Polgar Superstar Chess (Starchess)

[Arpad Rusz]

I have computed endgame tablebases up to 5 men for Starchess, a very interesting new chess variant played on a star-shaped board with 37 cells.
See the rules here: http://polgarstarchess.com/Rules.doc



Probably most of you never heard about this game before, so here is a link for more informations:
http://polgarstarchess.blogspot.com/

[Arpad Rusz]

I have build the tablebases in DTM format.
Some interresting results (maximal length wins):


M9


M12


M22


M49 (The bishop is much stonger than the rook!)


M41 (There are many stalemate traps, and the winning maneouvre Q25-22!-28!! is amazing.)


M87 (QR/B is a general draw!)

The "solutions" are here: http://polgarstarchess.com/Maximal%20length%20wins.doc

[Kirill Kryukov]

Interesting! Thanks for sharing!

I have some more questions (I hope you don't mind). How large is the complete 5-piece database? How long did it take to compute it (and on what hardware)? How much memory does the solver require? Is there a web-interface, or is it planned? Are you planning to do the 6-piece database too? What is the maximum DTM, and in what position?

Any additional details that you can think of are welcome as well.

[Arpad Rusz]

I am at the very beginning of this work and I haven't optimized yet the solver. I am just happy that it seems to work.
But optimization of the solver is the next step before I will start to generate the 6 men tablebases. I still have some bugs when I generate tablebases with pawns... That need to be fixed.
I have to learn about compression methods too. Of course the whole computation for the 5 men tablebases is done in memory. It was not an issue, as tablebases with pawns requare less than 1GB. I won't report solving times yet, as probably I can do it up to 10 times better.
I am planning a web-interface too and maybe I will need your advises for it. I have never done a database driven website.
And finally: the generator has a simple graphical interface, of course some day I will publish it.

The maximal depths for 5 men pawnless endgames and the number of reciprocal zugzwangs:
http://polgarstarchess.com/5%20men%20pawnless.xls

The maximum DTM for pawnless endgames is M87 (see my previous post for the diagram).

[Kirill Kryukov]

Thanks for the information. Sorry that I focus on just technical issues, because I am not familiar with this game, so I can't fully appreciate the aesthetic value. Although 87 moves seems pretty long.

Do you already have automatic database verification? I found it to be absolutely essential, because sometimes it discovers some totally unbelievable bugs. Once I had a generator bug that produced wrong DTM values for exactly 2 positions out of 1,936,519,455 (8-piece 3x4 chess). It was a reproducible non-random error resulting from the algorithm flaw. It's impossible to notice such rare errors by manual testing.

I'll be glad to help with the web-interface, or anything else.

[Arpad Rusz]

Do you already have automatic database verification?

I don't have that yet. You are right, that is essential. The database looks correct but you never know what hidden small mistakes can be there...

80 DTM maximal depth positions for 5 men pawnless endgames:
http://polgarstarchess.com/5%20Piece%20Pawnless.doc

That M87 was a big surprise, I didn't expect anything longer that 60 moves.

[Arpad Rusz]

A nice problem composed with the help of the tablebases:

[Arpad Rusz]

The longest DTM in the 5-piece pawnless endgames is DTM87. In the following position white needs 87 moves to checkmate the black King! The first 20 moves are unique, an alternative move appears only at move 21.



Here are some analyses of one of the possible lines down to checkmate:
http://www.polgarstarchess.com/The%20longest%20win.doc

The play has four rook and two bishop sacrifices, two stalemate traps, one mutual zugzwang position...
After black's 66th move the following position appears on the board:



You can replay the moves on the Starchess board:
http://www.polgarstarchess.com/Polgar%2 ... 0Board.bmp

[Arpad Rusz]

In starchess the rook is the weakest piece (Q>B>N>R).
The distribution of the DTM numbers is almost the same!

[Kirill Kryukov]

Interesting comparison, thanks for posting!

How do you compute the AverageDTM? Is it for all positions, where draw counts as 0, or only for won/lost positions? I'm curious to compute the AvgDepth in my variants.

MaxDepth tables look beautiful, I wonder how to do the same with 6 pieces, 7, 8... Or in general how to show data summary for a large number of endings (other than a huge table, which would be impossible to read).

[Arpad Rusz]

How do you compute the AverageDTM? Is it for all positions, where draw counts as 0, or only for won/lost positions? I'm curious to compute the AvgDepth in my variants.

My mistake: actually it is the Average_maxDTM what I have computed here. I will change the captions.
I would leave out the draws in the AverageDTM.

[Arpad Rusz]

MaxDepth tables look beautiful, I wonder how to do the same with 6 pieces, 7, ...

Thanks! I wish some day I will have the same problem...

[Kirill Kryukov]

By the way, do you know how many unique legal positions are possible with 5 pieces in this variant? (Also with 2, 3, 4 pieces).

[Arpad Rusz]

No, I don't have calculated that numbers yet but in the following days I will prepare an Excel document with more data.

[Arpad Rusz]

I have updated one of my previous posts with the 3-men and 4-men maxDTM data.