At the zoo

Yesterday I skimmed through my chess library, looking for an interesting book. When I have used a chess book extensively, it is worn out. I found a book that was looking almost new. Chess tactics from scratch, by FM Weteschnik. It covers pretty much what I'm busy with, so I decided to give it a try again. Since he learned chess at later age than most people, he had to work hard to improve his tactics, and he has experienced his improvement more conscious.

 "During that time, I also solved a lot of combinations to sharpen my tactical skill. I had developed my own little routine. Whenever I thought I had discovered some mechanism or characteristic of a position, I started taking notes. The work on thousands of positions grew first into a collection of unsorted tactical insights, but finally resulted in a structured overview of tactics. Over time, seemingly unconnected information, turned into a coherent concept."

Since I left the salt mines at march 26th, I have done exactly the same. I analyzed 174 positions in 124 days.

At the moment I'm looking at the different types of tempos I encounter. It turns out to be a whole zoo of different types. I look at the moves from the winning side from three perspectives:

• What does the piece leave behind
• What happens when the piece lands on a square
• What threat is the piece exerting when landing

What does the piece leave behind?
In short: an empty space. Clearance that is called when there are pieces around who can make use of the emptied line or square.

What happens when the attacker lands on a square?
It might block a few pieces if the square was empty (the opposite of clearance).
If the landing square is not empty, it is a capture. We measure the effect of the landing by the piece that is captured.

Offensive:

• What is its value?
• Is it a defender?
• Is it protected?
• Is it protected by an overworked defender?
• Is it a recapture?
• Is the capture designed to be recaptured by another piece that will be a target?
• Is the landing square an attacking square of a duplo attack?

Defensive:

• Does it avoid a check?
• Does it avoid a capture?
• Does it avoid a threat?

What threat is the landed piece exerting?

• This is about what the next move of the landed piece might be.
• Does it threaten to capture?
• Does it threaten to capture a defender?
• Does it threaten to capture a piece that is defended by an overworked defender?
• Does it threaten to move to an attacking square of a duplo attack? 
• Does it give a check?
• Does it give a double check?
• Does it threaten mate?
• Does it attack a pinned piece?
• Does it attack a target that is defended by a pinned piece?
• What is the value of the threatened piece?

As you see, it is by no means simple to tell the story of the tempos that make the combination work. Yet I belief we have to learn a few standard patterns concerning the story of tempos.

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

Removal of the guard

I hope you don't get bored by all those positions and analysis. I actually find it very exiting! I feel we are making steady progress, albeit slowly.

My list with positions where I want to learn to see the solution in  stead of just to calculate it, becomes slowly shorter. Meaning that it is indeed possible to replace calculation by seeing. I'm in no hurry, and I take my time to grasp every detail of a position, trying to devise some rules that can be applied in other positions. I'm not interested in the very position itself, because most details are accidental, and hence limited to only that single position. I'm only interested in the details of the combination. What makes that the combination actually works? Why does it gain wood? I make little changes to the combination, trying to keep everything else the same. I add or remove pieces, and see how that influences the outcome of the combination, while ignoring the effects on the position. I change the move order and see what difference that makes. I use Stockfish to check my conclusions.

The following position is about removal of the guard.

Diagram 1 White to move

r1qr2k1/pp2ppbp/1np3p1/4P3/2b1PP2/2N1B3/PPQ1B1PP/3R1RK1 w - - 1 1
Solution

The black knight protects the bishop. I realized that removal of the guard by 1.Bxb6 only works because it threatens the black rook on d8. It is a multi purpose move. A capture plus a threat.

Let us see what the effect is of removing the possibility of this threat. Does the combination still work? In order to find out, I removed the black rook on d8. In order to keep the material in balance, I removed the white rook on d1 too. We get the following position:

Diagram 2 White to move

r1q3k1/pp2ppbp/1np3p1/4P3/2b1PP2/2N1B3/PPQ1B1PP/5RK1 w - - 1 1

Now the combination doesn't work any more. Since 1.Bxb6 doesn't threaten the rook, black is no longer obliged to take back on b6 first. Black has time to get rid of his problem bishop by playing 1. ... Bxe2
This leads to the following
Rule: removal of the guard only works when it is a capture which gains a tempo. 
 In this case, by a threat.
This rule probably can be generalized:
Rule: look for captures which are accompanied by a threat.

I asked myself whether it is necessary to threaten a piece of higher value. So I decided to replace the black rook by a knight. Adding a white knight on b1 for material balance.  I saw that 1. ... Bxe2 threatens the rook on f1.  For clarity I decided to remove the remaining rooks too:

Diagram 3 White to move

2qn2k1/pp2ppbp/1np3p1/4P3/2b1PP2/2N1B3/PPQ1B1PP/1N4K1 w - - 1 1

The combination still works. This leads to the following
Rule: look for captures with follow up captures

What happens when black has a follow up move too? I replaced the white knight from b2 to f1:

Diagram 4 White to move

2qn2k1/pp2ppbp/1np3p1/4P3/2b1PP2/2N1B3/PPQ1B1PP/5NK1 w - - 1 1

Now the combination no longer works. If both sides have equal follow up moves, removal of the guard doesn't work.
Rule: you need one follow up capture more than your opponent

Giving black more than one follow up possibilities doesn't change the outcome. The one who started with the first capture can decide to break off the series of captures whenever he wants.


Rule: only the one who starts the series of captures has the chance to win a piece. He wins a piece when the opponent runs out of captures.

Does the move order make any difference? In diagram 1 there are 3 possible captures:

• 1.Bxb6
• 1.Rxd8+
• 1.Bxc4

The last capture shouldn't be considered as first, since it is a capture without a follow up threat.
What if  white plays 1.Rxd8+ Qxd8:

Diagram 5 after 1.Rxd8+ Qxd8 white to move

r2q2k1/pp2ppbp/1np3p1/4P3/2b1PP2/2N1B3/PPQ1B1PP/5RK1 w - - 1 1

If white now captures the knight on b6 with 2.Bxb6, then black can take back with 2. ... Qxb6+ and the combination doesn't work due to the check. But that should be considered an accidental feature of the position. If the king had been on h1, the combination would still work!

What does this tell us? We have to look for captures with an additional punch first. The winning tactical theme here is removal of the guard. Worries include the possibility for the now unprotected black bishop to counter attack. It becomes a desperado.

Other captures than 1.Bxb6 that have an additional bite, are in general equally well playable (=1.Rxd8+) without changing the outcome of the main tactical theme (removal of the guard). In essence, such captures with extra bite are postponement moves. They postpone the execution of the tactical theme by one move, since they require immediate action. You can play an infinite amount of postponement moves, but the main problem for black remains.

It is important to grasp the main ideas of the position, to reduce you calculations. But you still need to calculate every line. Since there might be a capture with a counter bite for your opponent as well that you might overlook. But calculations with a mind that is not already overloaded, is usually no problem.

Removal of the guard

Rules

This is the second or the third time I encountered this position. I devoted quite some time to it in the past. I might even have posted about it, I'm not quite sure. If so, I apologize that I post about it again. My excuse is, that I have apparently learned nothing from it, since I got the solution wrong. Again.
I think it is an important position, and I think it should be possible to see the solution at once. Maybe I can devise a rule or two during the process of learning how to see the solution.

White to move

r1bq1rk1/pp2ppbp/2np2p1/8/2PNP1n1/2N1B3/PP2BPPP/R2Q1RK1 w - - 1 1
solution

The last move of black was 1. .. Ng4. The black knight is hanging. The problem is, that if white takes it, the white queen becomes overworked. If white wants to stay ahead, he needs an extra tempo. Where does this extra tempo come from? After 1. ... Ng4 2.Bxg4 Bxg4 the white queen is hanging. If the queen takes on g4, black will get his piece back by capturing the knight on d4. White can gain a tempo by 3.Nxc6 in stead of 3.Qxg4. This power move accomplishes the following:

• White gets rid of his problem piece
• It captures a piece
• The black queen is under attack

Rule: use your problem piece to capture
Rule: choose the capture that poses a new threat

This might give you the impression that you can change the move order. Why doesn't that work?
1. ... Ng4 2. Nxc6 is answered by blacks power move 2. ... Nxe3
Now it is black who abides the two rules above:

• He gets rid of his problem piece
• He captures a piece
• He threatens the white queen

Which leads to a new
Rule: capture the piece of your opponent that can capture a piece of you with tempo first

If black takes the knight first 1. ... Ng4 2.Bxg4 Nxd4 then the rule "use your problem piece to capture" applies. 3.Bxc8 gets rid of your problem piece.

When to count?

I changed DGF into DIG, since that put the tasks in the right order, and it is easier to remember than DFG. DIG = domination square, invasion square, guard. So now we get M WIMP DIG.
I always used invasion square (or convergence square) in stead of focal point in the past, btw.

When I tested the system we are trying to develop against practice, I noticed that we might count at the wrong moment. I started with counting right away when I look for domination squares. The reason for this is that I want to prune squares which there might be a contact, but which are not interesting. But look what happens in this position when you start counting:

black to move

 5r1k/pp6/3bprqp/3p2p1/1P1P4/P2QPNPP/6K1/3R1R2 b - - 1 1
solution
Domination squares: f3, f1, d3, g3
Invasion square g4

If I count the situation on f1, then it is attacked twice and defended four times, so it scores minus two. But that score is irrelevant, since with two power moves, I can harass 3 of the 4 defenders. For instance: 1. ... g4 2.Nh4 Qxd3 3.Rxd3 winning the white rook at f1. This means it makes no sense to count before you consider the defenders and how to harass them. You can't prune anything based on counting for domination. Without counting for domination, you don't know whether you dominate a square. That makes the term "domination square" nonsensical. Maybe "contact squares" is a better term. That frees the D from Domination, which I can then use for Defender, the term that I am used to, in stead of Guard. Which reads M WIMP CID, which is a bit of a pity, since DIG is easier to remember than CID. But hey, it is a work under construction! We need to automate it anyway, so it is just a pair of training wheels.

See more, calculate less

My database with failures at CT has grown to 135 positions. After carefully studying them, I found 62 positions to be "easy". That is, I know them well enough to not make the same mistakes again in the future. I can now see the solution of them without any calculation or effort. 9 positions are too complex. Meaning that I cannot find the solution without serious calculation. I don't expect to see their solution any time soon without considerable study first. That leaves me with a selection of 64 positions which have a simple solution (with hindsight, after studying them well), but where I don't see the solution without calculation. I think I should be able to see the solution, though. I'm going to use these 64 position solely for exercising to see the solution in stead of calculating it.

I expect to need a few hours per position. What makes it even more difficult is that such exercise is definitely out of my comfort zone, and I constantly try to escape it by checking my facebook, twitter, the news, writing blogposts like this, etcetera. I now open five positions at the same time, and if I want to escape from one, I do so by going to the next position. That somewhat works.

For you to know what I'm talking about, I will give you a few example positions.

Diagram 1 White to move

 2r3k1/1R5p/p1q1rnp1/3p1p2/P7/2Q2B2/1P4PP/2R3K1 w - - 0 1
solution
As said, what I try to do is to see the solution without any calculation. I already have done that with a few other positions, and it is possible. I focus on the story of the initiative. How do I find forcing moves, and how does that translate to the gain of wood? Which squares am I dominating, who are the defenders and how do I harass them, what are the focal points? In short: M WIMP DGF?

Diagram 2 black to move

 4r3/p1k3pp/2p2p2/8/PrRnP3/1P2R1K1/3N2PP/8 b - - 0 1
solution

Diagram 3 black to move

5r1k/3B2pp/3P2n1/pp2p3/6P1/PP5P/1BPNpr2/3R1RK1 b - - 0 1
solution

Diagram 4 white to move

4R3/r4kn1/5P1B/2pp1qQ1/1p5P/3b2P1/5P1K/8 w - - 1 1
solution

I expect that what I learn from these exercises will transfer to other positions as well. I have mastered a few positions this way, and it seems that my intuition has grown. It happens more often that I can't resist to make a certain move, which happens to be the right one. In the past most of the time such moves were wrong. So it might work.

The fact that I have written this very post, already indicates that I'm still struggling with distractions though.

M WIMP DGF

I have been testing the three counting methods from the previous post. It turns out that only the first method is viable in practice. Counting dominated squares, or "interactions on squares" as Robert put it, is in itself not enough to solve every puzzle. A few extra characteristics must be recognized before you can figure out the whole combination. To remember them, I use the mnemonic above "M WIMP DGF"

M-Material balance
You can't do without evaluating the material balance.

WIMP
You must know what the position is about.

• W-Wood. Gaining wood
• I-Invasion
• M-Mate
• P-Promotion 

It is quite possible that the theme of the position is about more than one subject. WM - you try to M-mate, and the opponent can only prevent that by giving up W-wood, for instance.

D-Domination
It turns out that finding the squares you dominate is essential to understand any combination.

G-Guard
In many positions it is key to find the defenders, and the defenders of the defenders, since "removal of the guard" is the main issue in the position. You must be able to see the (chain of) guards.

F-Focal points
If you focus on domination, it turns out that you will miss some important squares. Invasion square, attacking square and the like. Focal points comprise these squares.

When I use the mnemonic above, I usually am able to find the solution. Given the importance of domination, it is probably a good idea to isolate that as a separate exercise.

The other two counting methods, counting tempo's and counting the value of obligations, are not practical. Counting tempo's, or obligations, is in fact counting the amount of dominated pieces. You must learn to see the effect on tempo's of a move. That should be treated as an isolated exercise too. Counting tempi might be of help initially, but the sooner you change to seeing the effect of a move, the better. It is really move related. We must see whether moves are single tempo or duple tempo. After the exercise of seeing the effect of a move on the obligations has been fully mastered, we will have a look at the third counting method, counting the value of the obligations. Hopefully it isn't necessary by then any more.

WIMP