Sunday, November 04, 2007


Counting Problems

Counting Problems or Problems with Counting?

To create a grand unified theory of counting for captures in chess it should be either applicable in general, or, if that is not possible, then we need to be able to at least distinguish the cases where it can be relied upon from those cases where it can not. Otherwise, we are left with something that can be applied only in situations where it works but we have no way of knowing which those are.

Blue Devil Knight and Temposchlucker seem to be attempting that feat and I urge you to read their posts on the subject for background, if you're interested. I do think that what they are doing is useful (in an educational sense) and is interesting but I'm not sure if there is any practical applicability to their research.

My challenge to them is to consider the following positions with regard to counting. These examples are taken from Chess Tactics for Advanced Players by Yuri Averbahk and are from real games. I am showing the diagram for the position after the key move, which was in each case, a capture. The line given is a main line but there are other variations possible.

Could we have predicted or expected the move via counting? If counting should not apply in this position or for this capture how can we know?

Ahues - Kurpuhn
White has just taken a Bishop on d6 with his Rook. Why isn't he just losing the exchange?
1.Rd1xd6 Qxd6 2.e5

Hubner - Tal
Biel, 1976
Black has just taken a pawn on h3 with his Knight. Why isn't he just losing his Knight for a Pawn?
1...Ng5xh3+ 2.Qxh3 Bxc3 3.Rxc3 Ne2+ 4.Kh2 Nxc3

Alekhine - Euwe
White has just taken a Knight on d7 with his Rook. Why isn't he just losing the exchange?
1.Rd1xd7 Bxd7 2.Ng5 Qb8 3.Bxa8 Qxa8 4.Nxh7

Pogrebysski - Kortschmar
Kiev, 1937
White has just taken a Pawn on c6 with his Knight. Why isn't he just losing his Knight for a Pawn?
1.Ne5xc6 bxc6 2.Nxd5 Kh8 3.Nxe7 Qxe7 4.Qb4 Rf6 5.Rxc6

If anyone can create a grand unified theory of counting that works for these positions (before the key move) or in which we can easily distinguish when it can be applied and when it can not I will be most impressed.

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Right now I'm in the middle of a new post, but after that I will take up the challenge.
At a conference now, so don't have time to analyze anything. I can say before looking that if the challenges aren't simply ways of determining if a sequence of exchanges at a single square will yield material gain, then the method can't help.

So on a first pass, for the first problem it will only tell you that the set of exchanges at the d6 square loses wood (in the short term). Whether this is a good move or not is up to you to decide.

So the counting method does answer a question that comes up quite often, it won't tell you whether that is the right question in the position, or the most important question.

But for patzers like me it is often the single most important question. It is all in the spirit of Heisman's article A counting primer.
I have taken a short look at the first position. The direction I would look in is the following:

Beancounting seams to have as its only goal to decide if a piece is well protected or not. In this case, the bishop on d6 is well protected.

To gain wood is only possible by a duplo-move (or a trap). The duplo-move here is obviously e5.

In order to know if it is possible to play e5, the beancounting method must be extended for the situation that the victim is an empty square. That should give an answer on the question how well is that square protected.

So the area's which have to be defined are:

Extended beancounting.
Chains of counterattacks
Chains of defenders

Chains of defenders should give you a clue here: e5 is defended by Bd6. To undermine e5 you have to anihilate the bishop.

These 5 areas should cover a vast amount of tactics.
Diagram 2. I know that position.

It starts at the end (backwards thinking) with the duplo-move Nf2.

The yet to invent extented beancounting tells you that f2 is 3 times protected against one time attacked.

The yet to invent chains of defenders tells you wich defenders to anihilate.

Beancounting of h3 shows a loss of 2 points.

Beancounting of c3 shows an equal trade.

The duplo-move gains you 5 points for the rook. Minus the 2 points investment this means you gain 5-2=3points.

1. I believe you mean Ne2 (not Nf2) in your discussion of Diagram 2.

2. I agree that you can use these "techniques" to describe the tactics. But (and what I see as the key question) are they reliable and practical tools to find the tactics?

3. I appreciate your optimism!
Ne2, yes.

I wasn't looking exactly for a method to find moves, but for a method to un-tax my short term memory. About my optimism: how could I be pessimistic since I didn't know that beancounting was such small area?:)
It are often the side-effects of such study is of help. For instance I discovered that it is ALWAYS a duplo-move which is responsible for the gain of would. I hadn't realized that that is true even for trade sequences and counterattacks.

The better you can describe what is happening in a position, the more structures you start to see in your games. I start to see how the different "tachniques" intertwine.

Should come in handy someday.

And yeah, maybe the answer to "un-tax" my memory is to start with Zen meditation. Who knows? Without questions, no answers.
gain of would; reads wood.
I think it is impossible to find these moves by counting alone. Just take the first example. Rook takes Bishop works only because the black King is on diagonal b8-h2 and because the square f4 is protected. Without these features the move would just lose the Exchange. Bean counting does not help here, and I suspect that it does not help in most situations, except at quiescence.

I think it is impossible to find these moves by counting alone.

I agree. I would further argue that there is no technique other than considering future positions and moves that can reliably find and validate the correctness of such moves. I have a truly marvelous proof of this proposition which this comment is too small to contain.

Tempo's and BDK's posts do have some useful practical application for humans but one must be careful not to apply counting inappropriately.
A Fermat's Last Theorem reference! That's perhaps one of my favorite mathematics stories of all time.

I love you, sir.
I have proven an important theorem about counting. The proof is so subtle, so brilliant, that I dare not post it here for fear that someone will try to scoop me and steal my Fields Medal.

But I will tell you the theorem...

Counting is important in a situation if and only if, for that particular situation, counting is important.

A if and only if A. Logicians since Russell and Whitehead have longed for its proof. Well I've got it. But I'm in San Diego at a conference so don't have time to publish it.

OK, I've been drinking a little.
What ever BDK is having I'll take one too. :-)

All this counting theory is interesting, but goes out the window when at the end of the trades there is a fork, pin or other tactic that creates a new loss of material. That seems to be the gist of these positions that Glenn has posted. There are those outside influences of tactics that change straight counting.
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