Monday, July 04, 2016

Counting tasks

I was surprised and even somewhat disappointed to see that the study of the initiative didn't yield me a viable method to prune the tree of analysis while thinking forward. Today I decided to focus on backwards thinking. It is logically to start with the targets. But when I tried to do so, I stumbled on another fact about the initiative, that has been somewhat under exposed. It is true that in general you should know the end before you can know the beginning, but if you see nothing, you need to start somewhere. If the characteristics of a position were purely geometrical, you would be able to find any idea by just looking at the board. But the functions of the pieces are virtual, and so are the geometrical patterns that accompany the functions. Our training tends to focus on the physical geometrical patterns and not on the virtual patterns. Which is why it doesn't work. Probing the position and fast checking lines is still done by forward thinking. It depends on the position and your forward thinking skills if forward thinking is helpful or doesn't work at all. In practice, you probably need both forward and backwards thinking.

From a certain position, I derived two diagrams that show what I'm trying to tell you.

Diagram 1 white to move
 White attacks the black bishop twice, but his pieces are skewered by the black rook.

For white
Attacks = 2
Tempi = 1
This reads as: white attacks black twice, black needs 1 tempo to save his target.

For black
Attacks = 2
Tempi = 2
Reads as: black attacks white twice, white needs to tempi to free himself.

An attack is counted as a direct contact between an attacker and a target.
Tempi is the amount of tempi that is needed to escape from all attackers. Be it by capturing the attacker, defend the target, interfere the line of attack or get out of harms way.

A move usually is worth 1 tempo. A duple attack is worth 2 tempi.
For defence you usually need 1 tempo. For defence against a duple attack, you need 2 tempi = a duple defence. This are the possibilities:
  • A move does nothing (0)
  • A move attacks a piece (1)
  • A move defences against an attack (1)
  • A duple attack (2)
  • A duple defence (2)
  • An attacking move which defends (1+1=2)
  • A duple attack which defends (2+1=3)
  • An attacking move which duple defends (1+2=3)
  • A duple attack which duple defends (2+2=4)
So a move can have a score from 0 to 4 on the scale of accomplished tasks.
In the position above, both Be8+ and Be2+ with check win a full rook. Be2+ scores 3 and Be8+ scores 4.

This way of counting is a simplification, and practice will show if it works well in all situations.

Theoretically, you can have triple, quadruple, quintuple etc. attacks or defences. That are rare occasions, though. For simplification, I neglect them for the time being.

Situation after move 1.Be2+
Safes the white bishop from 2 attacks
Does a discovered attack against R and K (+2)
Relieves one attack against the black bishop, but the attack of the rook remains (+1)
Puts the black R in a pin
Exposes the white rook to an attack

Attacks = 3
Tempi = 3

Attacks = 1
Tempi = 1

Situation after move 1.Be8+
Safes the white bishop from one attack
Does a duple attack (discovered attack) against R and K (+2)
Keeps the attack against the black bishop (+2)
Puts the black R in a pin
Exposes the white R (1)
Does a double attack on the black king and bishop

Attacks =4
Tempi = 3

Attacks = 1
Tempi = 1
Both 1.Be2+ and 1.Be8+ win the black rook.

The position below is more critical.

Diagram 2 White to move
Still,  white attacks the black bishop twice, and his pieces are skewered by the black rook.

For white
Attacks = 2
Tempi = 1

For black
Attacks = 2
Tempi = 2

The difference is, that the black king now is 1 square closer to the rook. This means that in case of a check,  the black king can make a multi purpose move. He escapes the check, while in the mean time he can defend the rook, and escape the pin, thus freeing the black rook as an attacker of the white bishop.

After 1.Bd3+ blacks plays Ke6 and white cannot win a piece.

After 1.Bd7+ Ke4 2.Rxd5 Kxd5 3.Bxa4 white has won the black bishop.

What I'm looking for is a simple formula with the 4 figures (attacks and tempi for both sides) so you can simply count which move performs best, gets the most tasks done. That should work better than just scanning all CCT moves. We might even develop a sense for the most effective move. I for instance, played 1.Bd3+ in diagram 2, since I thought 1.Bd7+ to be counter intuitive.


  1. The 4 figures (attacks and tempi for both sides) for every move you consider, tell something about the future. It is not a coincident that the move with the most attacks wins in diagram 2. In diagram 1, the two most active moves win. But it is not so easy to interpret the figures. To find a formula though, it is necessary to understand what the figures exactly mean. When your opponent defends via a standard method, like capture the attacker, pin the attacker, interfere the line of attack, protect the target once more, you have to look at the amount of attacks. For the last standard defense, escape the line of attack, you have to look at the amount of tempi needed for defense. Even when a piece is attacked six times, it can escape from all six attacks by one escape move.

    There is another figure to consider: what does it mean that a piece is attacked 4 times, while it is defended 3 times? Should we count that as 4-3=1 attack?

    What exactly do the figures of the opponent mean? If I have 4 attacks and he has 3 counter attacks, do I win a piece? These matters are not so simple, it might very well be that a formula that is always correct does not exist, and that you always have to calculate everything. But on the other hand, if we find a hierarchy for which candidate moves to consider first, we already may prune the tree of analysis considerably. I'm sure that better tacticians than we are, use a few rules of thumb without knowing it.

    1. There is an error on last variation above the last paragraph,

      After 1.Bd7+ Kd5 2.Rxd5 Kxd5 3.Bxa4 white has won the black bishop.

      1 ... Kd5 here the king cannot move to d5 as the same space is occupied by the rook

  2. Both diagram 1 and 2 have a lot in common. A lot of geometric features are the same for both positions. But one single feature, the fact that the king is one square closer to the rook, makes a difference for the best move. Which means that, despite we postulate that the FFA place a role, the geometrics of de position are of secondary importance. We need virtual patterns above all, not physical ones.

  3. Diagram 1 [1K6/8/8/RB2r2k/b7/8/8/8 w - b6 0 1]

    I will look at ALL the variations and explain them as best as I can. It may help others to see 'the invincible' resources.

    1. White can consider 4 candidate moves (4CM)

    a) 1.BxB
    b) 1.RxB
    c) 1.Be8+
    d) 1.Be2+

    Why just these moves? It is because all the other moves loses a Rook (simply RxR).

    a) 1.BxB RxB and Black Rook takes White. What's more important is stands on black square so white cannot capture (win) it.

    b) 1.RxB RxR and the we have an equal position (is not possible to make any skewer)

    c) 1.Be8+ and now Black has 5 replies: one capture and 4 escape moves (due to the pin).
    c1) 1.Be8+ BxB 2.RxR+ Kh6 RxB Black wins
    c2) 1.Be8+ and all the King moves are bad because White plays 2.RxR and defends his Bishop. However the best option for Black is to play 1...Kg4! as it allows to attack White Rook that defends the attacked Bishop! After 2...Kf4 there are two safe squares (e7 and e1) of different colour than Bishop and unavailable to attack next move by the King.

    The conclusion: the attacked piece (King) should make a counterattack - no matter how many moves it requires (the less the better). That's why 1...Kg4! is the best choice. Capturing the attacker (BxB) is not a good move here, because it creates (simple) duplo attack for White and after RxR+ Black Bishop cannot cover the line of attack (if the King would have stood at "i5" the Bishop could have been saved by "Bh5").

    d) 1.Be2+ and now Black has 4 replies (escape moves only) due to the pin.

    There are only 2 moves we should ignore. They are "edge moves" (1...Kh4 and 1...Kh6) as they do not make Black King closer to the attacking Rook.

    2 moves that deserve attention are: Kg5 and Kg6. Both of these are equally good here. After 1...Kg5/Kg6 2.RxR(+) Black King plays Kf6, but the Rook has too many choices to be captured. In addition it does not need to defend the Bishop because it is not attacked.

    The conclusion: playing 1.Be2+ is much better as the counterattack is gone. White does not have the obligation to realize any other tasks (like defending the bishop).

    The general conclusion: the move is {may be} considered better (then the other ones) when you do not have any unnecessary obligations (i.e no need to guard anything). From the theory of Tempo's it is simple to explain. After Be8+ your piece goes under two contacts (RxB and BxB). There are only one capture due to the Rook's pin. And when you play Be2+ your piece is only at only one contact (RxB), but it is no attacked (due to the pin).

    And it works in reverse too: if you want to complicate matters you have to created as many contacts as possible. This way your opponent's chances to go wrong rise exponentially. I am not sure when I have been reading the statement: "the more possible good looking moves, but bigger chances to go wrong - especially if there is only one correct way to continue". And in the case of tactics - they have to contain as many relationships as possible (contacts, captures, checks, themes and motifs combined/mixed, etc.).

    I hope my comments and short explanation may trigger discussion or maybe inspiration to all of us! :)


  4. Diagram 2

    There is a similar looking position, but some difference are important.

    1) The King and the Rook are one square away. It means the King can go to the Rook (and defend it!) in ONE move.
    2) There is only ONE coorect way to win the Bishop
    3) After 1.Bd7 Bxd7+ Black does not lose both pieces as the King defends the Bishop after Rook checks. It means Black has just lost the exchange.
    4) As the King and the Rook stands on white square there is a possible pin in the future (1.Bd7+ Ke4 and 1.Bd3+ Ke6)

    After 1.Bd3+ blacks plays Ke5 and white cannot win a piece... because the equal contacts have been restored (RxR twice and RxB twice).

    After 1.Bd7+ Kd5 2.Rxd5 Kxd5 3.Bxa4 white has won the black bishop... because the equal contacts have not been restored. Just have a look: 2.Rxd5+ Kxd5. Now it is White's move and even though the equal contacts are restored - White wins the (undefended) Bishop. It was possible because after 1.Bd7+ white has 4 contacts (RxR, RxB, BxB, BxK) and Black only 3 (RxR, RxB, BxB). It may be the reason why this move was a winning shot. Take notice that after 1.Bd3+ White maintains 3 contacts (RxR, RxB, BxK), but Black only 2 (RxR and RxB). I am not sure if your article says the same, but we are probably talking about the identical concepts.

  5. This is very interesting. When you come upon your insights, do you make a hypothesis before you solve certain problems, or do certain problems inspire your hypothesis? Or some other method? I enjoy reading your posts. Keep it up!

    1. When I analyze positions, I ask myself why I failed it, and what I need to see such things in the future. That is where the hypotheses start. Once formulated, I try to devise a scheme to solve the next problems, and evaluate that, mixed with some brutal and often painful honesty ;)

  6. I just realized something interesting regarding counting. I was viewing a video (link and FEN of the position below).

    How To Calculate Chess Tactics 5 Step Thinking Method Day 1

    [FEN: 3k4/1pr1r2p/p3R1p1/3p4/2qP1P2/6PQ/PP2R1K1/8 w - - 0 1]

    My first impression was to "look" at square e7, because there is a conflict there. Heisman's "B.A.D." (Barely Adequately Defended) piece" concept came to mind: the Black Rook on e7 is attacked by White two times (the two White Rooks), and defended by Black two times (the other Back Rook and the Black King). THAT'S COUNTING! Dr. Lasker's encircling motif ("the idea of superior force [COUNTING!] at a given point and that of immobility") then came to mind: how to gain superior force at e7 AND make the Black Rook immobile? The pin theme came to mind because of the geometrical motif [h4-d8], and with it, the first "interesting" move: 1. Qh4. By virtue of the threat to capture on e7 (White has at least a temporarily superior force attacking e7 [3:2] and the Black Rook cannot move), White has the initiative. The only defender available is the Black Queen, with only one defensive square available (b4), so, 1. ... Qb4. Counting again, that means if the Black Queen can be forced from b4, the Black Rook on e7 will fall. The Black Queen can be attacked with 2. a3, and after the Black Queen moves, White will win a Rook with 3. Rxe7.

    That sounds all nice and tidy (in a Kotovian sort of way) and obviously can be calculated. However, I didn't even try to "calculate" it step-by-step. It was just a series of quick thoughts, based on what I "saw" and what came (unbidden) into conscious awareness. Although it appears to be a logical sequence of thoughts, I didn't reason it out. The "insight" (counting on square e7) triggered the next thought in the sequence, followed by the next thought, etc. in rapid succession until I was already aware of the total "solution" before I realized it.

    That's when it struck me that "counting" could be a potential "shortcut" into subconscious knowledge. So, it changes (I hope!) how I "see" positions in the future.

    1. Counting tells something about the future of the position. It is a shortcut in the sense that it circumvents the necessity to calculate some things. I belief that even the counting can be done in a glance, just as how you count material in a new puzzle, even before the computer makes his move.

      I'm working on captures right now, and a lot can be seen in a glance once you know what to look for. It is about braking down seemingly complex move sequences into common trivialities. Somehow we must develop a sense for the initiative, since that is the glue that holds every combination together. Counting reveals how the initiative will progress. How it develops into the future.

  7. I concur with your observation regarding how quickly counting can be done. The material count takes almost no time at all; a quick count of the pieces and Pawns can almost be done in a glance. Other forms of counting also take almost no time. For instance, using the visual "square of the Pawn" rule for determining if a King can stop a passed Pawn is trivially adapted to "counting" how many moves to promotion. Since the geometry of the chessboard provides the same number of squares (points) on the diagonal as are on the rank and file (contra the Pythagorean theorem), it is (again) trivially easy to "count" the number of moves to promotion; the number can never be greater than 6. Even math-phobic people can count that high without difficulty.

    One of the things I saw recently (I forget now which book it was in) was that "chess skill" is not a single thing, but a collection of many mini-skills. ("Mini-skills" translates into "many skills.") Each little "shortcut" cuts down on the logical work required to "see" the essence of a position. That increases our overall skill level by allowing us to tackle (eventually) more complex and difficult positions without having to "load" the S-L--O---W logical step-by-step processor. How far we take that development determines our eventual skill ceiling.