Which pawn capture is best?

[Norm Pollock]

This is sort of a fun question about an unusual position that I conjured up.

First of all, it is perfectly legal and it can be reached in 7 moves. Secondly, the last move is e4, which creates an "en passant" target square at e3. Third, there are 4 black pawns that can capture the pawn at e4.

My question is: Which pawn should Black use to capture White's pawn at e4?

[d]rnbqkbnr/pp2p2p/8/3p1p2/P2pPp2/1P5P/2P3P1/RNBQKBNR b KQkq e3 0 7

[chesskobra]

En passant with d4, so all pawns remains supported. Also, Nc3 is not possible after that.

[Jouni]

Lc0 says:

1. -+ (-4.28): 7...fxe3 8.Qxd4 Nf6 9.Bb5+ Nc6 10.Bxe3 Bg7 11.Bf4 0-0 12.Bxc6 bxc6 13.Be5 c5 14.Qf4 Nh5 15.Qg5 h6 16.Qg6 Qb6 17.Qxb6 axb6 18.Nf3 Ng3 19.Rg1 f4 20.Nc3 Bxe5 21.Nxe5
2. -+ (-1.95): 7...Bg7 8.Qh5+ Kf8 9.exf5 d3 10.Ra2 dxc2 11.Rxc2 Nc6 12.Bd3 Nb4 13.Rd2 Qa5 14.Qf3 Nh6 15.Ne2 Nxd3+
3. -/+ (-1.01): 7...Nf6 8.e5 Ne4 9.Qh5+ Kd7 10.Qf7 Bh6 11.Qxd5+ Kc7 12.Qxd8+ Rxd8 13.Nf3 Be6
4. =/+ (-0.63): 7...Qd6 8.exd5 Qe5+ 9.Qe2 Qxd5 10.Qh5+ Kd8 11.Nf3 Qe6+ 12.Be2 Nf6 13.Qh4 Nc6 14.Ng5 Qg8

[Ajedrecista]

Hello Norm:

It is ingenious indeed. I never thought before about four pawns capturing the same pawn!

There are several transpositions leading to this position in 13 plies. The first in alphabetical order is:

1. a3 c5 2. a4 d5 3. b3 e5 4. d4 cxd4 5. f4 exf4 6. h3 f5 7. e4

While the last in alphabetical order or the first in reversed alphabetical order is:

1. h3 f5 2. f4 e5 3. d4 exf4 4. b3 d5 5. a3 c5 6. a4 cxd4 7. e4

How many transpositions are? Natch 3.3 says 25166 without taking into account the en-passant capture, that is, without forcing e4 to be the last move, so 25166 is an upper bound that can be reduced a lot.

rsbqkbsr/pp2p2p/8/3p1p2/P2pPp2/1P5P/2P3P1/RSBQKBSR
13 single moves

Code: Select all

.\Natch-3.3>Natch --hash-size 512 --language e --output Solutions.txt Problem.txt
Solutions found: 25166
Position analysed: 1
Resolution time: 0.51 s.

I could not make Natch work with the en-passant flag. A first guess could be 1/7 of 25166, which is 3595 more less. There are 3756 solutions with 7. e4 in the output file, but there are 2054 incomplete lines referencing other solutions, for example:

Code: Select all

[...]
Solution 40 (position 1)
1.Pa2-a3   Pc7-c5   2.Pa3-a4   Pg7-g5   3.Pd2-d4   Pc5xd4   
4.Pf2-f4   Pf7-f5   5.Pe2-e4   Pd7-d5   6.Ph2-h3   Pg5xf4   
7.Pb2-b3
[...]
Solution 25166 (position 1)
1.Ph2-h3   Pf7-f5   2.Pb2-b3   
... see solution 40.
[...]

I do not know how to count them properly since I am not a programmer. A finer guess would be 3756 + 2054/7 ~ 4049, so something between 4000 and 4100 makes sense, or even 3756 if I have not understood the concept of '... see solution' references.

Regards from Spain.

Ajedrecista.

[Vinvin]

Analyse by SF, 3 best moves, depth 35 :

FEN: rnbqkbnr/pp2p2p/8/3p1p2/P2pPp2/1P5P/2P3P1/RNBQKBNR b KQkq e3 0 7

Code: Select all

Stockfish_24111319_x64_avx2:

 35/60	 506.262k	1.508k	-1,64	1. ... Nf6 2.Bb5+ Nc6 3.e5 Ne4 4.Qh5+ Kd7 5.Bxf4 e6 6.Ne2 a6 7.Bxc6+ bxc6 8.g4 Qe8 9.Qxe8+ Kxe8 10.Nxd4 c5 11.Nf3 Be7 12.Nbd2 Rf8 13.g5 Rb8 14.Rg1 Kf7 15.h4 Rb4 16.c4 Bb7 17.h5 Rg8 18.Nxe4 fxe4 19.g6+
 35/59	 506.262k	1.508k	-2,41	1. ... Bg7 2.Qh5+ Kf8 3.exf5 d3 4.c3 Qc7 5.Ra2 Nf6 6.Qf3 d2+ 7.Rxd2 Bxf5 8.Bd3 Be4 9.Qd1 Bh6 10.Nf3 Bxf3 11.Qxf3 Nbd7 12.Rf2 e5 13.Bf5 Rg8 14.g4 Re8 15.0-0 Rg5 16.c4 Rxf5 17.gxf5 d4 18.c5 Nxc5 19.Ba3
 35/56	 506.262k	1.508k	-3,20	1. ... fxe3 2.Qxd4 Nf6 3.Qxe3 Bg7 4.Bb5+ Nc6 5.Ne2 0-0 6.Bb2 e5 7.Nd2 f4 8.Qf2 Qc7 9.Qc5 Be6 10.0-0 a6 11.Bd3 Nh5 12.Rae1 Rae8 13.c4 b6 14.Qa3 e4 15.Nxe4 dxe4 16.Bxe4 Ne5 17.Nd4 Nf6 18.Bf5 Bf7 19.Ne6 Bxe6 20.Bxe5 Qc5+ 21.Qxc5 bxc5 22.Bc2 Nh5 23.Bxg7 Kxg7 24.Re5 Ng3

[Ajedrecista]

Hello again:

[...]

There are several transpositions leading to this position in 13 plies. [...]

The possibility of four pawns capturing the same pawn can be reached one ply sooner, for example:

1. d4 d5 2. c4 f5 3. e4 Nf6 4. exf5 Nc6 5. cxd5 Nb4 6. f4 e5

In this case, it is white and not black who can capture en-passant, of course. I think there is not any shortest proof game featuring this kind of capture: white pushing four pawns (c, d, e and f in my example); two moves for capturing black pawns and have doubled pawns; and black pushing the pawn between the white doubled pawns in its sixth move.

Regards from Spain.

Ajedrecista.

[Norm Pollock]

For anyone curious, the move sequence I used for this position was:

1. f4 f5 2. d4 g5 3. a3 gxf4 4. h3 d5 5. b3 c5 6. a4 cxd4 7. e4

[Ajedrecista]

Hello Norm:

For anyone curious, the move sequence I used for this position was:

1. f4 f5 2. d4 g5 3. a3 gxf4 4. h3 d5 5. b3 c5 6. a4 cxd4 7. e4

Your last post made me realise that I wrongly pushed the black e-pawn in your position instead of the black g-pawn in my first post of this thread when listing the first and last alphabetical order sequence.

Anyway, it is fun that I can still see things that I never thought before (like four different pawns capturing the same pawn) despite being playing the game for twenty years.

Regards from Spain.

Ajedrecista.