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Parent - - By Uri Blass (*****) Date 2008-02-25 13:52
This is not clear that the number of these position is relatively small if you know how to define the classes.
The fact that today we do not know a good definition of classes of positions in chess does not prove that it is impossible to have them.

Uri
Parent - - By saxon (**) Date 2008-02-25 19:44
If we knew that way better ,top PC engines would be elo4000  now,wouldn't they?But that's not my point.
I'm talking about much smaller universe of  positions in 5×5 chess which is ,IMO,within "striking distance" of supercomputers of today.Mostly with  a "brute force" approach,this game can be  solved backwards (i think).
For start,I would think that something like 8 men tablebases is quite possible to have in 5×5 chess.
AFAIK,the fact is  nobody is interested in solvability of mini-chess so we don't have it at the moment.
The word *little* in project shouldn't be taken literally.Of course,solving mini-chess would be actually a huge project.    
Parent - - By Mark (****) Date 2008-02-25 20:14
While formally solving 5x5 chess would be a difficult (but possible) task, I wonder if a fast program with a deep search could find a forced win of material from the opening position?  That would give a pretty good idea as to the outcome of a more formal proof.
Parent - - By Uri Blass (*****) Date 2008-02-25 21:06
No because there is no opening position and there are even no known rules for chess 5*5(at least not for me).

When there is a simple generalization to define 8*m chess for m>=4 I see no way to have accepted definition of 5*5 chess.

King Queen Rook bishop knight are the normal chess pieces.

Are all of them in the first rank?
What is the initial position of them?
Can the sides castle?

Uri

Parent - By Roland Rösler (****) Date 2008-02-25 22:24
Make a search about "5x5" in this forum and you will find the "usual suspects" in this thread too.
Parent - - By Mark (****) Date 2008-02-25 22:29
There's an article on 5x5 chess in Wikipedia under "Minichess" showing the four main variants.  http://en.wikipedia.org/wiki/Minichess 

Apparently, it was popular in Italy, in addition to correspondence play.  I had modified my program (written in basic) to play 5x5, but it was very slow, especially compared to the best programs of today (and weak too: no null move, hash tables, etc.).  I'm sure a modified movei would be unbeatable at 5x5!
Parent - - By Roland Rösler (****) Date 2008-02-26 00:08
Some questions to 5x5 chess:

1. Can you give us your values for P,N,B,R,Q in 5x5 chess? I´m sure, they must be different to normal chess.
2. Do you think, that 5x5 chess is more drawish than normal chess?
3. Have you an opening book for 5x5 chess? If yes, how many positions, how many plies for interesting lines?
4. Have you tbs for 5x5 chess? If yes, how many pieces?
5. What do you think is the biggest difference to normal (8x8) chess? Please nothing about board!
6. Do you think, that solution of 5x5 chess give us any sign for 8x8 chess?
7. Is White in Zugzwang in the first move?

Many thanks for your answers!
Parent - - By Mark (****) Date 2008-02-26 02:53
Hi Roland-

1. I used the standard 1, 3, 3, 5, 9 values and they seemed to work fine.
2. My program didn't have 3 move draw repetition so it tended to shuffle pieces back and forth causing more draws than normal.
3. I never got around to making an opening book.
4. Didn't have any tablebases either.  I know tablebases have been made for 6x6 though.  I understand some of the mates are longer than if on an 8x8 board!
5. From the little that I've played, a big difference is the cramped feeling you get with 20 pieces on only 25 squares.  (In 3x3 chess, which has been solved, it's really cramped!)
6. I think it will give us an appreciation for just how complex 8x8 chess really is.
7. I wish I knew!  Like I said, my program wasn't good enough to really analyze the game in a lot of detail.  I'm sure some of the talented programmers here could make fantastic programs with a few weeks effort.

Regards  
Parent - - By Roland Rösler (****) Date 2008-02-26 03:12
Many thanks for your answers.
I have no clue, but I can´t imagine that piece values in 5x5 should be the same like in 8x8. Knight must be much more worth. And underpromotion in knight must be normal. Okay, you have to look to the games and then you can make a decision. I never seen an 5x5 game.
Parent - By Mark (****) Date 2008-02-26 12:54
True. Knights should more valuable than bishops.  Also, rooks have trouble finding open files!  I'm not sure what values are optimal.
Parent - - By AsosLight (***) Date 2008-02-27 15:08
It's almost funny to listen that we have to solve this game. it's almost so obviously drawn after 3-4 moves that you don't have to count almost anything. Opening book? Yes you can write one on ......paper. You don't have to write more than half a page. then you always have something like a2,c3,e2,Bc1,Ra1-b1,Ke1-d1-c2-b1 against a3,c4,e3,Bc5,Ra5-b5,Ke5-d4 and thats it. After the first innevitable exchanges the game is completly trivial. Of course if you play wrong for fun there are some funny refutations with sacrificial attacks. As for the values seriously speaking the position is so crampt that the values practicly change move after move.(in chess thats less important though strategic exchanges are also possible) but more appropriate might be 1,2,3,4,7.(knight is by no mean equal to bishop and rook bishop should at least hold the draw against the queen and also to pawns most ofen worth a knight probably a bishop also).
PS: no mini chess has nothing to do with classic chess it is like compering triliza with score4.
Parent - - By Mark (****) Date 2008-02-27 17:41
There are four different setups in the wiki article. Which setup are you using? (I can't follow your book moves.) Anyway, they all aren't that trivial.  The Mallett setup with two knights rook and queen vs two bishops rook and queen is pretty interesting!
Parent - By AsosLight (***) Date 2008-02-27 18:14
a1 rook, b1 knight, c1 bishop, d1 queen, e1 king. and a5-b5 etc fore black. the so called miniature chess. i wasn't aware for anything else. of course you should have the same material and oppose pieces else that has noting to do with chess any more. thats the only way to have it's side all the pieces. About the position i describe is almost forced after 1c2-c3.
Parent - - By Хайдук Date 2008-02-26 22:47 Edited 2008-02-26 23:06
I find the notion of classes interesting. Depends on how many classes and how you solve a class within itself. A few endgame classes can be proved on global theoretical grounds. However, I suspect most classes would have still to lean on the good old exhaustive search due to lack of (discernible) higher-level organizing patterns within the class. It might appear that there is no sensible partition of the huge chess configuration space into a manageable number of classes in a way that significantly reduces the comprehensive search within a class or in reducing to other classes.
Parent - - By AsosLight (***) Date 2008-02-27 15:30
I agree. Checkers have symmetries due to identical pieces and certain structure patterns like the very simple chess endgames but with lot of pieces on the board it's a different story. though in pawnless positions you can have a type of classification of course having 10 pieces without pawns would not have practical use except if someone can find a way to <<implant>> pawns to the possition with some way keeping the classification of the pawnless possition untouched.
Parent - By saxon (**) Date 2008-02-27 17:46 Edited 2008-02-27 17:49
+ There's a little difference between numbers ~3x10^43 (8×8 chess) and ~10^22(8×8 checkers) :)

P.S.
While I do also think 5×5 chess is draw,I definitelly disagree it's obviously draw after 3-4 moves :) 
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