5

I'm interested in chess patterns similar to the windmill. If you think there are none more than the ones that I'm listing I'm interested in a proof that satisfies me to stop looking for more of them. Wikipedia gives this definition for a windmill:

In chess, a windmill is a tactic in which a combination of discovered checks and regular checks, usually by a rook and a bishop, can win massive amounts of material. This tactic is also sometimes referred to as a see-saw.

I know two windmills. First the one in the "game of the century" between Fisher and Byrne (moves between 18 and 23 black does a windmill), it involves a bishop and a knight (also a rook, but it's not essential. For example see this game for a windmill knight-bishop without white rook.

[FEN "K7/8/8/2B5/4N3/7q/6pp/3r1b1k w - - 0 9"]

9.Nf2+ Kg1 10.Nxh3+ Kh1 11.Nf2+ Kg1 12.Nxd1+ Kh1 13.Nf2+ Kg1 14.Ne4+ Kh1 15.Nf2+ Kg1 16.Ng4+ Kh1 *

This can also be seen as a royal fork constantly attacking the black king, but windmill contains and "mechanic" that allows the knight to do whatever it wants but black is still restricted to move his king back and forth.

A second example is this article.

The other type of windmill is of this game. Starts at move 26, white does a windmill this time with rook and a bishop.

I want to know if you can share more types of windmills with me. I realized you can substitute the bishop that remains still in both tecniques (B+R & B+N) with a queen carrying out the same function. So I have 4 types. Do you know similar positions?

PD: I realized also that if I change the bishop for a queen that allows sometimes checkmate, for example smothered checkmate can be seen as a windmill with the queen.

  • It's better not to involve the queen to begin with in these, as its role in any "windmill" will be the stationary piece. Then it's easier to classify. The windmill needs either a bishop or a rook as a stationary piece. Then we will need an additional moving piece. This moving piece can either be a rook, bishop or a knight. It should be possible to create a windmill for every possible combination of stationary and moving piece, except bishop+bishop. – Scounged Jul 1 '16 at 1:16
  • Taking the rook is redundant since white cannot win any way, may as well just repeat moves with the double check – M.M Jul 1 '16 at 4:44
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    @M.M whether there is a win in the concrete example given is completely irrelevant. The question is concerned with the motif itself, which is that the moving piece can take material without being met with any resistance. – Scounged Jul 1 '16 at 7:09
  • (and as it happens there is a win, 12 Ne4+ and Ng3#) – Noam D. Elkies Aug 30 '16 at 22:19
  • Q+R & R+R are also impossible where the discovered check is along a rank or file. – Rosie F Aug 31 '16 at 18:14
5

Yet more possibilities . . .

: Two-way windmill, with either Rook or Bishop as the front piece; e.g. with a Rook:

5n2/3bb2k/6pp/4B1pr/8/8/8/5RK1 w - - 0 0

1. Rf7+ Kg8
2. Rg7+ Kh8
3. Rxe7+ Kg8
4. Rg7+ Kh8
5. Rxd7+ Kg8
6. Rg7+ Kh8
7. Rxg6+ Kh7
8. Rg7+ Kh8
9. Rxg5+ Kh7
10. Rxh5

(it's important to capture g5 last, else Black has Rh5xe5)

: Windmill against a piece other than a King:

5kr1/6pp/8/4N1p1/6p1/6P1/6BP/6K1 w - - 0 0

1. Bd5! Rh8 
2. Nf7! Rg8 
3. Nxg5 Rh8 
4. Nf7 Rg8 
5. Ne5 Rh8 
6. Nxg4

(with better winning chances than the immediate 1 Nxg4)

: That means that even the King can be the front piece of a windmill of sorts against a Knight:

8/8/1n1p1p2/3K1k2/8/1P6/6B1/8 w - - 0 0

1. Kc6! Na8
2. Kxd6 Nb6
3. Kc7

(or first 3. Bb7 and then 4. Kc7(c6); if 1...Nc8 then 2 Bh3+ wins.)

3

An example where the Bishop is the windmill piece.


[fen "7R/kr4P1/5P2/4P3/3P4/b1P5/P1PP4/K2R4 b - - 0 0"]

1...Bb2+ 2. Kb1 Bxc3+ 3. Kc1 Bb2+ 4. Kb1 Bxd4+ 5. Kc1 Bb2+ 6. Kb1 Bxe5+ 7. Kc1 Bb2+ 8. Kb1 Bxf6+ 9. Kc1 Bb2+ 10. Kb1 Bxg7+ 11. Kc1 Bb2+ 12. Kb1 Bxh8+

Since the requirement is that the windmill and the discovered piece move differently that is two with Bishop, four with Knight, and two with Rook as the windmill piece, for a total of 8 types of windmill attacks.

EDIT: Inserting windmill position with Rook and Knight.



[FEN "5rk1/R7/6N1/4p3/5p1p/8/8/K5R1 w - - 0 1"]

1. Nxh4+ Kh8 2. Ng6+ Kg8 3. Nxf4+ Kh8 4. Ng6+ Kg8 5. Nxe5+ Kh8 6. Ng6+ Kg8 7.
Nxf8+ *

  • 1
    This answer is a bit confusing to me. Could you give two distinct types of different windmills with the bishop being the moving piece? I doubt it's possible if we don't differentiate between light-squared and dark-squared bishops. I get four distinct patterns: R+B, B+R, R+N, B+N, where the first mentioned piece in each pattern is the stationary piece in the windmill, and the second piece is the moving piece. I cannot see any more combinations than this. Note that I do not consider Q+B to be distinct from R+B. – Scounged Jul 1 '16 at 7:15
  • You definitely can't use a knight as the stationary piece, which I think is where the overcounting occurred. Either that, or the queen was counted twice, once orthogonally, and once diagonally, which as you point out, should not be considered distinct from the rook and the bishop respectively. – Jivan Scarano Jul 1 '16 at 9:01
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    List better the windmills more explained and I will accept the answer. I can't accept like this is confusing. – Santropedro Jul 1 '16 at 16:51
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    Give examples of the windmills like the one you did. You will realize it's not so easy with knight and rook. – Santropedro Jul 1 '16 at 17:00
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    I did count the checking piece being different as a different windmill, therefore my count is twice yours. – Mike Jones Jul 2 '16 at 8:35
2

I do not have to time to create a diagram of every type, but it seems intuitive to me that it would be possible to contrive a windmill from any pair of (non-pawn) pieces where:

  • The stationary piece is a slider
  • The moving piece is any other type of piece not capable of attacking along the axis at which the stationary piece will give check
0

Here’s a complete list just for reference.

Windmill (Or In German: Zwickmühle): A series of attacks and discovered attacks with two pieces that is used on a piece, most often the King to gain material.

Two Points On How They Work:

  1. The stationary piece is one with infinite range. It will be a bishop, rook, or a queen.

  2. The moving piece does not attack along the same direction as the stationary piece. This means that a vertical/horizontal stationary would have a diagonal mover, and a vertical/horizontal stationary has a vertical mover. However, kings and knights can be used for both horizontal/vertical and stationary pieces.

There are two categories-one for horizontal/vertical and one for diagonal stationary pieces. The moving piece will be listed first, and then the stationary piece for each example listed. I am showing already known compositions, and they are all winning examples. While drawing problems do exist, these generally show the concept better.

Horizontal/Vertical Stationary Pieces-

Bishop+Rook/Queen

[Title "Alfred O. Karlström (6081), The Swallow, 02/1940"]
[FEN "k2K2n1/Bp6/1p6/1pp5/R2p4/4p3/5p2/6b1 w - - 0 1"]

1. Ra2 Bh2 2. Bxb6+ Kb8 3. Ba7+ Ka8 4. Bxc5+ Kb8 5. Ba7+ Ka8 6. Bxd4+ Kb8 7.  Ba7+ Ka8 8. Bxe3+ Kb8 9. Ba7+ Ka8 10. Bxf2+ Kb8 11. Ba7+ Ka8 12. Bg1+ Kb8 13.  Bxh2#

Source: German Wikipedia

I’ll give a bishop/queen example though just for fun.

[FEN "4r1k1/5p2/R5BQ/5p2/4p3/3n4/b1n5/br6 w - - 0 1"]

1. Bh7+ Kh8 2. Bxf5+ Kg8 3. Bh7+ Kh8 4. Bxe4+ Kg8 5. Bh7+ Kh8 6. Bxd3+ Kg8 7.  Bh7+ Kh8 8. Bxc2+ Kg8 9. Bh7+ Kh8 10. Bxb1+ Kg8 11. Rg6+ fxg6 12. Bxa2+ Re6 13. Bxe6#

Source: Aron Nimzowitsch, My System

Knight+Rook/Queen-From Mike Jone’s Wonderful Answer

[FEN "5rk1/R7/6N1/4p3/5p1p/8/8/K5R1 w - - 0 1"]

1. Nxh4+ Kh8 2. Ng6+ Kg8 3. Nxf4+ Kh8 4. Ng6+ Kg8 5. Nxe5+ Kh8 6. Ng6+ Kg8 7. Nxf8+

Here's an extension of that matrix.

[FEN "3rk2K/1NpR2p1/4N2B/2p2pp1/B2p1p2/8/8/4R3 w - - 0 1"]

1. Nexd8+ Kf8 2. Ne6+ Ke8 3. Nxc7+ Kf8 4. Ne6+ Ke8 5. Nexc5+ Kf8 6. Ne6+ Ke8 7. Nxd4+ Kf8 8. Ne6+ Ke8 9. Nxf4+ Kf8 10. Ne6+ Ke8 11. Nxg5+ Kf8 12. Ne6+ Ke8 13. Nxg7+ Kf8 14. Nxf5#

Diagonal Stationary Pieces-

Rook+Bishop/Queen

This one takes the concept of a rook and biship windmill to it absolute limit. Yes it is an illegal position, but it greatly shows the power of the windmill.

[Title "Josef Krejcik,, Pages 41-42 Of The February 1925 Wiener Schachzeitung"]
[FEN "5nk1/nbnbnbrR/6bn/6n1/6b1/2B3n1/1K4b1/r5n1 w KQkq - 0 1"]

1. Rxg7+ Kh8 2. Rxf7+ Kg8 3. Rg7+ Kh8 4. Rxe7+ Kg8 5. Rg7+ Kh8 6. Rxd7+ Kg8 7.  Rg7+ Kh8 8. Rxc7+ Kg8 9. Rg7+ Kh8 10. Rxb7+ Kg8 11. Rg7+ Kh8 12. Rxa7+ Kg8 13.  Rg7+ Kh8 14. Rxg6+ Kh7 15. Rg7+ Kh8 16. Rxg5+ Kh7 17. Rg7+ Kh8 18. Rxg4+ Kh7 19.  Rg7+ Kh8 20. Rxg3+ Kh7 21. Rg7+ Kh8 22. Rxg2+ Kh7 23. Rg7+ Kh8 24. Rxg1+ Kh7 25. Rg7+ Kh8 26. Kxa1 Nh7 27. Rg6+ Nf6 28. Rxh6+ Kg7 29. Rxf6

Source: Edward Winter’s Chess Notes

Knight+Bishop/Queen

[Title "Mate In 29, M. Kwiatkowski, 1992"]
[FEN "3n4/rBp1p3/2P5/2PK4/k2N4/pp2R3/bppB2Rp/q1n1r1b1 w - - 0 1"]
[startply "12"]

1. Rg4 h1=Q+ 2. Nf3+ Kb5 3. Rb4+ Ka5 4. Rbe4+ Kb5 5. Nd4+ Ka4 6. Ne2+ Kb5 7. Nc3+ Ka5 8. Nxa2+ Kb5 9. Nc3+ Ka5 10. Ne2+ Kb5 11. Nd4+ Ka4 12. Nf3+ Kb5 13. Rb4+ Ka5 14. Rbxb3+ Ka4 15. Rb4+ Ka5 16. Rbe4+ Kb5 17. Nd4+ Ka4 18. Ne2+ Kb5 19. Nc3+ Ka5 20. Na2+ Kb5 21. Ba6+ Rxa6 22. Nc3+ Ka5 23. Ne2+ Kb5 24. Nd4+ Ka4 25. Nf3+ Kb5 26. Rb4+ Ka5 27. Rb6+ Ka4 28. Rxa6+ Kb5 29. Ra5#

Source: Tim Krabbe's Wonderful Site

King+Bishop/Queen-From Professor Noam D. Elkies Thoughtful Answer

[FEN "8/8/1n1p1p2/3K1k2/8/1P6/6B1/8 w - - 0 0"]

1. Kc6! Na8 2. Kxd6 Nb6 3. Kc7
  • 5
    Note that you've been using a more liberal interpretation of the motif than other users; for instance you are the only one using several pieces for the role of stationary piece in the windmill combination. Also, I think that your example with B+B(+B) is not something that would normally be considered a windmill at all, since it involves no discovered attacks whatsoever. – Scounged Jun 6 at 23:23
  • @Scounged I have fixed my answer accordingly. – Rewan Demontay Nov 11 at 21:21

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