## Wednesday, July 27, 2016

### The total amount of captures

A main flaw of my chess thinking is the "wrinkled" view I have about the initiative. "White captures the black piece with tempo. " It turns out that there are many types of tempo. The story of the tempos of a combination is often hard to tell. I think the ability to tell such story is very important though. Since it are the tempos by which we assess the value of a combination. The same geometrics of a position can have a totally different outcome when they differ only one tempo. Imagine a position where he who is to move, wins, for instance. It is by no means easy to iron out the wrinkles in my tempo view.

Gain of wood
If we would allow a chess game to have one more move, we would take the king in the last move. That simplifies the game of chess as the art of gaining wood. A mating attack is then equal to a trap. With the only difference that the wood that is gained is of infinite value.
It is possible to see promotion as a way to gain wood too. If a pawn queens, about 8 points are added to the material balance.  Which is almost a similar advantage as capturing your opponents queen. The reason for simplifying mate and promotion to a mere gain of wood, is that it helps to find rules that are more broadly applicable. That way, we might find that rules that govern duplo attacks can have a broader application. The complicated rules around the king which isn't allowed to move into a check becomes simpler the moment that you realize that it could be taken the next move. That's why the kings cannot approach each other and why they must escape checks. A lot of rules would become immediately clear when you would allow to capture the king. The set of rules about king and check can be replaced by one simple rule: prevent that your king is taken at any cost.

CCT
The hierarchy of checks, captures and threats is based on their degree of forcefulness. Although that line of thought can be quite useful, I like to look at it from a functional point of view. Since that might help me to see "the bigger picture". Functionally, a check and a threat are the same. It is the value of the king versus the value of the threatened piece that makes that we treat them differently. But exactly the same is true for any piece of higher value in comparison to a piece of lower value.
A threat against your queen is handled before a threat against your knight.
A capture is definite, while a threat is temporary. That makes it dangerous to answer a capture with a threat in stead of a recapture. If the threatening piece is taken, both your piece and your threat are gone. The hierarchy of CCT invites you to start at the begin of the tree of analysis. Functionality helps you to start at the end. To enlighten the load of my STM, I like to have a functional chain of events before I start to worry about the administration of the value of the mutual gain of wood. Practicality before the correctness that only a computer can deliver fast.

The length of the mutual chain of attack
In a previous post and its comments, we found the importance of the length of the line of attack. The length is determined by the amount of captures. This reveals something about the chain of tempos that I have totally missed so far. I wrote about it in the past, btw.

When I capture an unprotected piece, my line of attack is 1, while the line of attack of my opponent is 0. Maybe it is better to speak about the chain of captures. This leads to the following rule that is actually still only a hypothesis.
Rule: the longest line of captures gains wood.
We chase the 'tits', saddling the opponent with the 'tats'.

Serial and parallel
If my bishop captures an unprotected knight and my opponent answers this by capturing an unprotected knight of me, the length of both our chain of captures = 1, so nobody gains nett wood.
If my white bishop captures a series of 4 pieces in a row (serial), and my opponent has 4 separate attackers which capture 4 separate targets (parallel), both chain of captures add up to 4, so no one gains nett wood. This implicates that the total amount of possible captures can consist of both serial and parallel attacks, for both sides. If your amount of captures is not at least 1 greater than the amount of captures your opponent can do, than the combination cannot work with equal value of the captured pieces. If both amounts are equal, then you can only gain wood when the captured value of the pieces is higher. This way, we can predict which lines can't possibly gain wood. Thus pruning the tree of analysis.

Captures and threats
Only captures collect wood. Threats don't. Threats postpone captures. Only moves with duplo threats can bring the opponent into trouble, when he isn't able to answer the two threats in one move. All duplo attacks are based on this principle. If the opponent lacks space, it might be possible that he can't find an answer to even a single threat. That is called a trap. Or mate, if the involved wood is the king.

 Trap

1. http://temposchlucker.blogspot.nl/2007/11/pull-on-chain-part-iv.html

2. Rule: the longest line of captures gains wood.

I think this is wrong, even if the exchange is at a single square.
You would have to exchange further even if it is not benefitial anymore:
Say there is after e sequence of exchanges some piece ( Ra1 ?) attacking Pa7 but the Ra8 is protecting it, then you would stop the exchange and leave the Pa7 where it is ;)

http://mediocrechess.blogspot.de/2007/03/guide-static-exchange-evaluation-see.html

1. You are right. In the first comment I posted a link to an interesting "tit for tat" position, which I advise to have a look at. It doesn't matter who has the longest. What seems to matter though, is who starts with the first capture. If your opponent starts, you can only hope to keep up with him. But if you make the first capture, there might be a chance you win a piece. If the chain of captures of your opponent is longer, the art is to break the chain of captures in time. Often, as in the example given in the comment above, you need a duplo tempo move for that. One tempo to save your attacker, and one tempo to capture your opponents attacker.

It's funny that back then in 2007, after a series of 5 posts about bean counting, I finally sort of concluded that chess tactics are too difficult for me, and started to study positional chess and the art of avoiding tactics :D

3. The hierarchy of Checks, Captures, Threats is interesting. Checks may (or may not) gain material as an integral result of the checking move. Obviously, captures do gain material. Threats do not gain material because they are displaced by at least one tempo from either a check or a capture. Perhaps this is the distinction Averbakh had in mind by differentiating between "attack," "first-order threat," and "second-order threat."

The degree of compulsion is important. A check MUST be answered by getting out of check (explicitly, by the rules of the game). A capture has a somewhat lower degree of compulsion, but a long-term commitment must be made to regaining at least material balance (or sufficient compensation of some sort). Threats are at the lowest degree of compulsion because of the separation in time - it's not compulsory to respond to a threat IFF something else proves to be more important to do at the time of the threat.

It is somewhat analogous to the differentiation between absolute and relative pins. An absolute pin prevents the pinned piece from moving (except along the same line as the attacker) by the rules of the game. A relative pin allows the pinned piece to move anywhere, not just along the line of the pinning piece. The usual error is to "think" that a relatively pinned piece cannot move (as if it were an absolutely pinned piece).

It was GM Botvinnik's view that (for practical purposes, although not part of the official rules) the game of chess could be reduced to the goal of gaining material. This was the basis of his thesis in the book Computers, chess and long-range planning. It is interesting that you arrive at essentially the same conclusion!

1. @Robert

Nice remarks. I want to commment on these.

If we take into account a checkmate as a final capture - we can say with absolute certainity: "chess is only about capturing". If you cannot capture (=checkmate) the King... you simply cannot win! Sounds obvious? :)

[A capture has a somewhat lower degree of compulsion, but a long-term commitment must be made to regaining at least material balance (or sufficient compensation of some sort)].

I disagree about the necessity to alway recapture pieces. You have to "gain something in return", but capturing is not the only way. My present knowledge and understanding say: "sufficient compensation" is the best descrpition and explanation. The easiest example is when you lose your Q, but gain a perpetual check. It does not matter how far ahead in material your opponent is... you have SUFFICIENT compensation for lost material. You do not have to capture any of his pieces.

[...it's not compulsory to respond to a threat IFF something else proves to be more important to do at the time of the threat.]
I would extend it to everything including captures. If you can gain sufficient compensation - there is no need to count who is ahead in material. The same is when you reach the endgame part - if you can FORCE your opponent to stay only with 2 Knights... against your bare King - it is the extreme case of "sufficient compensation". The same is with the ending B+p(a-h) without Bishop controlling promotion square. And the fortress when you are low on material, but your opponent CANNOT realize the advantage (and as a result - is not able to checkmate you!).

1) An absolute pin prevents the pinned piece from moving - it means the pinned piece can NEVER make any (legal) move! Unless it is absolutelly pinned - it cannot move.

2) Relative pin prevents the pinned piece from moving along ANY different way than the pining pin that influence it. If your piece is pinned by the Rook you can move ONLY along the pinned way.

3) False pin allows the (false) pinned piece to move anywhere, not just along the line of the pinning piece.

It would be great to use such terminology - not to make any confusion between us (readers). This way we can see the same picture by our own eyes. You can change "false pin" into "illusory pin", but the latter name is much longer (that's why I decided not to call it this way).

[The usual error is to "think" that a relatively pinned piece cannot move (as if it were an absolutely pinned piece).]

I have already solved so many puzzles that I do not see this kind of pin as an "absolute one". For me - it is only some type of TEMPORARY restriction of my pieces. However absolute and relative pin - they are the examples of CONSTANT pins (of course unless we break/destroy the pin). And that's a big difference (at least to me).

And last, but not least ;)

[Threats do not gain material because they are displaced by at least one tempo from either a check or a capture. Perhaps this is the distinction Averbakh had in mind by differentiating between "attack," "first-order threat," and "second-order threat."]

As far as I understood Averbakh's work he referred ordered of threats as the following moves - played one after the other.

For example if I can play 1.QxR 2.QxB 3.QxN 4.Qxp - Averbakh would say: "first-order threat" is to take R, "the second-order threat" is to take B, etc.]

I hope you now got the idea why I wanted to comment your reply. Some of the things you mentioned... I see in a bit different perspective (view). Of course I do not say "I can see better", but in another angle. I will be glad you comment my remarks my chess friend!

4. @ Tomasz:

Thank you for defining the terms regarding pins. I had a somewhat different definition (and I have no idea where I obtained it) that an absolute pin was against the king, even if the pinned piece can move along the same line as the pinning piece, and a relative pin was against any other piece. I can accept your definitions easily.

Perhaps there was confusion when I indicated ". . .long-term commitment must be made to regaining at least material balance (or sufficient compensation of some sort)." I think you are saying the same thing as I did: if material balance is NOT restored via captures, then one MUST gain "sufficient compensation." I purposefully did not specify how long it would take to regain either material balance or sufficient compensation. I did NOT intend to imply that one is forced into a series of recaptures.

I have a somewhat different view of Averbakh's designation. If there is an attacking contact then there is a direct attack. If a piece can move into a direct attack on the next move, then there is a first-order threat. If a piece can move into a first-order threat on the next move, then it is a second-order threat, and so forth. Personally, I think his theory has value in a theoretical sense, but maybe not as much in a practical sense. Although it is very helpful when trying to break a position down into its constituent parts, to me it can become distracting with too much detail. Does that makes sense to you?

1. There are a lot of strange definitions, but my vision is we should make them as clear and one-sided that everyone has to understand it only one way. The clearer (and simpler) the definitions, the easier to work with these. Anyway I am willing to accept any reasonable definitions, but I always try to make these as "only-meaning" as possible.

Thanks for claryfing your point of view (regarding captures and recaptures). If you ask me anything more about Averbakh works I will hurt you ;) :). And to be serious I did not catch his theory even if it is logical and coherent. I cannot see its practical application - the scientist could probably have been really happy, but not a practical player.

And I have the same feeling as you my friend ["Although it is very helpful when trying to break a position down into its constituent parts, to me it can become distracting with too much detail"]. And it does NOT make any sense to me - especially when there is too much theory and you cannot apply it without being Averbakh himself!

To me it is the same if I would tell you: "you have to do only four things at chess to win every game: 1) attack, 2) gain a necessary advantage, 3) realize it and just 4) checkmate your opponent's King".
Even if it is completely logical and you cannot refute any of its part (!) - how on Earth you will be able to win games? Do you see the big abyss? I can appreciate just the basics of Averbakh's theory - especially with the application to the endgame. Why? Because there is a few pieces left and you can see the relationship between pieces a way better. And you do not have to use the "first-order threat" or anything like that. Just the important elements and clear goals.

BTW. I think Averbakh's examples are way too difficult and that's one of the reason understanding his works is close to impossible to many amateurs. If he would have started with an extremally simple concepts and examples - he could be able to present his "scientific approach" at the most complex examples... when you could have been able to comprehend the lower level conclusions and relationships... to get the full concept at the end of the day!

2. I'll try to remember NOT to reference Averbakh again! ;-)

I think your point is excellent regarding the encapsulation of how to traverse the "abyss" into a few "simple" general rules. Although they may be true in all situations, they are essentially useless for helping to understand what needs to be done IN THIS SPECIFIC POSITION. Since Averbakh was writing for "advanced players" (according to the title of his book), I can only conclude that I am NOT an "advanced player." Maybe some day. . . In the mean time, I hope to improve as a practical club level player.

In the meantime, we have this marvelous blog to learn from! Thanks for your thoughts!