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Friday, August 12, 2016

Counting Pieces in Your Head

    A few years ago I did a post called Counting Pieces where I noted that in his book The Inner Game of Chess-How to Calculate and Win Andy Soltis discussed the problems of keeping track of material in a complicated position, especially in situations that result in a material imbalance. 
     While playing through one of the games in the chapter on "Counting Out" where Soltis discusses the problems involved in counting pieces, especially those involving material imbalances, he didn't bother to analyze this game after move 21 because the remaining moves were not relevant to his theme. Also because the book was published back in 1994, I was curious to check the validity of his conclusions with Stockfish and Komodo. Whether he was exactly right isn't all that important because his general advice on dealing with such positions is excellent. 
     While it may be difficult for us amateurs to evaluate the effectiveness of the pieces on the board, counting them is no problem. The problem is that when calculating a sequence of moves where there are multiple captures, especially if the material in not even, it can be easy to lose count of who has what left!
     For example, in the game Capablanca vs. Alekhine, Nottingham 1936, even the great calculator Alekhine lost track of the pieces left on the board when he was calculating his 24th move, f4. He thought he was winning two exchanges, but he actually gave up three pieces for two Rs. 

     There are two basic ways of determining what pieces are left when mentally calculating a long variation: 
1) Review the sequence in your head and keep track of the pieces captured by each side along the way. 
2) Visualize the final position and count the pieces remaining. Either way, it's not always easy! 

     This game is not only interesting in itself, but it illustrates that counting the pieces can be difficult. It was made even more so in this game because after a flurry of tactics beginning with 16.Nd5 Onoprienko won Liberzon's Queen and when we win the other guy's Queen, that always seems like a good thing, but the resulting position was very difficult to evaluate even using Stockfish.  


  1. I can’t remember where I read this, but here is a simple way of keeping track of material during a complicated exchanging sequence. This method uses the traditional (Reinfeld) value for the pieces and only requires you to keep track of one number.
    Calculate the material balance at the beginning of your calculation. Let’s assume material is even, so that the material count is zero
    As you calculate, each time you take an enemy piece, you add the value of that piece to the material count. If you play RxN, the count goes to +3
    When one of your pieces is captured, you subtract the value of the piece from the material count. If your opponent now plays BxR, you subtract 5, leaving a balance of -2.
    You continue adding and subtracting in your mind until the sequence ends. The value you are left with is the material balance at the end.
    This method does nothing to help you evaluate the dynamic values of the remaining pieces, or to assess the positional features of the resulting positions. But it pretty much guarantees that you will never experience that awful “Hey! I’m a rook down. How did that happen?” sensation again. And keeping track of a single number is so much easier that: “I take a knight, he takes my rook, now I take a bishop, he grabs a pawn, it take a rook, he takes my rook …”

  2. This sounds like a reasonable method, but when I tried it from moves 16 to 21 I needed a pencil and paper to keep track of the score! Since you can't write on your scoresheet I would need to keep track of the count on my fingers. If things got too complicated would it be OK to take off my shoes and socks and count on my fingers and toes?

  3. I think keeping track of the material balance through those tactics is relatively simple. 16.Nd5(0) exd5(-3) 17.exd5(-2) Nxd3(-5) 18.cxd6(+4) Nxf2(+3) 19.Qf3(+3) Bxc6(+2) 20.Qxc6(+5) Nxd1+(0) 21.Kf1(0) Nxb2(-1). Black is one-up in the classic material count (!)
    But visualizing and correctly evaluating the resultant position, as Black needed to do, is so far beyond me, I can’t even comprehend it. And of course, in positions with such mismatched material, the actual material balance is far less important than who has the initiative and whose pieces are better coordinated

  4. I like this counting method! Thanks!

  5. here is a hint that may help in case of a long string of captures...if one side makes both the first and last capture they have probably won material.

  6. There is actually a third method which is to look at the material taken off of the board after a series of captures. This is an easy way to see what just happened, BUT (1) the pieces can easily get confused with pieces from neighboring boards, and (2) tells you nothing about what is left on the board. I'm not advocating for this method, just highlighting a lot of beginners do this.

    For simple variations (only a few ply deep on one or two squares), I almost exclusively use the first method by tracking what is equal/imbalanced about the captures as they happen. If it is equal there is nothing to track, but if you win/sacrifice material, track just that imbalance, even if equal captures happen afterwards.

    For longer variations I normally use both methods. I start with the first, but almost always have to end with the second step, just to be sure.

    Also, I have noticed that when I "win the exchange" I end up visualizing the pieces that came off (say his rook and my knight), but that in fact does nothing to help me appreciate what is left on the board which may not include either piece!