Ozymandias wrote:

syzygy wrote: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.

Laskos wrote:

Ozymandias wrote:

syzygy wrote: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

Vinvin wrote: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 ?

kronsteen wrote: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.

# 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

Ajedrecista wrote:

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

abulmo2 wrote:

Ajedrecista wrote:

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.

kronsteen wrote:[...]

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)

[...]

Ajedrecista wrote:Hello Vincent:

Vinvin wrote: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 wrote:

Laskos wrote:

Ozymandias wrote:

syzygy wrote: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.