretical superiority for one of them cannot be justified.

Watson, John. Secrets of modern chess strategy: advances since Nimzowitsch. Gambit Publications, 1999. 232-33.

Friday, November 26, 2010

Bazaar Chess Theory

The Final Theory of Chess Project aims to create a comprehensive online encyclopedia of chess openings using what Eric Raymond has called the "bazaar" development model. The bazaar development model differs from most traditional methods of managing projects because of its heavy reliance upon voluntary contributions of members of a community of interest. Wikipedia and Linux are sometimes cited as examples of successful applications of this model.

The bazaar model is particularly well-suited to the study of chess opening theory for several reasons. First, numerous communities of chess players who enjoy studying chess openings already exist. Second, chess software provides an objective yardstick by which to measure the quality of contributions (i.e. the computer evaluation of the position as measured in centipawns). This objective yardstick aids in settling disputes between contributors over whose contribution is most worthy. Third, all contributors to the project necessarily begin their analysis at the same initial position. Because a game of chess always begins with the same piece setup, everyone is "on the same page" to begin with. Fourth, all analysis must proceed within the constraints imposed by the rules of the game.

The rules of chess are the "laws of nature" when it comes to the game of chess and they form the basis for a uniform logic of chess analysis. It is true, however, that chess theory has developed into competing paradigms such as the Classical school and the Hypermodern school. Nevertheless, the rules of chess ensure that the various schools of thought diverge less from one another than in other disciplines such as economics. For example, economists of different schools disagree over something as fundamental as the role of saving in the economy. On the other hand, chess players of any school can agree that a bishop always moves along a diagonal and a king cannot castle when in check.

Lastly, humans and computers make a good partners when it comes to chess analysis. Humans excel where computers are weak and vice-versa.

In 2005, the online chess-playing site hosted what it called a “freestyle” chess tournament in which anyone could compete in teams with other players or computers. ... The teams of human plus machine dominated even the strongest computers. ... The surprise came at the conclusion of the event. The winner was revealed to be not a grandmaster with a state-of-the-art PC but a pair of amateur American chess players using three computers at the same time. Their skill at manipulating and “coaching” their computers to look very deeply into positions effectively counteracted the superior chess understanding of their grandmaster opponents and the greater computational power of other participants. Weak human + machine + better process was superior to a strong computer alone and, more remarkably, superior to a strong human + machine + inferior process. Gary Kasparov