**One attacker, one target.**

- Attacker
- Road to attacking square
- Attacking square
- Road to target square
- Target square
- Road from target to target square
- Target

- Is the attacker already on the attacking square?
- Is the road to the attacking square blocked?
- Can the attacker reach the attacking square with tempo?
- Is the attacking square free from defense?
- Is the road from attacking square to target square blocked?
- Is the target square free from defense?
- Is the target already on the target square?
- Is the road from the target to the target square free?
- Can I force the target towards the target square?

With a duplo attack the scheme gets more complicated.

**One attacker, two targets.**

- Attacker
- Road to attacking square
- Attacking square
- Road to target square 1
- Target square 1
- Road from target to target square 1
- Target 1
- Road to target square 2
- Target square 2
- Road from target to target square 2
- Target 2

**Two attackers, two targets**

- Attacker 1
- Road to attacking square 1
- Attacking square 1
- Road to target square 1
- Target square 1
- Road from target to target square 1
- Target 1
- Attacker 2
- Road to target square 2
- Target square 2
- Road from target to target square 2
- Target 2

- PoP
- LoA
- Fun

**PoP**

In the passed week, I had analyzed six positions, and every position has showed 1-3 PoPs. I think it is a safe bet to assume that there always will be at least one PoP in any tactical problem. Theoretically I can design a tactical combination with no Pops, but I don't think that has a practical value, since the chance that you encounter such combination in practice will be very slim.

I associate a PoP with a piece. That piece can be a target or a defender (a piece with a function)

**LoA**

As with PoPs, I probably can design a combination without any straight LoA. Strictly speaking, Lasker says nowhere that a geometrical motif means a straight line of attack. But in practice, that is where you look for. But then again, such combination without any straight LoA would be extremely rare in practice. For now, I simply ignore those. Every position had 1-4 LoAs.

**Fun**

Pieces don't have necessarily functions. So a combination without any defending piece isn't necessarily rare. Yet beyond a certain complexity, you will not found combinations where no piece fulfills a function. Analyzing the functions is crucial to interpret what is going on. PoP and LoA are just identification methods of targets and roads, function describes the alteration of a piece. Unseen limitations of pieces.

I like the way you have distilled the essence of mister Lasker's motif concept into PoP, LoA, and Fun! It provides a usable shorthand that is easy to remember as a mnemonic. A solution [PoP]s into "sight," we laugh over the attack [LoA] we have "seen," and it's [Fun] to play this way! "Cue" the victory trumpets!

ReplyDeleteI provide the very first position from

by Emmanuel Neiman. (Idle curiosity: I wonder if he was named for Emanuel Lasker?!?)Tune Your Chess Tactics Antenna - Know when (and where!) to look for winning combinationsTry to solve it using the PoP, LoA, and Fun concepts. Keep track of how much time it takes.

FEN: k7/8/P1N5/8/2K5/6p1/5bB1/8 w - - 0 65

This is the ending of Lingnau, Carsten vs. Orso, Miklos, Budapest 1992 (4). The diagram in the book states "White to play and win". Good luck with THAT!

"In the actual game White was unable to win, and had to be content with a draw after:

65. Kd5 Bg1 66. Ke6 Bf2 67. Kd7 Bg1 68. Kc8 Be3 69. Na5+ Ka7 70. Bb7 g2 1/2-1/2

"White was not advised that there was a forced win, so he just continued in the 'logical' way, bringing his king toward the enemy monarch."

What did White NOT "

"?see(BTW, the author gave the position to GM Anatoly Vaisser to solve. It took him less than two seconds to determine the correct line of play. I speculate that he did

NOTuse the method of concrete calculations using logical thinking.)Well, I thought I posted a comment on this entry, but (apparently) it went into the ether. So, I'll try again. If the original shows up, I'll delete one of them.

ReplyDeleteThe value of

Pop,LoAandFuncan be readily "seen" in the following position. It is the first position in Emmanuel Neiman's book.Tune Your Chess Tactics Antenna: Know when (and where!) to look for winning combinationsNote the final result of the game below. Can you do better than a 2400+ Master?!? Can you do close to GM Anatoly Vaisser, who solved the position in

1-2 SECONDS?!?FEN: k7/8/P1N5/8/2K5/6p1/5bB1/8 w - - 0 65

PGN:

[Event "Budapest"]

[Site "Budapest"]

[Round "4"]

[Date "1992.??.??"]

[White "Lingnau, Carsten"]

[Black "Orso, Miklos"]

[Result "1/2-1/2"]

1.d4 Nf6 2.c4 e6 3.Nf3 c5 4.d5 d6 5.Nc3 g6 6.e4 Bg7 7.h3 O-O 8.Bd3 e5 9.Bg5 h6 10.Be3 Kh7 11.g4 Ng8 12.h4 Bxg4 13.Ng5+ Qxg5 14.hxg5 Bxd1 15.Rxd1 a6 16.Rb1 Nd7 17.b4 cxb4 18.Rxb4 Rfb8 19.Ke2 b6 20.Rhb1 hxg5 21.Bxb6 Nxb6 22.Rxb6 Rxb6 23.Rxb6 Bf8 24.c5 dxc5 25.Bxa6 Kg7 26.a4 Nf6 27.Bb7 Ra7 28.Bc6 c4 29.f3 g4 30.fxg4 Nxg4 31.Bb5 f5 32.Rc6 Nf6 33.d6 Ne8 34.Ra6 Rxa6 35.d7 Re6 36.dxe8=Q Rxe8 37.Bxe8 Bb4 38.Nd5 Ba5 39.Ne3 c3 40.Kd3 fxe4+ 41.Kxe4 Kf6 42.Kd3 g5 43.Bh5 Ke7 44.Bf3 Ke6 45.Be4 Bb6 46.Nd5 Ba5 47.Nxc3 g4 48.Nd5 g3 49.Kc4 Kd6 50.Kb5 Be1 51.Nb4 Bf2 52.a5 Kc7 53.Nd3 Bd4 54.Nc5 Kd6 55.Na4 Kc7 56.Nc5 Kd6 57.Nd3 Kc7 58.Nb4 Bf2 59.Nc6 Kb7 60.Nxe5+ Ka7 61.Nc6+ Kb7 62.Bg2 Bg1 63.a6+ Ka8 64.Kc4 Bf2 65.Kd5 Bg1 66.Ke6 Bf2 67.Kd7 Bg1 68.Kc8 Be3 69.Na5+ Ka7 70.Bb7 g2 1/2-1/2

Interesting experiment: Stockfish took

ReplyDelete47 secondsto return the winning line of play! If a grandmaster can "see" the solution in 1-2 seconds, then there MUST be some process other than brute force calculation going on in the grandmaster's "chess module"! This gives credibility to the current approach, because it facilitates QUICK "sight" of the direction of the proper line of play. Of course, (in most real situations), there is still hard work to be done.“

The beginning is the most important part of the work.”― Plato, The Republic

There are some kinds of positions you simply KNOW the best move (or a plan that your opponent cannot refute nor stop). This position is extremally easy if you know what idea you are looking for. Some authors uses the term "dream position". I hope you know what I mean ;) :)

DeleteIt certainly would be a "dream position" in an ending to have immobilized the opponent's King with it on the same color square as the only remaining Bishop! "Always check: it might be MATE!" ;-)

DeleteAnother interesting position to apply Pop, LoA, and Fun:

ReplyDeleteFEN: r1b1k2r/pp3ppp/2n5/qB1Nn3/5B2/8/PP3PPP/R2QK2R w KQkq - 2 13

[Event "2016 Summer Marathon"]

[Site "https://lichess.org/XVxAs2nk"]

[Date "2016.08.06"]

[White "destran"]

[Black "BackaPalanka"]

[Result "1-0"]

[WhiteElo "2081"]

[BlackElo "1985"]

[PlyCount "63"]

[Variant "Standard"]

[TimeControl "300+0"]

[ECO "B10"]

[Opening "Caro-Kann Defense"]

[Termination "Normal"]

[Annotator "lichess.org"]

1. e4 c6 { B10 Caro-Kann Defense } 2. Nf3 d5 3. exd5 cxd5 4. d4 Nf6 5. c4 e6 6. Nc3 Nc6 7. Bf4 Bd6 8. Ne5? { (0.36 → -0.65) Mistake. Best move was Bxd6. } (8. Bxd6 Qxd6 9. c5 Qc7 10. Bb5 Bd7 11. O-O O-O 12. a3 b6 13. b4 Rfb8 14. Bxc6 Bxc6) 8... Bxe5? { (-0.65 → 0.66) Mistake. Best move was Qb6. } (8... Qb6) 9. dxe5 Nd7?! { (0.59 → 1.18) Inaccuracy. Best move was Ne4. } (9... Ne4 10. Nxe4 dxe4 11. Qxd8+ Kxd8 12. O-O-O+ Kc7 13. Be2 b6 14. Rd6 Bb7 15. Rhd1 Rad8 16. Kc2) 10. cxd5 exd5 11. Nxd5? { (1.27 → -0.06) Mistake. Best move was Qxd5. } (11. Qxd5) 11... Ndxe5 12. Bb5 Qa5+?? { (-0.06 → 3.41) Blunder. Best move was O-O. } (12... O-O 13. Bxc6 Nxc6 14. O-O Be6 15. Nc7 Qf6 16. Nxe6 Qxe6 17. Re1 Qf6 18. Be3 Qxb2 19. Rb1) 13. Nc3?? { (3.41 → 0.00) Blunder. Best move was b4. } (13. b4 Qd8 14. Bxe5 O-O 15. Bc7 Qg5 16. O-O Bh3 17. Qf3 Nxb4 18. Nxb4 Qxb5 19. Qxh3 Qxb4) 13... O-O 14. O-O Be6 15. Re1 Nc4 16. Rxe6? { (0.49 → -1.11) Mistake. Best move was Bxc6. } (16. Bxc6 bxc6 17. Qc1 Rad8 18. Ne4 Rd4 19. b3 Qf5 20. f3 Ne5 21. Bxe5 Qxe5 22. Qc5 Qxc5) 16... fxe6 17. Bxc4 Rxf4 18. Bxe6+ Kh8 19. Qd2?! { (-1.21 → -1.82) Inaccuracy. Best move was Bb3. } (19. Bb3 Re8) 19... Raf8 20. f3 Qc5+ 21. Qf2 Qxf2+ 22. Kxf2 Nd4? { (-1.88 → -0.78) Mistake. Best move was Rd4. } (22... Rd4 23. b3 Rd2+ 24. Kg1 Rfd8 25. Rb1 Nd4 26. Bc4 Nf5 27. Re1 Rc2 28. Ne4 Rxa2 29. Ng5) 23. Bc4? { (-0.78 → -2.39) Mistake. Best move was Bd5. } (23. Bd5 Nc2 24. Rd1 Rd4 25. Rxd4 Nxd4 26. g4 g6 27. Be4 Kg7 28. Ke3 Nc6 29. f4 Re8) 23... Nc2? { (-2.39 → -1.23) Mistake. Best move was Nxf3. } (23... Nxf3 24. gxf3 Rxc4 25. Rd1 Rc7 26. Rd2 g6 27. Nb5 Rcf7 28. Rd3 b6 29. Kg3 Kg7 30. Nd6) 24. Rc1 Rxc4 25. Rxc2 b5 26. Re2 b4 27. Nd5 Rd4 28. Nc7 a5? { (-1.35 → 1.51) Mistake. Best move was Rc8. } (28... Rc8) 29. Ne6 Rdf4?? { (1.52 → 5.71) Blunder. Best move was Rdd8. } (29... Rdd8 30. Nxf8) 30. Nxf4 g5?! { (5.43 → 6.35) Inaccuracy. Best move was Kg8. } (30... Kg8 31. Nd5) 31. Ne6 Re8?! { (6.20 → 6.93) Inaccuracy. Best move was Rf5. } (31... Rf5 32. Ke3) 32. Nxg5 { Black resigns } 1-0