[Retros] Mirror Chess

[Francois Labelle]

Hi all,

Here's an interesting chess variant:

Mirror Chess: Black's play is always the mirror image of White (White 
must either mate or play such that Black can mirror the move).

I learned about it from the integer sequence http://oeis.org/A136257 
(which I extended).

It's similar to one-sided chess in the sense that White dictates the 
entire game. It's different because White can prepare a mate by working 
on both sides.

With my computer I found examples of the quickest Mirror Chess mates by 
playing a specific piece:

Mate by queen:
(3.5): 1. c4 c5 2. Qa4 Qa5 3. Qc6 Qc3 4. Qxc8#

Mate by knight:
(5.5): 1. Nc3 Nc6 2. e3 e6 3. Qg4 Qg5 4. Nd5 Nd4 5. Qh4 Qh5 6. Nxc7#

Mate by rook:
(5.5): 1. Nh3 Nh6 2. Ng5 Ng4 3. Nxh7 Nxh2 4. Nxf8 Nxf1 5. Kxf1 Kxf8 6. Rxh8#

Mate by bishop:
(6.5): 1. b3 b6 2. Bb2 Bb7 3. Bxg7 Bxg2 4. e3 e6 5. Be2 Be7 6. f4 f5 7. Bh5#

Mate by pawn:
(6.5): 1. Nh3 Nh6 2. f4 f5 3. g4 g5 4. gxf5 gxf4 5. Ng5 Ng4 6. f6 f3 7. f7#

Mate by king:
(8.5): 1. d3 d6 2. Kd2 Kd7 3. Kc3 Kc6 4. Kb3 Kb6 5. Ka3 Ka6 6. Be3 Be6 
7. Bb6 Bb3 8. axb3 axb6 9. Kb4#

Only the mate by queen and mate by king are Mirror Chess proof games. 
For the other ones, to get proof games we need more moves:

--------------

Quickest Mirror Chess proof-game mates:

Mate by queen:
(3.5): (see above)

Mate by knight:
(6.5): 1. Nc3 Nc6 2. Nd5 Nd4 3. Nxe7 Nxe2 4. Nd5 Nd4 5. Qh5 Qh4 6. Qg5 
Qg4 7. Nxc7#

Mate by rook:
(6.5): 1. Nf3 Nf6 2. Ne5 Ne4 3. Nxd7 Nxd2 4. Nxf8 Nxf1 5. Ng6 Ng3 6. 
hxg3 hxg6 7. Rxh8#

Mate by bishop:
(7.5): 1. e3 e6 2. Qf3 Qf6 3. Qxb7 Qxb2 4. Qxb8 Qxb1 5. Qxa7 Qxa2 6. Ba3 
Ba6 7. O-O-O O-O-O 8. Bxa6#

Mate by pawn:
(7.5): 1. e4 e5 2. Qh5 Qh4 3. Ke2 Ke7 4. f4 f5 5. Kf3 Kf6 6. Qe8 Qe1 7. 
h4 h5 8. fxe5#

Mate by king:
(8.5): (see above)

The Mirror Chess proof-game mates by pawn and by king are the unique 
examples of their respective lengths.

Note that the Mirror Chess proof-game mates by queen, rook, and bishop 
happen to be unique proof games in orthodox chess too, but this needs 
not be the case in general. A proof game in Mirror Chess is not the same 
as a proof game in orthodox chess that happens to have a mirror 
solution. The latter is more constraining.

Enjoy!

     François