Sunday, October 28, 2007

Mother of all Tactics: counting trades

After studying for 5 days the position below, it has become obvious how universal that position is. The position itself is not too difficult, you can imagine the sequence of trades well within a reasonable time. It is in fact a counting problem. It is obvious how to generalize this position. It's a matter of changing the amounts and the values of the attackers, the defenders and the victim (the piece on d4). Counting problems are extremely common.

Because counting problems are so common, I want to find a shortcut. A method which makes it obsolete to work out the actual sequence everytime. In the same way as the rule of the square in the endgame makes it unnecessary to imagine every pawn and king move in the run to promotion.

The point is that imaging a sequence of alternating moves is taxing for the short term memory. Not impossible, but taxing. Especially if you at the same time must do the bookkeeping of how much wood both black and white have gathered sofar. The fact is, that the position of the diagram below is part of a more complex position. Beginning with an added white bishop on b5 and a black bishop on g6.

I found that the addition of a bishop on b5 immediately lead to a memory overload error. Due to the fact that the load of the underlying counting-problem already has taxed the short term memory to a certain degree. Causing you to check every possible candidate move while often repeating yourself. The all too common paralysis by analyzis.

If you can solve the counting problem in the position without taxing the short term memory, you will find that adding a bishop wouldn't give you problems. Since there is enough room in the short term memory to handle that.

A counting method that handles this position after it is generalized - by changing the amounts and values of defenders, attackers and victim - will have an even broader application. In this position all alternating trades of black and white take place on the same square. In the scenario of a counterattack the alternating trades of black and white take place on different sides of the board. I'm convinced that a counting method will be applicable under that circumstances too. And if that is the case, and I'm convinced it will be, then a lot of complex middlegame positions that caused me trouble and that I have showed you in the past will be solved in a whiff (ahem). Take for instance this example of counterattacking.

See here the MOAT (Mother Of All Tactics):

White to move.

The value of the victim and the first attacker.
In this position the victim is pawn d4 and the first attacker is Ne2.
Let's generalize. There are 3 critical situations:
  • The attacker has a lower value than the victim. In that case, the defender will lose wood, no matter what.
  • The attacker has an equal value as the victim. All risk lies by the defender. All the defender can hope for is to keep the material balance.
  • The attacker has a higher value than the victim. This means that the attacker has to invest. All risk lies with the attacker
After the first trade, the attacker and the defender change position. The result of the first trade is the starting point for the second trade.

There are 3 subjects: the victim under attack and the # attackers vs # defenders. This is the easiest way of looking at the position. The victim d4 is attacked 4 times and defended 4 times. So it should be defended enough. There are many cases that this way of shortcutting will do. The situation when there are an equal amount of attackers and defenders is critical. If you can solve this well, it will be no problem when there is an extra attacker or an extra defender. But there are disturbances of such utter simplicity:

The value of the pieces and the access to the square of trade. It is easy to see in the diagram above that rook d8 has no direct acces to d4 while a defender with a much higher value (Qd6) has. That changes the evaluation of the position.

Right now I'm working out the different values and the difference in access to the square of trades. It's going very slow. But I still have high hopes.


  1. Tempo,

    There are a number of links you should see. the ChessVille Weekly came out today, with a review of Ward Farnsworth's two volume set of tactics books. You should take a look at that, because Farnsworth uses intense verbiage to describe combinations -- similar to what you're getting at in your posts. Farsworth's books are hard-copies taken directly from his site:

    Another site (and book) that you will be just as interested in is here:

    This fellow has compiled counting and visualization exercises similar to what you're working on.

    Both books are self-published. Farnsworth uses the POD method at, and the other one seems to be an independent venture, although the author's web site claims his book was accepted by everyman and the deal fell through.

    Another book that uses verbal explanations to describe tactics is Quality Chess's "Understanding Chess Tactics" by W-- (I don't remember the long last name, but I remember that it begins with a W).


  2. Heisman has a series of four articles on counting and its ins and outs, which I find helpful (well, I've only read one, and will read the rest soon). There are:
    1. A counting primer.
    2. The most important tactic
    3. Is it safe?
    4. Two types of counting problems

    Heisman's new book 'Back to basics' has some bits from that series, and he has about thirty counting problems, and goes through a full game looking over all the counting problems that come up. It's cool.

    Incidentally, counting is just a phase. When pattern recognition takes over, there's no need to count anymore in 98% of the cases. I dont' remember what genius said that, but I know at the time it was very helpful as I was trying to find a source of practical problems to work on.

    OK, my wife tells me I never forget a grudge. I can now let it go. :)

  3. A counting method that handles this position after it is generalized - by changing the amounts and values of defenders, attackers and victim - will have an even broader application.

    I am not sure I understand what you mean by generalisation. Do you mean similar/identical positions where the number of attackers and defenders are different and also the values, ie. a rook on e6 instead of a queen?

  4. In the mid 90s Chess Life had a good article on this topic. I vaguely recall the author used a system similar to what card counters use, labelling the values + or - depending on who was ahead.

  5. Blue,
    I have read the articles. He doesn't come any further than "it is often extremely important to count well" larded with various simple examples. He acknowledges two types of counting though, just as I did: all trades on the same square or trades on different squares during a counterattack.

  6. That book by W doesn't have anything more on this topic.

  7. i often said that 'friendship is enrichment' as in the heart of life, not money, but to know and be known.

    it seems to me, in reading your post and following along that, for us, we too hear can touch riches.

    thank you.

    in poetry, it is said dont say, 'i felt happy' or 'he loved her deeply' but rather, things like:

    'blue moons bulged inside me such as standing room only, till only fallen branches gave way' or 'holding her wet branches, the cracking of ice in winter'.

    so here, you give us riches:
    'riches for the fortnight, we gather the harvest, from tempo, till our sacks full break our backs then dancing all night'

    warmest, dk

  8. A very interesting series of posts you have done on this particular position. There are so many games where I've gotten into horrible time pressure because I kept recounting attackers versus defenders over and over again to make sure I had it right. The worst is when one spends all that time making sure it's right, and then launches into the trades only to discover it was wrong.

    I'm going to have look at all these posts over again, because my head is spinning from trying to absorb your comments.