Friday, September 22, 2006

Where are the counting problems?!

Counting problems are problems in which you have some material attacking a piece, your opponent has some material defending it, and you need to determine whether to make the capture, and which piece to use. Where are all the counting problems? They are great exercises for patzers like me to build calculation muscle, as they force you to visualize simple game trees.

Here is a very simple example, from Wolff's book (see below). White to move.

There isn't much written on such problems. Perhaps authors consider them too simple. They usually just give the rules for solving them, and provide a couple of examples (usually authors say that if there are more attackers pointing at a piece than there are defenders guarding it, and/or the sequence of exchanges will leave you with the better position, then take the material). A simple rule, no? A monkey could do it! Well, in practice, in the thick of a game, with multiple potential captures, with time constraints, things aren't that simple. Not for me, with my inefficient thinking and poor visualization skills.

There is some writing about such problems. A Counting Primer by Heisman provides a good introduction, as does The Complete Idiot's Guide to Chess by Wolff. Heisman has other relevant stuff: for instance, an article on queiscience errors here, and he talks more about counting errors here. The above two authors' puzzles amount to fewer than 30 such problems!

A set of 1000 such counting problems, in increasing order of difficulty, is what I need. If it does exist, or something close, I will send whoever points it out to me first a copy of a chess book in my collection. I'll have to check it out to make sure it is truly a bunch of counting problems, not general 'tactical' software, of which there is no shortage. Many tactical puzzles end up being having counting problems as subproblems, so that is helpful, but they aren't straightforward counting problems.

You might say "Just play lots of games to improve at this" I could, but just like basic tactics, I could pick it up a lot faster with 1000 counting problems! I should be able to solve these simple problems effortlessly, but according to Dan Heisman, players under 1400 make lots of counting errors.


Blogger Loomis said...

The 23,000+ problems at CTS are auto-generated from real games. My understanding is that there exists a chess program that analyzes games and outputs tactics problems from them. There must be a way to make a similar program that generates counting problems. I wonder if it is a straightforward modification from the existing program. If so, you could easily have 1000 counting problems in no time! Of course, that's a long way around the barn if there already exists such a collection.

9/23/2006 02:45:00 PM  
Blogger Unknown said...


The easiest method I use is this: I count the number of pieces hitting a square from both sides. If equal, load up some more. If I'm less, load up some more. If I'm greater, then I can go ahead and make the evaluation. . .I don't actually add up piece values - too silly in my opinion. Just look for equivalances. If you're hitting it with pieces and your opponent is hitting back with at least one pawn - you lose - so don't do it. If I'm hitting the square with at least one piece greater in value, than it should be the last piece to capture. If it can't be the last piece to capture, forget it.

This is a general algorithm that usually works.

9/23/2006 05:50:00 PM  
Blogger Temposchlucker said...

Counting is just a phase. When pattern recognition takes over, there's no need to count anymore in 98% of the cases.

9/23/2006 06:39:00 PM  
Blogger Blue Devil Knight said...

Tempo: and what better way to build up this pattern recognition skill than with tons of problems? That's exactly what I want, to help me get out of this phase.

9/24/2006 04:31:00 AM  
Blogger Blue Devil Knight said...

Jim: That sounds like a good algorithm, but I really want to just work through a bunch of problems. The algorithms, as I said, are all useful and simple, but using them well and quickly OTB is another story.

Loomis: that sounds like too much work. I actually started to build a database of counting problems in Fritz, but soon realized it would take me way too much time.

9/24/2006 04:33:00 AM  
Blogger Temposchlucker said...

I agree. But it's just that it sounds like a themed database, something you frowned upon some time ago.

9/24/2006 05:05:00 AM  
Blogger Blue Devil Knight said...

Tempo, I have never frowned upon themed databases. Quite the opposite. If I have learned a pattern, really learned it, it doesn't matter what format it was in. If its stuck in my head, I'm happy.

In general, my strategy is to go through problem sets by theme a couple of times before switching to no theme. This is part of my circles.

If lots of counting problems were included in any of my tactical problem sets, I wouldn't be complaining. I have (re)discovered a gaping hole in beginner chess training software.

9/24/2006 11:30:00 AM  
Blogger takchess said...

At times I initiate a combination and find I am down a piece and I have no idea how it occurred. Fortunately, this is happening less and less. The thing that helps is the algorithm Jim suggests. The good news is you have plenty of opportunity to practice it in most every game with in most cases not playing tactics. As for a large problem set,my guess is you can get by on a set of about ten where you force yourself to think in a structured way. This is the type of thinking one must learn in the heat of battle and with practice it is not hard to do.

9/25/2006 07:35:00 AM  
Blogger takchess said...

also... I visualize the piece swapping and figure who the last man standing on the square is. Normally pieces of greatest value end up last on the square except when they force a swap leading to mate.

9/25/2006 08:29:00 AM  
Blogger katar said...

i think the most common "counting" problem is a back rank mate exercise.
if the king is trapped on the back rank, then mate occurs when R or Q checks.

counting is relatively simple. the problem is foreseeing a "zwischenzug", or a forcing move that interrupts the mass exchanges. i think training to see the zwischenzug is more topical thn just counting. GL

9/25/2006 08:54:00 PM  
Blogger Blue Devil Knight said...

10 PRINT "Learning an algorithm is not the same as learning a pattern"

20 PRINT "I want a problem set to learn counting problems, not another algorithm or more rules"

30 GOTO 10


9/26/2006 10:26:00 AM  
Blogger Blue Devil Knight said...

The above is for those who like algorithms. It should hammer home what I am after.

9/26/2006 10:32:00 AM  
Blogger Temposchlucker said...

The guys who make problemsets are in the phase of recognizing the patterns in stead of counting, in 98% of the cases. They have no idea anymore when you feel like counting. So it's not likely that they are able to create the database you desire. So I'm afraid you have to work your way around it. But you allready guessed that yourself, right?

9/26/2006 12:16:00 PM  
Blogger takchess said...

Perhaps this counting pattern problem set may help.

9/26/2006 04:31:00 PM  
Blogger Zweiblumen said...

Takchess: I totally hate it when I enter into a set of exchanges and find I'm just down material when it's done. In moments like that I feel like I just have no clue what I'm doing...

9/27/2006 04:00:00 PM  

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