Sunday, October 23, 2005

Quantifying mobility

Piece mobility is an important criterion for evaluating a position. What is the best way to quantify it? Seirawan, in Play Winning Chess, has a counting method in which your territory is equal to the number of squares in enemy territory (i.e., beyond the fourth rank) that you could move to it if it was your turn to move

I see two weaknesses with this measure. First, every square you can move to is counted without regard for safety. For example, if your queen can move to h6, that square is counted as territory in Seirawan's method even if it would be captured on the next move by g7xh6. It seems that you should only count as your territory those squares to which you can safely move (more accurately, can move without a net loss of material). Second, I don't see why you shouldn't count spaces on your own side of the board. Mobility seems important all over the board, not just on the opponent's side. I realize that ultimately the goal is usually to attack by bringing material to the opponent's side, but if your pieces are hemmed in on your side this ain't gonna happen.

Perhaps a better way to quantify space is just a simple count of the number of squares to which your pieces can move without losing material.

However, I am just a patzer, so it would be interesting to hear how other Knights quantify or think about mobility.

13 Comments:

Blogger knightwiz said...

I'd think about mobility just as how many squares I can move to. Some sharp combinations starts with moving to -- or being able to move to -- squares you'd "lose material". For example, if you can move your queen to the enemy back rank, but there's a rook there, maybe that's not profitable doing so right now, but that creates trouble to your enemy if, for example, you'd get to the back rank with check or mate were him to move the rook.
That's a case where the threat is greater than it's execution.

10/24/2005 09:28:00 AM  
Blogger Druss said...

I agree - it is better to count safe squares. Or even squares that you own ... i.e. got more pieces attacking it than the other side has defending it.

A number of strategies are based around fighting for control of squares. Especially 'holes' in the opponents territory which are weak - usually because of some pawn move.

I wouldn't really bother with your own space, apart from being aware of what squares your opponent controls in it.

10/24/2005 10:25:00 AM  
Blogger Temposchlucker said...

Interesting subject! I made a post about it.

10/24/2005 10:57:00 AM  
Blogger DreadPirateJosh said...

Are you still reading Don Quixote?
(I'm just curious)

10/24/2005 04:19:00 PM  
Blogger Pawn Sensei said...

Whoah. Too complicated for me. I have a hard enough time not dropping material =)

PS

10/24/2005 04:53:00 PM  
Blogger Pawn Sensei said...

BTW, good to see you on ICC. I think you are the Knight I see the most. Maybe next time we can have a friendly game.

PS

10/24/2005 04:53:00 PM  
Blogger Siliconpawn said...

I am with PS. I don't count squares. I am just beginning to understand the benefits of grabbing the open file with my rook, posting my knight to anchor points and getting my bishops on open diagonals.
The strategy section of PCT has plenty of problems teaching there principals.

10/25/2005 03:49:00 PM  
Blogger Pale Morning Dun - Errant Knight de la Maza said...

I am in a mode right now where my ultimate and primary concern, above all else, is not to drop material to a tactic. Chess is not all tactics but the last ten losses I've had on the board have all been because of tactics. Now if piece mobility could be definitely equated with tactical opportunities, then I think I would focus more on it. For now, I just don't wat to drop any pieces.

10/25/2005 07:38:00 PM  
Blogger Blue Devil Knight said...

Thanks for all the comments. It looks like the knights have quite varied perspectives on this theme.

I stopped Don Quixote about 120 pages in: I hate to say it, but it got somewhat boring and repetitious. I'll probably pick it up sometime when I have more time to really blast through it quickly.

PS: it'd be a lot of fun to play sometime.

10/25/2005 08:11:00 PM  
Blogger King of the Spill said...

Hmm... Well I use that method both in my own and other's games, so here's my thoughts.

First, your right about this method leaving out details. I see it as a starting place, something that can be done quickly with practice, and good method to determine who has the advantage in a materially equal position. After the counting you still need to add consideration for anything specific, like a promotion threat, absolute pin, exposed King, etc. Certainly those things can override space or mobility plusses.

Second, when I use it I am counting the number of times that attacking pieces influence the opposite half of the board minus the same for the other side. This isn't exactly the same as mobility, because of blocked pawns, absolute pins, other threats, etc.

Lastly, this method of counting probably is best when viewing positional style classical opening games. Hypermodern openings concede space and central control initially, and then gang up on it afterwards, or perhaps concede space in a way that kills an opponent's plan. That's certainly beyond the scope of his book.

I think Seirawan's advice for beginners is oversimplified, but for good reason. I see him as warning you that being down just one pawn almost always translates to a lost game, so if you and your opponent both play well you will stay materially even and you must consider space and nobility to be the places where you vie for a winning advantage.

10/26/2005 04:42:00 AM  
Blogger Mousetrapper said...

I think every piece should do a job. Raw mobility is just one aspect, but even more important are the targets to be attacked or the own points to be defended. If a piece protects against mate but has very little mobility, it is important all the same. So, in conclusion, I doubt that simplistic counting methods bring much advantage. Every position must be evaluated separately. There is no universal chess formula. Our game will remain a mystery forever.

10/26/2005 05:46:00 AM  
Blogger Temposchlucker said...

The main idea is very simple. A balanced position is: you attack something, your opponent defends against it by protecting it or moving it away. There are only two methods that can give you an advantage.
1. A duplo attack. I call a duplo attack all the ways you can attack to targets as a double attack, a pin, a skewer, a phork etc.. In general: tactics.
2. A trap. In that case you hunt down a specific piece that has lack of space, so it can't escape. All positional play is about diminishing space of specific hostile pieces (and to increase the space your own pieces).

10/26/2005 06:33:00 AM  
Blogger takchess said...

http://nhchess.org/tournaments.htm

If you find yourself in NH on November 12th to see family. here is a tourney I am playing in .
Takchess

10/26/2005 04:09:00 PM  

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