Saturday, March 25, 2006

Space = Territory + Mobility

Note: See King of the Spill's nice discussion of this topic here. I think he hits the nail on the head.

In the chess-for-novices literature, the factor of 'space' is (often implicitly) used to describe two factors : territory and piece mobility.

Territory is the amount of real estate that your pawns fence off: it is the number of squares behind this fence. If you have an advantage in this factor, it is easier to mobilize the pieces behind your wall for defense and attack. Conversely, your opponents will have relatively less space to maneuver. As King of the Spill points out in the post linked above, if your pawn fence is further forward than your opponent's, you also pose a greater threat of promotion. This is huge.

Piece mobility is simply the number of squares which you control, which includes squares upon which your pawns can capture (note they are in front of your pawns, unlike the territory they demarcate), and all squares to which your pieces can move.

That's basically it. There are some wrinkles (e.g., you can have an advantage in territory or mobility queenside, center, or kingside), but the concept of space is simple. A weakness in Wolff's book is that he does not take pains to distinguish these two factors. Silman's book Amatuer's Mind and Seirawan's Winning Chess Strategy are both better on this topic (thanks to Tempo for suggesting the Seirawan book: it is infinitely better than his fireplace-worthy Play Winning Chess).

Heisman calls territory a pseudo-factor, but his argument is unconvincing: he finds one example where the side with more territory is worse off because it has less mobility, and based on this one example says that territory is good only because it affords more mobility. Single examples don't disprove the importance of territory: they just highlight the obvious fact that we need to carefully weigh multiple factors when evaluating the board.

Also, even if the usefulness of territory is ultimately parasitic on mobility, in practice this doesn't diminish the usefulness of considering territory as a factor in real games! We aren't constructing an axiomatic system, where we need to worry about finding the smallest independent set of axioms that can prove all the theorems. We are playing chess, where we presumably want to evaluate the board using factors that are useful and help us make good decisions quickly. By analogy, the fact that certain principles of pawn structure evaluation can be derived from other principles does not take away their utility.


Blogger King of the Spill said...

Overall, it looks like you have figured out what I have: space must be interwoven with other factors to assess a position.

I see what your getting at as another case of simultaneous advantage. Just the move 1. e4 could be looked at as yielding many advantages:

- can occupy and move pieces through e2 and e3
- controls d5 & f5
- threatens e6
- is closer to promotion
- blocks Black's e pawn from moving forward beyond e5

- weakens d4 & f4, d3 & f3 by permanently taking away a potential defender
- weakens e3 and e2 permanently by removing the option for the White e pawn to defensively interpose with that pawn on those squares
- moves the pawn further away from the defending King (i.e. if you trade all pieces and pawns except that e4 pawn, the White King cannot get in front the pawn and force promotion)
- moves the pawn closer to the attacking King
- hangs the pawn!

In general, breakthrough pawn combinations work best for the side with more advanced pawns, but of course there are countless exceptions and King placement is really crucial to those positions. Nonetheless, this potential is a reason to consider gaining alot of space as an endgame investment.

On the other hand, having less space might mean you have wasted less tempi and have your King in a superior position in the endgame. Clearly, space means something much different in the first half of a typical game.

Four other things come to mind :-). The first is going through annotated Sicilian games. Usually there are a large number of book moves, and afterwards there are usually alot of specifically Sicilian thematic ideas being threatened. I never much think about space when read or listen in those games. It's almost like all the pawns were removed from the board and replaced with little mutant Bishops, stopping other pieces from occupying (diagonally forward) and advancing to threaten pieces. Suffice it to say that Black's typical lack of space/more cramped position seems to be much less important than the specific threats Black is able to muster.

The second thing that comes to mind is I was taught "piece mobility" count a little differently: add up the number of squares each side controls in the opposite half of the board, 32 v. 32. If one side is ahead, that side usually has an "space" advantage. Food for thought. I guess the hypermodern thought here is that space might not ultimately be so great if it is achieved at the cost of getting tied down defensively in a passive position.

The third thing is mobility verses activity. I think that when people say activity they sometimes mean mobility and at other times really mean moves that involve stopping or creating meaningful threats. Sorry to add to the confusion.

Which brings me to the fourth and final thought (*wohoo*): In a fairly even position it often is an advantage to be able to threaten more good moves than your opponent. This is general, and there are tons of exceptions. So to add to your idea that space leads to mobility and territory, here is a caveat: at moments where gaining space does not either add your good moves or subtract from one's opponent's good moves, the move practically wastes a tempo.

3/26/2006 08:31:00 PM  
Blogger Temposchlucker said...

The pawns form the border of your territory. What is important is how weak they are and how much pieces you need to keep the border intact. If you pushed too many pawns too far your position is "overstretched". Which means the pawns are vulnarable and easy subject to enemy attacks.

3/27/2006 06:14:00 AM  
Blogger Blue Devil Knight said...

King of the Spill, good points all. They are worth reading twice. It is important for me to remember that it isn't worthwhile to obsess about extending one's pawn fence if I am about to get my royal family forked!

Tempo, the books I have read can't resist the analogy with Rome, which overstretched its border and got pummelled by raiding parties.

3/27/2006 08:01:00 AM  
Blogger katar said...

I agree with Heisman that territory is a pseudo-factor. IMO, territory is useful ONLY to the extent that it promotes mobility.

As black, I play Chigorin defence and also Portuguese attack. I give up territory (& even a pawn too!) in exchange for active piece play (mobility). Here is an example line showing mobility vs territory:
1.e4 d5 2.exd5 Nf6 3.d4 Bg4 4.f3 Bf5 5.c4 e6 6.dxe6 Nc6 7.d5 Nb4

White has more territory (having made only pawn moves!!) but i much much much prefer Black.

I reckon that the side with greater mobility can control the territory, regardless of whose pawns mark such territory.

3/27/2006 06:59:00 PM  
Blogger Blue Devil Knight said...

I guess I should work up a counterexample to Heisman, where the side with more mobility, but less territory, is at a disadvantage. Give me any two factors, and it shouldn't be too hard to show single examples where one is more important than another. Single examples show that you need to be careful, not that one of the factors is pseudo.

The quibbles about what the real factors are is a tempest in a teapot. Whatever helps someone win games is useful. Clearly, good players like Silman, Seirawan, and others, find it a useful heuristic, even if it does ultimately derive its utility from mobility (like I said, this isn't math, where we need to get concerned about what is logically prior to what).

Patrick: I've got your book all packed up, but didn't send it (I went to Kinko's today and they wanted a ridiculous amount to send it, so I'm going to the post-office tomorrow).

3/27/2006 10:10:00 PM  
Blogger Pawnsensei said...

Hey BD,

I agree that you shouldn't obsess about extending your pawn fence, but I would suggest trying it a couple of times to see why it's bad. That's one of the major lessons I've learned from playing more chess.


3/28/2006 01:42:00 PM  

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