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The Greatly Misunderstood and Potentially Challenging Tactic "Counting"

  • NM danheisman
  • | Aug 30, 2012
  • | 9203 views
  • | 19 comments

When I coined the term "Counting", many thought I was simply referring to knowing the value of the pieces, but that's just a minor aspect. By Counting I meant determining whether any sequence of exchanges led to gain or loss of material on any square. This not only included knowing the average value of the pieces, but subsumed many other well known ideas such as en prise, number of attackers and defenders, and desperado.

Counting problems can be as easy as en prise but can also be so difficult that it would take a computer to solve - the permutations of captures, especially when multiple squares are involved, often becomes enormous.

A few years ago, after my book "Back to Basics: Tactics" was first published, I received an email from a player rated 1600 USCF. He wrote that I did not know him, but he had bought that book to brush up on his tactics. He said that when he saw the title of the first chapter, "Safety and Counting", he skipped it, figuring he already knew that stuff.

However, he decided to do the problems at the end of the chapter. In the email he continued: "Imagine my shock when I got the first six problems wrong! I went back and read the chapter and realized you were discussing an aspect of tactics I had never seen in detail in any other tactics book." He urged me to let the average tournament player know that this was important material and they needed to study and understand it. I replied by thanking him, but thought that if I said that (as I am doing here Smile), people would just figure that I was trying to sell my book, so it would be more effective if people like him told their friends!

I have at least five online articles on Counting:

Let's consider a couple of Counting problems, the first one a fairly easy two-parter and second fairly difficult:

Part 1a: Is 7.d4 safe? (click on 6...Bc5) [Note: "safe" means your opponent has no forced sequence of moves in reply that win material or checkmate]:

This should be easy if you just address the Counting aspects. The answer is yes, since the knight on c6 is pinned, e.g. 7...exd4 8.Nxd4 Bxd4 9.Qxd4 and White is in no danger of losing material.

1b) Suppose after 7.d4 Black counterattacks the bishop on b5 with 7...a6. Is that safe?

The answer is no - this is a straightforward multiple-square Counting sequence involving c6 and c5, respectively. If White finds the capturing sequences 8.Bxc6+ bxc6 9.dxc5 then he wins a piece. You might laugh that this is easy, but the player who was Black in this game was a decent intermediate player and, after he miscalculated and played 7...a6??, he asked me to show everyone his mistake so that they would understand and have less chance of making a similar one. Note that this error cannot be classified as anything else; I even went out of my way to get the blessing of the good doctor GM John Nunn for calling this tactic Counting.

Now let's consider a more difficult question - one I needed a computer to verify the correct answer. In the following position White, in danger, desperately sacrificed 1.Nxe6. What should Black play in reply to maximize his material winnings?

This is not so easy. Black has an array of plausible moves such as 1...fxe6, 1...Nxf1, 1...Nxc4, 1...Rc8, and maybe even 1...b5. Did you consider all of them? Because if you just chose one that was good for Black, but overlooked one that was possibly much better, that can greatly affect your chances of winning. In computer evaluation parlance, it is much easier to win a game where you are +2.5 than it is to win a game where you are +1.5 (see "The Margin for Error" at http://www.chesscafe.com/text/heisman82.pdf).

I'm a master but it would be very difficult to prove what the right move is in this problem without a computer. However, with the help of Houdini 2, I can list the top four moves for Black, at 26+ ply:

  1. 1...Rc8 (-1.65; i.e. Black has the equivalent of a 1.65 pawn advantage)
  2. 1...fxe6 (-1.09)
  3. 1...b5 (-1.07)
  4. 1...Nxc4 (-0.83)

The good news is that in this particular case, you can't go far wrong with any of these, but getting that extra half pawn by picking 1...Rc8 could be huge. In many complex Counting positions the difference between the best move and the second best is MUCH greater, and it's easy to make mistakes in these types of positions. If you want more examples, easy! See the links above or get my book (2nd printing 2011 is the one you want). Smile

I once had a new student, who began his first lesson with the fair question "What are you going to do to make me a better player?"

My reply was "I don't know yet - I have not diagnosed your strengths and weaknesses. However, judging from your rating [it was low] I would bet that I can help you make less Counting errors."

His immediate reply "I never make Counting errors!"

So we looked at two of his games. In one of his games he was White and had a pawn on a3 guarded by another pawn on b2. But he played 1.b3, in effect removing his own guard, allowing the en prise a-pawn to be captured with 1...Bxa3. When I asked what type of mistake it was, he said it was a blunder. I replied that he was correct in that a blunder is a bad move, but did he know how to classify what type of tactic that allowed? He said he did not. I informed him that it was a Counting error since he previously had one defender to the one attacker but, after his move, there was still an attacker but he had zero defenders (en prise). So that was a Counting error (or I guess you could also classify it as "self removal of the guard" which in this case creates a Counting error). His reply, "Oh! So that's what you mean by Counting!" Smile His other game included a Counting error, too.

One of my few crusades in chess is to let everyone know what Counting is and why it is so prevalent and important. Watch any two absolute beginners playing each other and they will make moves which are trivial Counting errors. For example they often allow the Counting error where one of his/her piece is attacked twice and only guarded once (yes I know that doesn't always mean it isn't safe, but it often does) and can lose material to capture, capture, capture - and then opponent often misses it! They will make this type of Counting mistake far more often than they will miss a pin or a removal of a guard - not even close!

I strongly believe Counting needs to be taught after the rules and the average values of the pieces, but before multiple square motifs like pins and removal of the guard. See the basic Counting Problems on pages 4-7 of http://www.chesscafe.com/text/heisman15.pdf as an example of what you can show any newcomer to teach them how to Count to see if a move is safe.

Finally, there's a difference between Counting and "just" keeping track of material as part of a trading sequence. Hopefully it will not surprise you that I have an article on different methods you can do to perform the latter at Counting Material (http://www.chesscafe.com/text/heisman119.pdf). Even my intermediate students sometimes have difficulty keeping track of material during a series of trades. This difficulty may be due to either visualization errors or forgetting which pieces were captured, but the effect of an error when doing so can be disastrous, since which side is ahead in material - and how much - is a paramount evaluation issue. Keeping track of material as it is traded is a different problem than Counting, but surely an important and related cousin.

Comments


  • 23 months ago

    Bartleby73

    thank you, Mr. Heisman! Your examples go into my repetoire of presentations to  beginner children. Much appreciated.

  • 23 months ago

    NM danheisman

    Thanks everyone. Yucca: Yes, for GM Kaufman's latest average piece values (from his new repertoire book The Kaufman Repertoire For Black & White) see http://danheisman.home.comcast.net/~danheisman/Articles/evaluation_of_material_imbalance.htm#2012-Update.

    Jminkler - Yes, I am linking to the Chess Cafe Archives which, once archived for a month, cannot be changed. You can see I edited this article to contain a link to the corrected diagram on my website.

  • 23 months ago

    yucca

    Just saying but chess.com gives a mid-game "score" using the old n=b=3 pawns and q = 9 pawns assumptions.  Is it worth changing this?  Don't think Heisman mentions this in this article but he says n=b=3.25 and q=9.75 are better in one of the linked articles

  • 23 months ago

    jminkler

    In your counting primer on the 3rd page, the same diagram is used twice, for different positions.

    Good stuff

  • 23 months ago

    pollystar

    good to move Rc8 if Nxc4, then white reply with Nc7 treathening Ra8, if fxe6 then white move is Bxe6+!

  • 23 months ago

    NM fpawn

    From my experience, the bigger challenge of the Nxe6 puzzle is identifying all of the candidate moves.  Considering that several moves are good for black, there is a real temptation to stop looking for an even better choice.  No doubt most people will bite on fxe6 or Nxc4, and altogether miss the cold-blooded Rc8.

    The fact that this position is presented as a difficult puzzle allows the reader to cheat a bit.  We know there must be something more tricky than the obvious fxe6 or Nxc4.  Alas, the player in a tournament game may not think so much, and may be content with a modest advantage.

    On the other hand, if the 2nd, 3rd, etc choices all favored white, then black would desperately look for anything that could possibly work, and more likely would find Rc8 (and b5).

  • 23 months ago

    Englix

    Great article, thanks Cool

  • 23 months ago

    NM danheisman

    Thanks for your interest in my article! Two notes about the comments:

    1.It's good the readers have also taken an interest in the second position "move" rankings. Hopefully they did not miss the point: sorting out capturing sequences, especially in complex positions, can be not only very difficult, but can have an enormous effect on the game. In many cases being able to accurately calculate capturing sequences has much more effect on the outcome of the game than knowing some common positional issues (which admittedly could come up more often, so are still important).

    2.I gave Houdini 2 the move 1.Nxf1 in the second problem. At 27 ply its score was -0.5, which was not that close to 4th, and a full pawn behind its highest rated move. The PV began 1...Nxf1 2.Nxf8 Nd2 3.Ne6. I forced 3.Bd3? instead of 3.Ne6 and Black's advantage jumped to -1.75 after 3...Kxf8 4.Rc1 Na6. Conclusion: If White finds 3.Ne6, then Black is not doing as well after 1.Nxf1 (not that this really affects the idea of the article...)Smile

  • 23 months ago

    Berder

    Bab3s, after your line 1. ... Nxf1 2. Nxf8 Nd2 3. Bd3 Bxf8 4. Nc3 black has the response 4. ... Ba6 and Crafty gives this a score of -2.08, maintaining black's big advantage.  White could try to block it with 5. b5 but black can simply retreat with 5. ... Bb7 and the knight can get out via Nb3 - Nc5.

    4. ... b5 would indeed be a blunder.  Check your work with another engine before you claim an engine made a tactics mistake...

  • 23 months ago

    NM Bab3s

    The reason why not 1...Nxf1 2. Nxf8 Nd2 is 3. Bd3, and while Black can play 3...Bxf8, the knight is trapped on d2 after 4. Nc3 and eventually the knight will be won back with a close to level position. It is, however, a bit tricky because Black's knight can actually get out of the web, but at a price, 4...b5!? 5. Nxb5 Ne4 6. Nc7 Nd7 7. Nxa8 Bxa8 with a very unclear position involving a rook and two pawns against two minor pieces; since those extra minor pieces are both knights, who lack great squares (the one on e4 is going to get kicked by f3 sooner or later), and since the rooks have some nice open lines, I prefer White.

    Based on my own examination of this position, I conclude that Berder's Crafty needs to take a harder look at that position; it's quite clear to me that 1...Nxf1 would be a big mistake, while 1...Rc8 is a relatively easy win.

  • 23 months ago

    VanillaBean

    I said just the other day that Dan Heisman taught me how to count. Smile  I have read (part of) Back to Basics: Tactics and, like SeanPlaysChess, found the chapter on counting invaluable.  One of the things it helped me realize is that attrition is an important part of chess and getting up in material is a worthy goal in and of itself.  I also own Yasser's books and worked through the problems, but remember thinking, "OK, they might be ahead, but how do they WIN (mate)?"  Now when I see a tactic that wins (or saves--those are fun) material, I understand the purpose behind it better.  So I think I better understand the game of chess now.  It's not just about find the brilliant moves that leads to mate.  It's about setting interim goals to get an advantage and working towards a position that will win.

  • 23 months ago

    zebra7

    redbirdpat, the "engine" answer is Nxf8 partly because Nf8-e6-c7xa8 is threatened.

  • 23 months ago

    zebra7

    Fritz12 agrees pretty much with Houdini.  If you have been relying on Crafty you may want to figure out why it is missing (did you give it time to search deep?).

  • 23 months ago

    redbirdpat

    Berder, I also chose Nxf1 for the solution.  But I didn't have access to an engine to tell me why it was wrong.  I wonder what Houdini says about that move.

  • 23 months ago

    Seanplayschess

    I am nearing finishing Back to basics: tactics and it has been a challenging book. I say this because I have read other tactics books such as Yasser's playing winning chess: tactics and others. I can say Dan's book has showed me I have a lot yet to learn on tactics such as better understanding of counting. I went and picked up one of Dan's recommended books; chess visualization course and it is very good as well!

  • 23 months ago

    Berder

    In the second problem 1. ... Nxf1 really didn't even make the top 4 for Houdini?  Crafty on my dinky computer thinks it's worth -1.89, almost as good as Rc8 and even slightly better than fxe6.

  • 23 months ago

    KeyserSzoze

    TGIF,i'll study it :)

  • 23 months ago

    Ironknight777

    extremely imp article.thanks. 

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