I am John Daniel Bryant FIDE 2367

[byakuugan]

I don't do any programming for tablebases, but I'm a big fan of using them. My long-term goal is to memorize 6-man tablebase, then maybe 7-man if available in the future. If you want to check out my insight into certain endgames on www.youtube.com/user/byakuugan86 I've uploaded almost 100 positions.

[Codeman]

First of all, hello and welcome to the board!

Your skill sounds truly impressive.
One major problem of egtbs is there immense size. It takes around a terabyte even to store all the 6men egtbs. 7men will be a lot larger. A great difficulty we are facing now is that it is very hard to compress these files. For the currently available formats some standard file compression methods are used but these are not very chess focused. To give an example, just by telling the computer the simple rule "in an KPK endgame the game is won if the defending king is out of the square of the pawn" the size of this file would shrink significantly. I am sure there must exist such rules (or at least good heuristics) for other endgames too although they will become significantly more complex.

I wonder how you are proceeding with your memorization. I suppose you are working mainly with such general rules as it would be impossible to work like a machine and remember the outcome for each position. Now I ask you, is it possible to convey your rules in a computer understandable way? This would be a significant leap forward for endgame tablebase development!

regards,
Edmund

[byakuugan]

In my vision of tablebase in the future, endgames will be broken up into key positions that the computer can recognize by following a set of guidelines for the position. When a position satisfies a certain set of guidelines, the tablebase will display a message like, "White wins because...." rather than, "Mate in 230." The message displayed will explain how to reach the next key position, allowing the human to understand the seemingly random moves in-between each key position.
It would be harder to create tablebases for "fragmented" pieces since there is less symmetry. If you take away some abilities from a piece, the endgame might: 1)Have the exact same evaluation, 2)Have the same evaluation, but more complicated, 3)Have a completely different evaluation.

[Arpad Rusz]

Following John's idea about key positions: maybe it is possible to create tablebases with a new metric: DTK - Depth to Key. These are some kind of compressed DTM tablebases where chess knowledge is also used. DTM is actually DTK where only the checkmate positions are considered as key positions.
One needs to identify other "key positions" (these are like the attractors from chaos theory). A position is a key position if there are many winning lines which go through that position.
Finding the key positions... that's the hard task. It is possible to do it efficiently just using the WDL tablebases, or one needs the full DTM tablebases?

[byakuugan]

Does anyone know how I could obtain a program that can calculate tablebases where other pieces are treated as kings, like a 2-man tablebase where the goal is simply to stalemate/checkmate the other piece. A simple example would be Queen vs. Knight with no kings on the board, there is a simple algorithm the queen uses to force checkmate against the knight on any size board, which seems like it would be simple to teach a computer, and maybe even find a formula for determining the exact number of moves it will take.
It seems more logical to start out with 2-man endings, since many of these endings are simply repeating the same formations over and over again, like how Wazir vs. Wazir is a win for whoever has the opposition, and how Ferz vs. Same-Colored Ferz is a win for whoever has the opposition. In fact, any "leaper" chess piece with 4 moving paths can stalemate another piece of the same type. Leapers with 8 moving paths can escape each other. I am not sure if there is another terminology to describe the number of symmetrical moving paths a piece has, but I use "octosymmetrical" and "quadrisymmetrical"

I figured out why all pythagorean triples can be defined by a chess piece, but it would probably take a 10-part video series to describe proof of the theorems. I will make this video series as soon as I get the proper equipment to actually film myself drawing on a board.

Short description:
All "octosymmetrical" leapers, like knights, camels (1,3), giraffes (1,4), zebras(2,3), etc. have 3 corresponding quadrisymmetrical leapers, by taking away half of the piece's moves. The aura of the piece will now be a rectangle rather than an octagon.
The 3,4,5 pythagorean triple is the KNIGHT TRIPLE, since the 3 quadrisymmetrical knights are colorbound, 3, 4, and 5-ways. I call these pieces DiagoKnight, StraightKnight, and SquareKnight.

If x and y represent the movement of a leaper, then the 3 formulas are:

2xy determines the colorboundness of a quadrisymmetrical leaper whose aura is a rectangle with sides that are ranks/files
(x+y)(|x-y|) determines the colorboundness of a quadrisymmetrical leaper whose aura is a rectangle with sides that are diagonals
xx+yy determines the colorboundness of a quadrisymmetrical leaper whose aura is a square.

It is easy to figure out that (2xy)^2 plus (x+y)(|x-y|)(x+y)(|x-y|) equals (xx+yy)^2, but it would take a lot of animation to provide a visual representation of why it works. I am not sure how pythagorean triples would help in the evolution of understanding tablebase endings, but at least it is a start.

[Arpad Rusz]

In fact, any "leaper" chess piece with 4 moving paths can stalemate another piece of the same type. Leapers with 8 moving paths can escape each other. I am not sure if there is another terminology to describe the number of symmetrical moving paths a piece has, but I use "octosymmetrical" and "quadrisymmetrical"

octosymmetrical leaper = doublet leaper (see Variant Chess Magazine 47 and 64)
http://www.mayhematics.com/v/v.htm

[Kirill Kryukov]

Does anyone know how I could obtain a program that can calculate tablebases where other pieces are treated as kings, like a 2-man tablebase where the goal is simply to stalemate/checkmate the other piece.

Solving variants with fairy piece and exotic rules is exciting topic. Currently my resources are consumed by 4x4, but I'd be curious to study other variants in the future. Also, please post if you'll ever find such software.

[byakuugan]

I remember hearing that somebody generated shatranj tablebases, so how hard is it to create tablebases with different piece types? A piece I am studying is a hexasymmetrical knight, which has 6 of a knight's moves (the moves taken away from the knight must have same slope). This piece is different than the hexagonal knight, which is a square portrayal of a knight that came from a hexagonal board, it moves like a positive diagknight, negative diagcamel, and negative diagzebra, it seems much stronger than the hexagonal bishop, which moves like a positive diagknight and negative bishop and is colorbound 3-ways

An interesting think about hexasymmetrical pieces, is that when you create a hexagon using all 6 of the piece's potential moving abilities, the hexagon can be divided into three rhombuses that create the illusion of a cube (you can draw three more corresponding rhombuses to create a hollow cube illusion) the areas of the three rhombuses are always going to be a pythagorean triple.

Example:
Draw a square knight from c5-d7-f6-e4-c5
Draw a vertical knight from f6-g4-f2-e4-f6
Draw a diagonal knight from f2-d3-c5-e4-f2
So the revolution rhombuses of the three types of the quadrisymmetrical piece can be combined to create the revolution of the one type of hexasymmetrical piece.