7-men Syzygy attempt

[Laskos]

There is no reason to believe that TBs help less at long TC. I suspect that the opposite is the case.

With Houdini 4, I tested an Elo increase of at least 20 points (I don't have the exact figure at hand), and that's just going from 5-men to 6-men, not from 0 to 6. I've never see anything close to that figure, being reported.

Ronald is right.

http://www.talkchess.com/forum/viewtopic.php?t=66486

[syzygy]

There is no reason to believe that TBs help less at long TC. I suspect that the opposite is the case.

With Houdini 4, I tested an Elo increase of at least 20 points (I don't have the exact figure at hand), and that's just going from 5-men to 6-men, not from 0 to 6. I've never see anything close to that figure, being reported.

Ronald is right.

http://www.talkchess.com/forum/viewtopic.php?t=66486

But I may have misunderstood Juan when I thought he was implying that TBs help less at longer TCs.

[Ajedrecista]

Hello Vincent:

Please, can somebody gives a rough estimation of 7-men Syzygy sizes.

1) Number of files ?
1) Number of pawnless files ?
2) Size of DTZ for all files ?
2) Size of WDL for all files ?

I do not know how Syzygy TBs work, e.g. if a specific endgame (for example KRPPkrp) has one file for wtm (white to move) and other for btm (black to move), or if endgames of the same kind (for example KRPPkrp and KRPkrpp) are merged into a single file or not; so I can not answer your questions.

Once said that, there is an Excel file called 'TBs combinatorics.xls' at CCRL Endgame Tablebases Forum which is still available for download:

analysis of 1 specific 6-7-8 piece position

To calculate the overall number of positions in a given ending, you place kings first, then pawns (if any), then the remaining pieces.

In the case of krppkrp :

There are 1806 different positions of kings (taking a vertical symmetry into account) among which 106 leave 48 free squares for pawns (both kings on 1st/8th ranks), 724 leave 47 (1 king on 1st/8th ranks) and 976 leave 46 (no king on 1st/8th ranks).
This gives (106*48*47*46+724*47*46*45+976*46*45*44)/2=85166148 positions for kings+pawns (divide by 2 because the two white pawns are interchangeable).
Then place the rooks on the 59 remaining squares : 59*58=3422 possibilities.
Total = 85166148*3422*2 (multiply by 2 for white to move/black to move) = 582877116912 positions.

Positions recorded have the following characteristics :
- kings are never adjacent to each other
- pawns are always on legal squares (no pawn on 1st/8th rank)
- however many positions are illegal since the side not to move is in check (but these are impossible to enumerate with a simple formula, of course)
- positions with castling or en passant possibilities are not taken into account (also not so easy to enumerate, they represent only a very small percentage)

Here is a file containing combinatorial calculations for all 3-8 men endings (I didn't expect to release it so it doesn't have many comments - if something is unclear please let me know)

TBs combinatorics.rar
(351.75 KiB) Downloaded 169 times


To translate Gpos into Gb for file size expectations, you can use the following rules (occasionnally very wrong but not so bad in the majority of cases and more accurate for global sets) : 4 pos/byte in DTM, 7 pos/byte in DTC, 8 pos/byte in DTZ or DTZ50, 50 pos/byte in WDL.

You can have a look at that. According with this Excel, there are 1001 different 7-man endgames: 396 pawnless, 330 with one pawn, 180 with two pawns, 72 with three pawns, 20 with four pawns and 3 with five pawns.

The number of positions that this Excel estimates for all 1,001 7-man endgames (wtm + btm) is 618,389,394,344,832 (around 6.18e+14).

Just for comparison, this Excel estimates the following number of positions (wtm + btm) up to 8-man:

Code: Select all

# man     # EG     Positions (wtm + btm)     log10(pos)
=======================================================
3-man        5                   397,176       5.5990
4-man       30               145,558,288       8.1630
5-man      110            31,384,645,344      10.4967
6-man      365         5,130,471,463,616      12.7102
7-man     1001       618,389,394,344,832      14.7913
8-man     2520    59,821,595,741,850,880      16.7769

I hope no typos.

Once these numbers are delivered, maybe Ronald can provide a rough estimate of file sizes.

Regards from Spain.

Ajedrecista.

[guyhaw]

Presumably, the side with 6 men will try to force=sac a man as quickly as possible to get to a 5v1 win

g

[Nordlandia]

I'm trying to figure out the difference between probing 5-men during game plus 6-man adjudication compared to probing 6-men.

Probing 6-men is stronger but i'm not sure how much?

[abulmo2]

Code: Select all

# man     # EG     Positions (wtm + btm)     log10(pos)
=======================================================
3-man        5                   397,176       5.5990
4-man       30               145,558,288       8.1630
5-man      110            31,384,645,344      10.4967
6-man      365         5,130,471,463,616      12.7102
7-man     1001       618,389,394,344,832      14.7913
8-man     2520    59,821,595,741,850,880      16.7769

Two remarks:
1) I am not sure those numbers are exact. For kpk endings, my program counts only 165,676 legal positions; whereas the above number includes 168,024 of them.
2) Many positions are easy to solve without a table. For example, kbk and knk 3-men combinations are always drawn and you do not need a table to resolve them. On the other hand, krk and kqk are mostly won, apart for a few trivial cases that a 1 ply search can decipher. Only the kpk combination with 111,282 wins (from the pawn side) and 54,394 draws are complex enough to make a table worth. Of course the same can be said for many 4-men to 8-men tables. Maybe a solution would be to have only frequent and hard to solve piece combinations.

[Ajedrecista]

Hello Richard:

Code: Select all

# man     # EG     Positions (wtm + btm)     log10(pos)
=======================================================
3-man        5                   397,176       5.5990
4-man       30               145,558,288       8.1630
5-man      110            31,384,645,344      10.4967
6-man      365         5,130,471,463,616      12.7102
7-man     1001       618,389,394,344,832      14.7913
8-man     2520    59,821,595,741,850,880      16.7769

Two remarks:
1) I am not sure those numbers are exact. For kpk endings, my program counts only 165,676 legal positions; whereas the above number includes 168,024 of them.
2) Many positions are easy to solve without a table. For example, kbk and knk 3-men combinations are always drawn and you do not need a table to resolve them. On the other hand, krk and kqk are mostly won, apart for a few trivial cases that a 1 ply search can decipher. Only the kpk combination with 111,282 wins (from the pawn side) and 54,394 draws are complex enough to make a table worth. Of course the same can be said for many 4-men to 8-men tables. Maybe a solution would be to have only frequent and hard to solve piece combinations.

It looks like they are reasonable upper bounds. I have just found the following remarks just checking the original post (bold added by me):

[...]

Positions recorded have the following characteristics :
- kings are never adjacent to each other
- pawns are always on legal squares (no pawn on 1st/8th rank)
- however many positions are illegal since the side not to move is in check (but these are impossible to enumerate with a simple formula, of course)
- positions with castling or en passant possibilities are not taken into account (also not so easy to enumerate, they represent only a very small percentage)

[...]

So understanding those numbers as reasonable upper bounds, we could calculate upper bounds for file sizes. If Syzygy can store (X positions)/byte in average, the whole set of 7-man Syzygy would be around [(6.1839e+14)/X] bytes ~ [(562.4)/X] TB at most. For example, if X = 2 (just an invention), then the whole set of 7-man Syzygy would be around 281.2 TB at most and easily below 250 TB or even 200 TB in that example of X = 2. It looks like the key words here are upper bound.

Regards from Spain.

Ajedrecista.

[Vinvin]

Thanks for those numbers !
AFAIK, Syzygy only use WTM positions. That divides the overall size by 2.

Hello Vincent:

Please, can somebody gives a rough estimation of 7-men Syzygy sizes.

1) Number of files ?
1) Number of pawnless files ?
2) Size of DTZ for all files ?
2) Size of WDL for all files ?

I do not know how Syzygy TBs work, e.g. if a specific endgame (for example KRPPkrp) has one file for wtm (white to move) and other for btm (black to move), or if endgames of the same kind (for example KRPPkrp and KRPkrpp) are merged into a single file or not; so I can not answer your questions.

[syzygy]

WDL TBs are 2-sided, DTZ TBs are 1-sided (but not necessarily WTM).

There would indeed be 1001 7-men WDL files and the same number of DTZ files.

[Ozymandias]

There is no reason to believe that TBs help less at long TC. I suspect that the opposite is the case.

With Houdini 4, I tested an Elo increase of at least 20 points (I don't have the exact figure at hand), and that's just going from 5-men to 6-men, not from 0 to 6. I've never see anything close to that figure, being reported.

Ronald is right.

http://www.talkchess.com/forum/viewtopic.php?t=66486

But I may have misunderstood Juan when I thought he was implying that TBs help less at longer TCs.

You understood correctly, a test generated from just one endgame position, a weird one too, only clarifies things for that particular position; I'm yet to see tests results with 20 Elo point gains (or more), at longer TCs.

Other than the empirical fact derived from my own tests at ultrafast TCs, and the absence of said experience at longer TCs, there's also the intuition that more time generates better chess, at all phases of the game, leading to smaller Elo gaps between players. As with any intuition, I could be wrong.