Castlemate contest

All Things Chess
1

Definition 1. A player on the move is castlemated in case all of the following are true:

a. The player has a king which has never moved, and a rook which has never moved (nor been captured).
b. The player cannot presently castle legally.
c. The player has no legal moves except with king or that rook.

(In effect, the player is permanently prevented from castling even though he has never moved the king nor the rook.)

Definition 2. A player on the move is help-castlemated in N in case all of the following are true:

w. The player has a king which has never moved, and a rook which has never moved (nor been captured).
x. The player cannot presently castle legally.
y. There exists a sequence of N legal move-pairs during which the player never moves his king nor that rook, yet the player can never castle legally during these N moves.
z. After N moves, the player is castlemated.

(In effect, the two players are cooperating to try to prevent one of them from being castlemated, but the best they can do is N move-pairs before castlemate sets in.)

In the following example (white to move), white is help-castlemated in 2:

Contest: Find a position where white is help-castlemated in N. The winner is the person who does so for the largest N.

Prize: The winner gets to castlemate the runner-up N-M times in the public square. (M is the runner-up’s version of N.)

To avoid legalistic technicalities, please limit your entries to positions where white has only the one rook (or, if there is a second rook, it is no longer on its original square).

No “help-castlemates in infinity” allowed. That’s a separate, interesting question – does there exist a position where neither white’s king nor rook have moved, yet white can never castle, despite the best efforts of both players, even though the game can go on indefinitely with neither the king nor the rook being moved?

Bill Smythe

2

White Ke1, Pd2, Pf2, Rh1, Bc1

Black Pe2, Pf3, Pd3, Kany

White cannot castle through check and the black pawns trapping the white king cannot be taken except by the white rook (which would then eliminate white’s castling privileges).

3


an even simpler infinity castlemate

Black king can move for inifinity and so can the white bishop.

4

OK, enough of the infinity stuff. Does anybody have an entry into the help-castlemate-in-N contest?

Just to clarify:

If white’s king and rook have not moved, and there is a sequence of N move-pairs not involving white’s king nor this rook, but there is no such sequence of N+1, then the position is considered a help-castlemate in N.

Bill Smythe

5

Take the starting position
49 knight moves by each side
50) b3
49 knight moves by each side
99) … b6
48 knight moves by each side
148) Ba3 Ba6
149) e3
49 knight moves by each side
198) … e6
199) Be7 Be2

The bishops prevent either side from castling in either direction. Now there can be hundreds of moves before enough pieces are traded off to finally bring about a help-castle-mate (if you ignore the 50-move rule then N is unlimited, and it can exceed 3,000 if you pay attention to the 50-move rule).

6

That’s not what I meant. I am looking for a position where, even with both players cooperating, there exist at most N move-pairs before castlemate sets in. Clearly, there is no value of N which makes this work for the starting position (or for any other position reached in your example). 200) Bxe2 Bxe7 201) O-O O-O trivially cooks your example.

And, yes, we can ignore the 50-move rule, since it requires a claim. (It is legal not to claim a draw after 50 moves.)

Look at my original example. In that position, there exists a sequence of 2 move-pairs before castlemate sets in, but there is no sequence of 3. So in that position N=2.

Perhaps a clarification (or a better definition) is in order:

White is help-castlemated in N in case:

a. It is white’s move.

b. White has a king which has never moved, and a rook which has never moved (nor been captured).

c. There exists a sequence of N move-pairs during which white never moves his king nor his rook.

d. There does not exist a sequence of N+1 move-pairs during which white never moves his king nor his rook.

Bill Smythe

7

Am I correct in thinking that you are not looking for a HELP-castlemate, but rather a FORCED-castlemate?

8

Yes, I guess “forced” would be a better term than “help”. Maybe “unavoidable castlemate after N” would be best.

Bill Smythe

9

Then start with a basic position
White
Ke1, Rh1, Ph2
Black
Bg2, Pe2/f3/h3

Now you have seven pieces movable, but essentially frozen (the B can bounce between f1 and g2 but the e2/f3/h3 pawns trap it - f3 can free the bishop only at the cost of forcing a K-move).

Add white Pd2/d3/b2/b3, black Pd7/b7 and a K.
White has d4, d5, d6, d3, d4, d5, b4, b5, b6, b3, b4, b5 (12 moves). Then add white Pg3/g4 and black Pg7 to add g5, g6, g4, g5 (now 16 moves).

You can get the first 12 moves differently (h and f files instead of b and d) by
White Ke1, Ra1, Nb1, Pa3/c3/d2
Black Pa4/c4/d3/e2
Then
White Pf2/f3/h2/h3 Black Pf7/h7.
Adding white Pb4 and black Pb7 only adds two more moves, so putting a frozen knight in uses up too many pawns.

White Ke1, Ra1, Pb2/f2/f3/h2/h3, Black Pe2/d3/b3/f7/h7, Bc2 is a near mirror image of the first with an initial 12 moves.
Adding White Pa3/a4 and Black Pa7 also gets up to 16 moves. That leaves an available White Pd4 and Black Pd7 to allow d5 and d6 to get up to 18 white moves. So everything is wonderful except for one itty, bitty problem. The black B can go to a2 and its coverage of b1 would not prevent 0-0-0. That leaves 16 as the maximum I can see so far unless there are enough captures available to put a black P on a2. The e2 pawn can make two captures from the g-file. The d3 pawn is one capture from the e-file. The a2 pawn is two captures from the c-file. Those five captures could be five of white’s missing 6 pieces. White’s pawns require the pawns captures gh, ef, cb and ba, accounting for four of black’s missing 6 pieces (black also has an extra pawn available to be captured). That puts the count of 18 back in play.

10

White Ra1, Ke1, Ph2/h3/f2/f3/d2/d3/b2/b3
Black Kc6, Pb7/d7/f7/h7/e2

White b4, b5, b6 (then black Kxb6), d4, d5, d6 (then Kxd6), f4, f5, f6 (then Kxf6), h4, h5, h6 (then Kxh6 and Kg7), b3, b4, b5, b6, d3, d4, d5, d6, f3, f4, f5, f6, h3, h4, h5, h6 for 28 moves.

11

Yikes!! 28 moves – about 2 or 3 times as many as I would have thought possible. Let’s get this into a diagram, so that the lazier among us can easily see what’s happening:

To summarize: White has never moved his king nor rook, but cannot presently castle. The players (cooperating with each other) can play on for 28 moves, but white can never castle, and on the 29th move, the bubble bursts and white is forced to move his king or rook.

Congratulations, Jeff!

Bill Smythe

12

Cook: There does exist a sequence of 28+1 move-pairs from the diagram (actually infinity) during which White never moves his king nor his rook, before castle-mate sets in:

  1. h4 Kb5
  2. h5 Kb4
  3. h6 Kxb3
  4. h3 Kxb2
  5. h4 Kc2
  6. h5 b5
  7. f4 b4
  8. f5 b3
  9. f6 b2
  10. f3 b1=N!
  11. f4 Nc3!
  12. dxc3 Kb2
  13. c4 Kc2
  14. c5 Kd2
  15. c6 Kc2
  16. c7 Kd2
  17. c8=N

now White can move his new knight around for infinity and Black can move his King around for infinity, and White doesn’t have to castle.

13

But this is a help-castlemate: that there’s an alternative longer (“never”) solution doesn’t matter.

Oops, never mind. My head hurts.

14

During the past 24 hours I realized there is an even worse cook – one which allows white to castle:

For the first 12 moves, white pushes his f- and h-pawns. Meanwhile, black spends four moves capturing the b3 and b2 pawns, one move getting the king off the b-file, five moves promoting to a bishop on b1, and two moves maneuvering the bishop to e6. Then white captures the bishop, queens at e8, and captures at e2. Meanwhile, black moves his king back out of the way. Then white castles:

  1. f4 Kb5
  2. f5 Kb4
  3. f6 Kxb3
  4. f3 Kxb2
  5. f4 Kc2
  6. f5 b5
  7. h4 b4
  8. h5 b3
  9. h6 b2
  10. h3 b1=B
  11. h4 Ba2
  12. h5 Be6
  13. fxe6 Kb3
  14. e7 Kb4
  15. e8=Q Kb5
  16. Qxe2 Kb6
  17. O-O-O

Phooey.

Bill Smythe

15

So we freeze the black king and move a bishop:

Black Kh8, Bc2, Ph6, g7, a2 (from f7), b3, d3, e2, a7, c7
White Ra1, Ke1, Pb2, h7 (from f2), g6 (from e2), h2, h3 (from g2), c4 (from d2), c3, a3

White moves a4, a5, a6, c5, c6, c4, c5, h4, h5, h3, h4 (11 moves - the pawn on a2 is prevented from being on f6 and allowing the Pc4 to start at f2 and reach 13 moves)

or

Black Ka8, Bg2, Ph3, f3, e2, b7, g7, d7
White Ke1, Rh1, Ph2, a7, b6, g3, d2, b2, d3, g4

White moves b3, b4, b5, d4, d5, d6, d3, d4, d5, g5, g6, g4, g5 (13 moves)

or

Black Kh8, Bg2, Pg7, h3, f3, e2, d7, b7
White Ke1, Rh1, Ph2, h7 (two captures), g6 (two captures), d2, d3 (one capture), b2, b3 (one capture), g3

White moves b4, b5, b6, b3, b4, b5, d4, d5, d6, d3, d4, d5, g4, g5 (14 moves)

A different K-freeze is
Black Ka4, Bc2, Pa2, b3, b5, d3, e2, d7, f7, h7 (four captures)
White Ra1, Ke1, Ba3, Pb2, b4, d4, f2, f3, h2, h3 (three captures)

h4, h5, h6, h3, h4, h5, f4, f5, f6, f3, f4, f5, d5, d6 (14 moves) - it is possible to add a pawn to f4 or d5 but that does not increase the number of moves

or

Black Kh5, Bg2, Pe2, f3, h3, g4, g6, c7, a7, e7 (three captures)
White Ke1, Rh1, Bh4, Ph2, g3, g5, a2, a3, c2, c3, e3 (five captures)

White moves a4, a5, a6, a3, a4, a5, b4, b5, b6, b3, b4, b5, e4, e5, e6 (15 moves)

Note that in the latter two there were more pawns used to freeze the black king but that helped avoid pawns stacking up and blocking other moves.

16

For a different type of castlemate, the following was culled from ajschess.com/lifemasteraj/short_games.html

Edward Lasker - Sir George A. Thomas;

London, 1912

  1. d4, f5; 2. e4, f5xe4; 3. Nc3, Nf6; 4. Bg5, e6; 5. NxP/e4, Be7;

  2. BxN/f6, BxB/f6; 7. Nf3, 0-0; 8. Bd3, b6; 9. Ne5, Bb7; 10. Qh5, Qe7;

Ten very reasonable moves, and yet the game is over!

  1. QxP/h7+!!, KxQ/h7; [Forced] 12. NxB/f6+, Kh6;

12…Kh8; 13. Ng6#

  1. N/e5-g4+1, Kg5; 14. h4+, Kf4; 15. g3+, Kf3;

  2. Be2+, Kg2; 17. Rh2+, Kg1; 18. Kd2 Mate.
    (18. 0-0-0 mate! was also possible.)

17

I once directed a CCA tournament in Florida in which one of the games ended with black playing … O-O mate.

I saw the possibility coming about five moves before it happened, and started staring (discreetly, I hope) at the players’ scoresheets to make sure castling was still legal (in case an argument developed). I concluded that it was. Then, after black executed the mate, white responded, “Huh?? That’s still legal?”, but quickly realized it was.

White’s king had been driven up to f6. … Rf8 alone would not have been mate, because then white could play Kg7.

Bill Smythe