Diagram 1. White to move |

[solution]

**Encircling**

c2 type of immobility: lack of time

b6 type of immobility: function

**Geometry**

c1 - c8

**Function**

c7 protects c2, e7

b6 protects c7

e7 protects d5

**Error**

Taking the juicy queen b6 in stead of the meager looking rook on c2

Not firing cue 1: zwischen check Rxc1+

Not firing cue 2: black queen has no safe place to protect c7

PART I:

ReplyDeleteDid you find a complete copy of

? I only ask because theLasker's Manual of Chessdesperadoandattackmotifs are discussed after thefunctionmotif, and you indicated that you had only found a partial copy of the book online.In any event, here are the beginning two positions used for introducing the

functionmotif. [I translated from descriptive to algebraic notation, so if there is an error, it’s my fault.]Third Book. The Combination.Diagram 14:FEN: 8/8/8/1PkN4/1p6/8/8/1K6 w - - 0 1

14.—This motif is of frequent occurrence in end games where a passed pawn is used to protect distant pieces or pawns.

The Knight cannot protect the Pawn by 1. Nc3 or 1. Nc7 for long, but the Pawn can protect the Knight by 1. b6. For, if 1. ... KxNd5 2. b7 and Queens next move. Therefore Pawn and Knight do protect each other allowing the White King to approach the Black Pawn to capture it and then decide the battle.

This illustrates a motif of GREAT IMPORTANCE — the motif of "

FUNCTION." [Emphasis added.] The power, the domain of force of a piece is DECREASED as soon as that piece has a certain task to do, as, for instance, in above position the power of the Knight is decreased by its having to watch the passed Pawn. A task or a multitude of tasks, such as, for instance, to obstruct a Rook or to parry the threat of mate, if to be done by a certain piece, may be called the "function" of that piece, an expression borrowed from Biology. By studying the various functions of the hostile pieces and the effects these functions have of impeding those pieces we discern new motifs for combinations.Diagram 15:

FEN: 4rrk1/pp1q1pp1/3p2np/3N4/2P5/1P6/P2Q1PPP/R4RK1 w - - 0 1

15.—Black’s Pawn on g7 has the task of guarding the Pawn h6 as well as the forking check [by Nd5] threatened on f6. Therefore, White wins an important Pawn by 1. Qxh6. The Black g6 Pawn cannot successfully perform both his tasks.PART II:

ReplyDeleteHere is where I often get in trouble when trying to “solve” problems (as well as play games). I “saw” the Knight fork, picking up a Pawn BUT also “saw” trouble brewing for the White Knight AFTER the sequence ended. After 1. Qxh6 gxh6 2. Nf6+ Kg7 3. Nxd7 Rg8!, I realized that White is going to have a problem getting his Knight back out safely. For Lasker’s purpose of illustrating the concept of

function, there is no need to look beyond that goal. (We also cannot fault mister Lasker for NOT using a computer to check the final position.) This kind of “intuition” (if that is what it is?) is what gives me fits while trying to QUICKLY solve problems!I couldn’t see a way to rescue the Knight. So, I put the position into Stockfish and let it run for a while. Here are the results, which justifies my uneasiness about that position.

FEN: 4r1r1/pp1N1pk1/3p2np/8/2P5/1P6/P4PPP/R4RK1 w - - 0 1

Analysis by Stockfish DD 64 SSE4.2:

1. -+ (-1.61): 4.Rfd1 Re7 5.Nf6 Kxf6 6.Rxd6+ Re6 7.Rd7 Rge8 8.Kf1 R8e7 9.Rd2 h5 10.Rad1 h4 11.g3 Ne5 12.Kg2 hxg3 13.hxg3 Nc6 14.Kf3 Kg5 15.Kg2 Re4 16.Rd5+ f5 17.R1d2 Re2 18.Rxe2 Rxe2 19.Rd7

2. -+ (-1.67): 4.Rad1 Re7 5.Rxd6 Rd8 6.Rfd1 Nf8 7.Kf1 Rexd7 8.Rxd7 Rxd7 9.Rxd7 Nxd7 10.Ke2 f5 11.Ke3 Kf6 12.Kd4 Ke6 13.h3 Ne5 14.c5 Nc6+ 15.Kc4 Ke5 16.b4 Nd4 17.a4 h5 18.b5 Ke4

3. -+ (-2.00): 4.f4 Rd8 5.f5 Nh8 6.Nb8 Rxb8 7.Rad1 Rbd8 8.Rd3 Rge8 9.Rfd1 Re2 10.a4 Rb2 11.a5 Re8 12.a6 bxa6 13.Rg3+ Kf6 14.Rxd6+ Kxf5 15.Rf3+ Kg5 16.Rg3+ Kf4 17.Rf3+ Ke4 18.Rxh6 Rg8 19.Rh4+ Ke5 20.Rh5+ Ke6 21.Re3+ Kd6 22.g3 Ng6 23.Rd5+ Kc6 24.Rf3

4. -+ (-2.36): 4.g3 Re7 5.Nb6 axb6 6.f4 Re2 7.Rf2 Rxf2 8.Kxf2 Rd8 9.Rd1 Ne7 10.g4 d5 11.Rd4 Kf6 12.Kf3 Ke6 13.g5 Ra8 14.cxd5+ Nxd5 15.a4 hxg5 16.fxg5 Rc8

5. -+ (-2.54): 4.h3 Rd8 5.Rfd1 Rxd7 6.Rd4 f5 7.Kh2 Rgd8 8.Rad1 Ne7 9.Kg3 d5 10.Kf3 Rd6 11.g3 Kf6 12.Kg2 R6d7 13.g4 b6 14.Kg3 h5 15.gxh5 Kg5

6. -+ (-2.56): 4.Nb6 axb6 5.Rfd1 Re6 6.g3 Ne7 7.Rd4 Rc8 8.Rad1 d5 9.cxd5 Rd6 10.Kg2 Rc5 11.Kf3 Rdxd5 12.R1d2 Kf6 13.Rf4+ Ke6 14.Rxd5 Rxd5 15.Rb4 Rf5+ 16.Ke2 Re5+ 17.Kd3 b5 18.a4 Rd5+ 19.Kc3 bxa4

7. -+ (-2.56): 4.f3 Rd8 5.Nb6 axb6 6.Rfd1 d5 7.cxd5 Rd6 8.Rac1 Nf4 9.Rc7 Kf6 10.Rc4 Nxd5 11.Rcd4 Rgd8 12.a4 Kg6 13.Kf2 f5 14.Re1 Nf6 15.Rxd6 Rxd6 16.Re7 Rd2+ 17.Re2 Rxe2+ 18.Kxe2 Nd5

8. -+ (-2.62): 4.a4 Rd8 5.Nb6 axb6 6.Rfd1 d5 7.cxd5 Rd7 8.Rd2 Rgd8 9.Rad1 Rd6 10.g3 Ne7 11.Kg2 Rxd5 12.Rxd5 Rxd5 13.Rxd5 Nxd5 14.Kf3 f5 15.Ke2 Kf6 16.Kd3 Ke5 17.f4+ Ke6 18.h3 h5 19.Kc4

9. -+ (-2.62): 4.a3 Rd8 5.Rfd1 Rxd7 6.Rd4 Re8 7.Kf1 d5 8.Rad1 Red8 9.R1d2 Ne7 10.h3 Kf6 11.Rf4+ Kg6 12.Rfd4 f5 13.g3 Kf6 14.Kg2 h5 15.f4 b6 16.Rd1 Ke6 17.Re1+ Kf7 18.Red1 Ke8 19.Re1 dxc4

10. -+ (-2.74): 4.Rac1 Re7 5.Rfd1 Rxd7 6.Rd4 Rgd8 7.Rcd1 Ne7 8.g3 d5 9.Kg2 Nf5 10.Rxd5 Rxd5 11.cxd5 Ne7 12.d6 Nc8 13.Kf3 Rxd6 14.Rc1 Nb6 15.Rc5 Nd5 16.h4 b6 17.Rc8 Rd7 18.Rc4 Nf6

11. -+ (-2.74): 4.Rfc1 Re7 5.Nb6 axb6 6.Rd1 Rd8 7.Rd2 d5 8.cxd5 Red7 9.Rad1 Rd6 10.g3 Ne7 11.Kf1 Nxd5 12.Kg1 f5 13.a4 R6d7 14.Re1 Kf6 15.Red1 Kg5 16.Rd4 Nf6 17.h4+ Kg6 18.Rxd7 Rxd7 19.Rxd7 Nxd7

(Coble, Asheboro, NC 22.12.2016)

I'm

NOTclaiming anything regarding mister Lasker's oversight(?). I'm sure that he chose the position (or created it) solely to illustrate a concept. It does, however, highlight the problem(s) I often have while solving. I look at the end position, and have an uneasy feeling that "it ain't over until the fat lady sings," and the fat lady ain't singing. So, I then go back to the beginning, trying to find out what I missed - and I lose points on the timed problems.I have a full copy.

ReplyDeleteI had the same feeling about the trapped knight. The difference is, that I don't bother. When I have understand the idea that Lasker tries to bring across, I'm satisfied. The rest is redundant. I said it a few times, I would rather have positions without kings when I try to explain a point. Since positions are distracting people from the essence.