CCRL Discussion Board

Wilhelm by Rafael Andrist can perform these kind of searches and more.

Allen Lee sampled random selection of problems from the 3x3 chess web-site and assembled them into a nice looking PDF. With his kind permission I am attaching it here. It includes mates in 1, 2 and 3, 100 problems of each.

Hi syzygy,

Congratulations on this release! Looks like a lot of work went into this. Hopefully this format will receive wide adoption.

What name should be used for your new tablebase format?

Ola Mikael, very interesting. Sorry I don't have the correct statistics for Nalimov's tables, hopefully someone else can contribute since obviously the numbers should be known. Actually, turns out I couldn't attach the spreadsheet - "The extension ods is not allowed" - but I'd be happy to ...

Some statistics can be found here. Also you can check the tbs files available from this page.

I decided to make a small web-site dedicated just to counting chess endgame positions: NULP. I will gradually add more data and discussion to those pages. Please enjoy and let me know if you'll have any comments, questions or requests.

Number of unique legal positions in 7-piece chess endgames: 423,836,835,667,331. This number is for standard set of rules: pawns start on 2-nd rank, can double step, with en-passant capture and with castling.

More test runs. Number of unique legal positions (NULP) in endgames on square boards from 3x3 to 8x8, pawns start at 1-st rank, no double step, no castling. http://kirill-kryukov.com/chess/various/Number%20of%20positions%20-%20square%20board,%201-1-s-n-n,%20NULP%20vs%20Pieces.png . . . http://kirill...

NULP values from some test runs. Always square board, no double pawn move, no castling, pawns start at 1-st rank. All possible piece combinations (endgames) are included. Board sizes from 3x3 to 20x20, 2 to 5 pieces (total number including the kings), NULP values below 1 trillion. http://kirill-kryu...

I always make the effort to count symmetry-reduced positions twice when I take the statistics. This because I am interested in answering the question: "when you set up a random position, how large is the probability it is won (lost)?". When two different positions are symmetry equivalent,...

Ok, that is very reasonable, because it could get complicated if you had to consider if those rights might ever be used when counting. ... Similarly, 2 ULPs would have the pieces on the squares as above due to different en passant values? Yes, 2 ULPs. Exactly, the idea is to keep the counting as si...

Unless I'm missing something, it should be 16 (4x4), because with this piece placement both white and black can have 4 different possibilities of castling rights.

Done.

Gabor Szots wrote:PS for us: Why is this topic under the registration thread?

I guess because this thread was not locked, as it should have been. It should be possible to split the Shallow discussion into its own thread, if it makes sense.

The uniqueness concept is similarly simple: The number of unique legal positions should count only one position out of all of its symmetrical equivalent variants. This includes swapping the side to move, and also diagonal symmetries and rotations of the board. What about swapping pieces of identica...

For 3 pieces and more it would depend on the kind of piece, right? The more powerful the piece, the more positions there are where it would check the King, and these would all be illegal with that side to move (in your definition). Yes, of course. I never bother calculating legal positions; I alway...

Knowing the exact number of positions in a chess endgame is important for solving an endgame, because it allows to compare statistics with those from independently obtained solutions. In my experiments I use the number of unique legal positions (NULP for short) for reporting statistics (even though ...

New data: Number of unique legal positions (NULP) in 3x3 chess:
In total: 54,687,564.

Nothing in particular, Kirill, except that I enjoyed playing that game (through zillions-of-games) and that is the smallest chess with all pieces. And I am mainly interested in the variant with pawns on the 2nd and 4th rank, and symmetric pieces on the 1st and 5th. Apparently, some opening theory w...

...and a subset of 4x4 chess (up to 9 pieces so far). I hope that someday you'll get to 5x5 minichess !... :) Hi Ernest. What kind of questions do you hope to see answered in 5x5 chess? Some particular endgames or positions? I don't think the 20-piece starting position is easy to solve by tablebase...

To Kirill: Now you did 3x3 Chess, can you do 3x4 (Dobutsu) Shogi? It only has 8 pieces (while in 3x3 Chess you could have 9, and the material combinations are less restricted). So I could imagine the EGT would actually be smaller. Of course there is the complication that the holdings act as extra s...

Very interesting work, thanks a lot for sharing! Also, welcome to this forum!

Erhan Cubukcuoglu notified me that he made a real physical 3x3 chess puzzle: Link. Looks very nice.

Thanks for suggestions. I don't have time at the moment to implement any of this, but will look into this in the future.

Ray wrote:

We have some indications that Komodo does much better than normal against other engines at time controls like 1' + 5".

Does this imply that Komodo's time management is worse than in other engines?