Chess and the Triangle Offense

Let me preface this by noting that I'm not a very good chess player. I'm decent enough, but have won more often by virtue of dumb luck or opponents' blunders than by any combination of skill and acumen on my side. Before Kirsten and I left Chapel Hill, my friend Vinny came down from New York. He stayed with Alan, who was also hosting Jim once Jim had moved out of his place. Nearly every time I stopped by Alan's, the chess board was out. I played a handful of games, was fortunate enough to win a couple, and remembered how much I liked chess.

I've spent much of the past year thinking about backgammon strategy, but what with all of my recent interest in space and movement during the European Championships, turning my attention back to chess seemed appropriate. A little over a year ago, I'd visited Vinny in the City, and he'd taken me by a small chess shop down the street from Washington Square. We sat down to play in one corner, attracted the attention of some passers-by long enough for them to realize neither of us was particularly accomplished, and proceeded to mumble and stumble our way through a very enjoyable game. On my way out, I picked up a book of chess puzzles, which I proceeded to attend to with decreasing diligence. Since then, I haven't really read that much.

But the other day, I found a sale-priced copy of Bruce Pandolfini's Weapons of Chess. I haven't made it all the way through, but have been trying to glean what I can from a fairly readable (if not particularly linear) reference guide. One of the interesting (and perhaps more broadly applicable) sections dealt with the types of pawn centers.

As Pandolfini notes, there are five types of pawn centers: open, closed, fixed, mobile, and dynamic. An open center in one in which the d- and e-files have no pawns. It allows rapid advances by both bishops and a wide field of movement for the queen. As result, it's a situation in which one should castle as quickly as possible to remove the king from easy attack. A closed center is one in which both files have pawns which cannot be attacked (one possible opening would be 1.e4 e6 2.d4 d5 3.e5 ...). Attacking through the center is much more difficult in this situation, resulting in the importance of developing attacks on either flank. Castling, while sometimes helpful, is not as crucial in this situation. A fixed center is one in which one file is open while the other has two matched pawns (an improbable sequence might be 1.e4 e5 2.d4 d6 3.dxe5 dxe5). In this situation, neither pawn is particularly vulnerable to attack. The priority, it seems, is to develop pieces forward to d5 and f5 (for white) or to d4 and f4 (for black). Pandolfini cautions against rapid pawn movement in this type of game, given that moving the c pawns or f pawns forward too quickly allows one's opponent to attack more easily, especially along the d-file in this game. A mobile center is the fourth type of situation, and perhaps the most opaque to me. Pandolfini writes that a mobile center exists when "You have two connected, movable pawns in the center, and your opponent has a single pawn". If White is mobile, he then controls the way in which the pawns advance. Black's position in this case depends on drawing White forward prematurely or otherwise in error. The last situation is a dynamic center, where both sides have two pawns in the central files and decisions by either side may lead to an open center, a closed center, or a fixed center.

All of which is a long way of saying that it's fundamental to recognize the types of centers available to you in the course of the first opening moves, and to play towards a center which is most comfortable for you.

As to how this kind of thinking might be more broadly applicable, it seems that both basketball and soccer share certain aspects (though admittedly, I'm a far worse basketball or soccer player than I am a chess player). In the first place, if you think of the basket or the goal as a kind of king, then you're dealing with a situation fairly similar to the beginning of a chess match. The first crucial difference, of course, is that you can't castle a basket or a goal (though imagine if you could!). As a result, play is always directed from the sides of the court or the pitch in towards the center.

Basketball, because of the smaller court size and the increased control than hands offer, seems to be more amenable to playing from the middle of the court to the wings. In addition, the halfcourt line dramatically limits opportunities for the ball's movement back once it passes halfcourt, encouraging play that keeps it away from either corner. Thinking a bit more specifically about the Lakers and the triangle offense that they run, it seems that Pau Gasol and Lamar Odom both played a kind of knight role, something that might come about in the fixed center explained above. In other words, one or the other moves to the high post (say, White's d5) from which point several attacking options open themselves up. You might also be able to think about wing players as bishop figures, at their best when they have lanes through which they can slash, attack, or otherwise get to the cup. The analogy breaks down, of course, when you start talking about picks as pawns, but I think the analogy holds so long as you talk about understanding what the defense is giving you and playing in such a way as to maximize your strengths.

Soccer, because of the sheer size of the field and the fact that the ball can be played back as far as needed, seems a bit more problematic. At the same time (and I was thinking here), the very size of the pitch relative to the number of players seems to emphasize the importance of tactics, systems and strategy during the course of the game. Watching the Championships this summer, it seemed to me that there were broad ways of attacking. One involved control of the attacking half of the midfield with balls then played forward to the central striker. Spain might be an example of this (I'm thinking of Torres' goal in the finals, where he broke forward from the middle portion of the field). On the other hand, some teams seemed to depend on the ball moving forward on the wings, where it was then played back into the middle to trailing attackers. Portugal's attack seemed to be a bit more like this, at least when Ronaldo had the ball. Of the two, my uninformed opinion is that it's always better to be able to control and create from the midfield (witness the United States' weakness in this regard) rather than playing the ball consistently the wings and hoping they create. Sure, it's isn't exactly like the five types of centers outlined above, but it does seem that control of the center - and the ability to play to space from that center - is fundamental to any attacking situation.

As for what's left, I'm still really interested in the ways in which both pitches and game boards were imagined. There's a particular spatial imagination at work there, a kind of abstraction, that is not natural. I wonder if it's possible to point to ways of thinking, ways of seeing, ways of mapping, as one tracks through the history of the soccer pitch (see here and here for links) or the history of the chess board. It all seems to hinge on an understanding of space - at least, that's the case for me. If anyone has any thoughts or links to other way of understanding either chess (especially mathematical probability) or soccer and basketball, I'd be really interested.


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