Mate in 69 on 4x4 board

[JornBurker]

I see that you do not allow pawn in the second rank to go 2 squares forward.

(As a side note, for standard chess I calculated the exact number of positions with castling rights, en-passant rigths, and both rights, for up to 8 pieces, in case anyone is curious: https://kirill-kryukov.com/chess/nulp/ )

So any progress on the 8-men DTZ Tablebase? Is there still a plan about the 7-men and 8-men DTM Tablebase now?

[Kirill Kryukov]

So any progress on the 8-men DTZ Tablebase? Is there still a plan about the 7-men and 8-men DTM Tablebase now?

No news or plans from me, as I'm not studying 8x8 chess currently. But I'm sure someone is working on this (or thinking about this), and can probably provide a better udpate.

[Kirill Kryukov]

In 4x4 chess, the kqqrbnp-kbnnp endgame has 6,688,343,790 unique legal positions with white to move. Only one of these positions is a stalemate, which makes it the rarest stalemate (per ESM), for all 2 to 12 piece endgames. I wonder if anyone wants to try constructing this position.

[Uri Blass]

In 4x4 chess, the kqqrbnp-kbnnp endgame has 6,688,343,790 unique legal positions with white to move. Only one of these positions is a stalemate, which makes it the rarest stalemate (per ESM), for all 2 to 12 piece endgames. I wonder if anyone wants to try constructing this position.

You mean that white is the side with 2 queens otherwise many solutions
Here is one of them

[d]8/8/8/8/4bn1r/4p1kq/4P1NN/4q1BK w - - 1 1

[Uri Blass]

Q cannot be in the centre because in that case it control 8 squares and only 6 of them can be of white pieces different than the queen and it can go to another square because no pin can prevent queen to capture the pinning piece.

Queens also cannot be in 2 corners because they control 6 squares and white has only 5 pieces except the queen to block them.

It seems to me that white must have 2 queens in a1 b1 or a1 a2 or a4 b4 or a3 a4.

bishop also cannot be pinned by a bishop so it must be blocked by the own pieces

I did not solve the problem and got the following that is almost stalemate in 4*4 board but the rook can move
*.

[d]8/8/8/8/1nnk4/b1p5/RNP5/QQKB4 w - - 1 1

[JornBurker]

In 4x4 chess, the kqqrbnp-kbnnp endgame has 6,688,343,790 unique legal positions with white to move. Only one of these positions is a stalemate, which makes it the rarest stalemate (per ESM), for all 2 to 12 piece endgames. I wonder if anyone wants to try constructing this position.

Here it is:
[d]1pBQ/1KRQ/nnNP/1k1b w

[Ajedrecista]

Hello:

In 4x4 chess, the kqqrbnp-kbnnp endgame has 6,688,343,790 unique legal positions with white to move. Only one of these positions is a stalemate, which makes it the rarest stalemate (per ESM), for all 2 to 12 piece endgames. I wonder if anyone wants to try constructing this position.

Here it is:
[d]1pBQ/1KRQ/nnNP/1k1b w

I did not know that pawns could be at first and fourth ranks. Furthermore, if there is only one stalemate, what about the mirror position?

[d]QBp1/QRK1/PNnn/b1k1 w - - 0 1

Waiting for Kirill's answer... I agree with Uri about white bishop being blocked by own pieces.

Regards from Spain.

Ajedrecista.

[Uri Blass]

Hello:

In 4x4 chess, the kqqrbnp-kbnnp endgame has 6,688,343,790 unique legal positions with white to move. Only one of these positions is a stalemate, which makes it the rarest stalemate (per ESM), for all 2 to 12 piece endgames. I wonder if anyone wants to try constructing this position.

Here it is:
[d]1pBQ/1KRQ/nnNP/1k1b w

I did not know that pawns could be at first and fourth ranks. Furthermore, if there is only one stalemate, what about the mirror position?

[d]QBp1/QRK1/PNnn/b1k1 w - - 0 1

Waiting for Kirill's answer... I agree with Uri about white bishop being blocked by own pieces.

Regards from Spain.

Ajedrecista.

I guess mirror position is considered to be the same position and he meant one position if you do not consider symmeteric positions.

Practically you only need to consider positions when the white king is in the a-b files becase c-d files are always symmetric to a-b files assuming no casrling rights.

[Ajedrecista]

Hello again:

Hello:

In 4x4 chess, the kqqrbnp-kbnnp endgame has 6,688,343,790 unique legal positions with white to move. Only one of these positions is a stalemate, which makes it the rarest stalemate (per ESM), for all 2 to 12 piece endgames. I wonder if anyone wants to try constructing this position.

Here it is:
[d]1pBQ/1KRQ/nnNP/1k1b w

I did not know that pawns could be at first and fourth ranks. Furthermore, if there is only one stalemate, what about the mirror position?

[d]QBp1/QRK1/PNnn/b1k1 w - - 0 1

Waiting for Kirill's answer... I agree with Uri about white bishop being blocked by own pieces.

Regards from Spain.

Ajedrecista.

This is a snippet from Kirill's site:

[...]

Rules

We use a 4x4 board (Fig. 2), with files labeled "a" to "d" and ranks "1" to "4". a1 is a dark-colored square. 4x4 chess includes all possible legal placements of chess pieces on this board. We use a relaxed definition of legality: a positions is called legal if it has exactly one white and one black king, no pawns on their last (promotion) rank, and side to move does not give a check (does not have a piece attacking the other side's king). Any combination of chess pieces is allowed, and the set of pieces is only restricted by the board size and legality requirement. For example, positions with 15 white (or black) pieces are included. Also note that pawns can be placed on their first rank.

[...]

Bold and blue font added by me. If that, we should have a winner!

https://calc.biokirr.com/4x4c/query?met ... mode=Query
https://calc.biokirr.com/4x4c/query?met ... mode=Query

Regards from Spain.

Ajedrecista.

[Kirill Kryukov]

This was quick, thanks to everyone! And congratulations to JornBurker! I credited you on the 4x4 chess page. (If you don't want to be mentioned, or want to correct the spelling, let me know).

No, I did not know this position, but I was curious to see it. I could have coded a scan to find it, but thought it may be more fun to construct it manually.

Yes, the side with the two queens has the right to move, pawns are allowed on first rank, and all symmetries are taken into account, so the two positions are counted as one. (Thanks to Ajedrecista and Uri for the help clarifying this!).