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'''Syzygy Bases''', <ref>[http://www.talkchess.com/forum/viewtopic.php?t=47681&start=45 Re: New 6-piece tablebases] by [[Ronald de Man]], [[CCC]], April 10, 2013</ref><br/>
a compact six piece endgame database developed by [[Ronald de Man]], published on April 01, 2013. Since August 2018, '''seven piece''' Syzygy Bases are available after an effort by [[Bojun Guo]] started in March 2018 <ref>[http://talkchess.com/forum3/viewtopic.php?f=7&t=66797&start=472 Re: 7-men Syzygy attempt] by [[Bojun Guo]], [[CCC]], August 19, 2018 </ref>. Syzygy Bases consist of two sets of files, '''WDL''' files storing win/draw/loss information considering the [[Fifty-move Rule|fifty-move rule]] for access during [[Search|search]], and '''DTZ''' files with [[Endgame Tablebases#DTZ50|distance-to-zero]] information for access at the [[Root|root]]. The generator is released under the [[Free Software Foundation#GPL|GNU General Public License Version 2]], the [[Thread|thread safe]] probing code is released without restrictions <ref>[http://www.talkchess.com/forum/viewtopic.php?t=47681 New 6-piece tablebases] by [[Ronald de Man]], [[CCC]], April 01, 2013</ref> . As of February 2015, all 3-5 and most important 6-men Syzygy Bases are commercially available on 4 [https://en.wikipedia.org/wiki/DVD DVDs] by [[ChessBase]] as ''Endgame Turbo 4'' for their products [[Fritz|Deep Fritz 14]], [[Komodo#8|Komodo Chess 8]], [[Houdini|Houdini 4]] or [[ChessBase (Database)|ChessBase 12/13]] <ref>[http://shop.chessbase.com/en/products/endspiel_turbo_4 Endgame Turbo 4] by [[ChessBase]]</ref> <ref>[http://en.chessbase.com/post/syzygy-tablebases-newest-fastest-smallest Syzygy Tablebases: newest, fastest, smallest] by [[Albert Silver]], [[ChessBase|ChessBase News]], February 08, 2015</ref>.
=Data=
==File Types==
==File Sizes==
==Comparision==
Syzygy EGTB is significantly smaller than all any [[Endgame Tablebases#DTM|DTM]] EGTBsEGTB. It is 7 times as small as Gaviota for 5 men, 8 times as small as Nalimov for 7 6 men, 8 times as small as Lomonosov for 7 men. However, when all DTM EGTBs have full data of two sides, Syzygy EGTB omits data of one side for DTZ data to save space. [[Ronald de Man]] estimated that if keep them all, the Syzygy's 6 men size may increase 158 GB, become 307 GB in total, double on size, 4 times as small as Nalimov 5 6 men.
=Generation===Up to 6-man==On the first release (Apr 01, 2013) the generator was ready to generate all endgames up to 6 men. The generation is multithreaded and processes completely in RAM. To generate all 6 men, it requires a system with at least 32 GB of RAM and may run in 5 days (the period was measured with a computer 6-core i3930K @ 4.2Ghz, 64 GB). ==7-man==Ronald de Man wasn't initially interested in the creation of 7-men Syzygy Based <ref>[http://kirill-kryukov.com/chess/discussion-board/viewtopic.php?f=6&t=7618#p83771 Re: 7-piece syzygy] by [[Ronald de Man|syzygy]] in a reply to , [[Pham Hong NguyenComputer Chess Forums|Nguyen PhamCCRL Discussion Board]], April 15July 03, 2014</ref> since the generation would require about 1 TB of RAM, too expensive at that time. Generation time would be about 64 x per table, 2020 which means around 175 x time total <ref>[http://talkchesskirill-kryukov.com/forum3chess/discussion-board/viewtopic.php?f=76&t=73598 7396#p83338 Re: Almost perfect DTM tablebaseSyzygy tb generator for windows] by [[Dann CorbitRonald de Man|syzygy]], [[Computer Chess Forums|CCRL Discussion Board]], April 15June 01, 20202014</ref> .His original generator could not create them. But in 2018, he supported [[Bojun Guo]] in his 5-month attempt to generated them <ref>[http: Syzygy WDL is double sided, DTZ is single sided//www.talkchess.com/forum/viewtopic. So to know whether a php?t=66797 7-piece position is winningmen Syzygy attempt] by [[Bojun Guo]], [[CCC]], losing or drawn (or cursed)March 10, the engine needs to do only a single probe 2018</ref>. His hardware was estimated at over US$ 90K. In August of a 72018 their creation was completed <ref>[https://syzygy-piece WDL tabletables. (It may in addition have to do some probes of 6info/ Powered by Ronald de Man's Syzygy endgame tablebases, 7-piece WDL tables if any direct captures are availablegenerated by Bojun Guo and a public API hosted by lichess.) If the engine needs to know the DTZ value (which is only necessary when a TB root position has been reached)org], August 19, the probing code may have to do a 1-ply search to get to the "right" side of the DTZ table2018</ref><ref>[http://tablebase. For 6-piece TBs, DTZ is 81lichess.9GB when storing only the smaller side ovh/tables/standard/7/ Index of each table. Storing both sides might require perhaps 240GB/tables/standard/7/ on lichess], August 19, 2018</ref>.
=7-man=Generation of 7-man tablebases would require about 1 TB of RAM. Generation time will be about 64 x per table, which means around 175 x time total <ref>[http://kirill-kryukov.com/chess/discussion-board/viewtopic.php?fChecksums=6&t=7396#p83338 Re: Syzygy tb generator for windows] by [[Ronald de Man|syzygy]], [[Computer Chess Forums|CCRL Discussion Board]], June 01, 2014</ref> . Ronald de Man wasn't initially interested in creation of 7endgame files may contain 128-men Syzygy Based <ref>[http://kirill-kryukov.com/chess/discussion-board/viewtopic.php?f=6&t=7618#p83771 Re: 7-piece syzygy] by [[Ronald de Man|syzygy]], [[Computer Chess Forums|CCRL Discussion Board]], July 03, 2014</ref>. But in 2018, he supported [[Bojun Guo]] in his 5 month attempt to generated them <ref>[http://www.talkchess.com/forum/viewtopic.php?t=66797 7-men Syzygy attempt] by [[Bojun Guo]], [[CCC]], March 10, 2018</ref>. In August bit checksum keys at the end of 2018 their creation was completed<ref>[https://syzygy-tablesthose files.info/ Powered by Ronald de ManIt also has its own code for checksums (based on Google's Syzygy endgame tablebases, 7-piece tables generated by Bojun Guo and a public API hosted by lichess.org], August 19, 2018</ref><ref>[http://tablebase.lichess.ovh/tables/standard/7/ Index of /tables/standard/7/ on lichess], August 19, 2018</ref>cityhash library).
=Search=
==During the Search==
During the [[Search|search]], with the WDL tables stored on [https://en.wikipedia.org/wiki/Solid-state_drive SSD] <ref>[http://www.talkchess.com/forum/viewtopic.php?t=47931&start=2 Re: SSD and the use of Tablebases] by [[Ronald de Man]], [[CCC]], May 08, 2013</ref> , it is possible to probe the tables at all [[Depth|depths]] without much slowdown. They have been tested in Ronald de Man's engine [[Sjaak]] (playing on [[FICS]] as TrojanKnight(C)) a couple of months quite successfully, don't probing in [[Quiescence Search|quiescence search]].
At the [[Root|root]], since pure DTZ50-optimal play (i.e. minimaxing the number of moves to the next [[Captures|capture]] or [[Pawn Push|pawn move]] by either side) can be very unnatural, it might be desirable to let the engine search on the winning moves until it becomes clear that insufficient progress is being made and only then switch to DTZ-optimal play (e.g. by detecting [[Repetitions|repetitions]] and monitoring the [[Halfmove Clock|halfmove clock]]) <ref>[http://www.talkchess.com/forum/viewtopic.php?t=47681&start=8 Re: New 6-piece tablebases] by [[Ronald de Man]], [[CCC]], April 05, 2013</ref>.
=QuotesPros & Cons=by [[Ronald de Man]] in a reply to [[Guy Haworth]], April 06, 2013 <ref>[http://kirill-kryukov.com/chess/discussion-board/viewtopic.php?f=6&t=6971&startPros==6 Re: New 6-piece tablebase generator] by [[Ronald de Man|syzygy]], [[Computer Chess Forums|CCRL Discussion Board]], April 06, 2013</ref> : I create both WDL and DTZ in one go, so I don't use WDL in the creation of DTZ* Small sizes. The algorithm used It is about 8 times as small as the [[Retrograde Analysis#Algorithm|grandfather algorithm]] with 2 plies per iteration (I think [[Harm Geert Muller|HGM]] calls this leapfrogging, but I might be wrong)second-best EGTBs. I tried Having small sizes is the outcounting method, but main success key of Syzygy Bases since it didn't seem is much easier to be competitive (and it makes things more complicated). <ref>[http://www.open-chess.org/viewtopic.php?f=5&t=779 Retrograde tablebase methods] by [[Mark Watkins|BB+]]create, [[Computer Chess Forums|OpenChess Forum]]store, November 26provide, 2010</ref> <ref>[http://home.hccnet.nl/h.g.muller/EGT7/retro.html Leapfrog: Retrograde Analysis] from [http://home.hccnet.nl/h.g.muller/EGT7/7-men.html Leapfrog tablebase generator] by [[Harm Geert Muller]]</ref>download than other EGTBs A pure WDL/DTZ pair is not of much use for creating WDL50+/DTZ50+. I create tables in RAM that have all the information necessary for WDL50+ * Free and DTZ50+, then permute them more popular (than other EGTBs) to different indexing schemes and compress. I do test runs find on subsets of the data to find good permutations. (The idea to try permutations is from Internet* Support [[Jesper Torp Kristensen|Jesper Torp Kristensen's]] master thesis.) <ref>[[Jesper Torp Kristensen]] ('''2005'''). ''[https://issuu.com/jespertk/docs/master_thesis Generation and compression of endgame tables in chess with fast random access using OBDDs]''. Master thesis, supervisor [[MathematicianEndgame Tablebases#MiltersenDTZ50|Peter Bro MiltersenDTZ50]], [https://enmetric.wikipedia.org/wiki/Aarhus_University Aarhus University]</ref> <ref>[https://en.wikipedia.org/wiki/Binary_decision_diagram OBDD - Ordered Binary Decision Diagram from Wikipedia]</ref> =Endgame News= In his 2014 ''Chess Endgame News'' in [[ICGA Journal#37_2|ICGA Journal, Vol. 37, No. 2]] <ref>That metric can help engines to have better results than [[Guy Haworth]] ('''2014'''). ''Chess Endgame News''. [[ICGA JournalTablebases#37_2DTM|ICGA Journal, Vol. 37, No. 2]]</ref> , [[Guy Haworth]] classified Syzygy Bases as '''new''' data in '''three''' ways:# 5-valued scale for evaluating positions in the context of the [[FIDEDTM]] [[Fifty-move Rule|50-move rule]] (50mr) which constrains the length of phases of play## +2 ≡ unconditional win for the side to move## +1 ≡ ‘win’ which can be frustrated is supported widely by best play and a 50mr draw-claim## <span style="color: #ffffff;">_</span>0 ≡ unconditional draw## -1 ≡ ‘loss’ saved by a 50mr draw-claim## -2 ≡ unconditional loss# depths for ‘50mr draw’ positions with value ±1# depths in symmetric, information-preserving ply ‘p’other EGTBs
=ProsData publish=* Small sizes. It is about 8 times as small as the second-best EGTBs. Having small sizes is the main success key of Syzygy Bases since it helps to create, store and provide it much easier than other EGTBs* Free and more popular (than other EGTBs) to find on the Internet* Support [[Endgame Tablebases#DTZ50|DTZ50Ronald de Man]] metrichas provided only open source code for generators/probers but not endgame files themselves. That metric can help engines to Using his tools some people have better results than [[Endgame Tablebases#DTM|DTM]] which is supported widely by other EGTBsgenerated endgames and published them via DVD or online.
=Cons=DVD==* Hard to integrate with chess enginesAs of February 2015, all 3-5 and most important 6-men Syzygy Bases are commercially available on 4 [https://en. wikipedia.org/wiki/DVD DVDs] by [[Ronald de ManChessBase]] has not provided probing code as an independent library. Instead''Endgame Turbo 4'' for their products [[Fritz|Deep Fritz 14]], [[Komodo#8|Komodo Chess 8]], he provided it as a part of [[StockfishHoudini|Houdini 4]] or [[ChessBase (Database)|ChessBase 12/13]] chess engines. The code has integrated too deeply with that chess engine code and it requires a lot of effort to de-integrate<ref>[http://shop. All make the reuse of the code for other chess engines become hard jobs* Hard to understand and contribute to the projectchessbase. ETGB itself is a hard topic. Syzygy EGTB has also integrated with many advance techniquescom/en/products/endspiel_turbo_4 Endgame Turbo 4] by [[ChessBase]]</ref> <ref>[http://tricksen. It is written in old-style C languagechessbase. All make it become very hard to understand andcom/post/or modify to improve or for other purposes* syzygy-tablebases-newest-fastest-smallest Syzygy Tablebases: newest, fastest, smallest] by [[Endgame Tablebases#DTZ50|DTZ50Albert Silver]] metric may lead the engines to win in much longer ways, compared with [[Endgame Tablebases#DTMChessBase|DTMChessBase News]] one, February 08, 2015</ref>.
=Endgame =Free Download==[[Ronald de Man]] has provided only open source code for generators/probers but not endgame files themselves. Using his tools some people have generated endgames and published them online via There are some free FTP servers for downloading such as FTP server of [[Bojun Guo]], and [[Lichess]] serverservers.
===3-6 men===
1) KRPPvKRP 2) KBPPvKBP 3) KPPPvKPP 4) KRPPPvKR 5) KQPPvKQP 6) KNPPvKNP 7) KNPPvKBP 8) KRBPvKRP 9) KQPPvKPP 10) KQPPPvKP
11) KBPPvKNP 12) KRPPvKRB 13) KRPPvKPP 14) KBPPvKRP 15) KRNPvKRP 16) KRBPPvKR 17) KBPPvKPP 18) KRPPPvKP 19) KRBPvKRB 20) KRPPvKRN
=Probe Code and Tools=
==1) Stockfish==
[[Ronald de Man]] did not provide the probe code as an independent library. Instead, he published it firstly as an already integrated code for [[Stockfish]] chess engines. It is c++ code and it has been rewritten, updated several times by [[Stockfish]] team.
==2) Fathom==
'''Fathom''' is a stand-alone Syzygy based probing tool and [https://en.wikipedia.org/wiki/Application_programming_interface API] by [[Basil Falcinelli]], introduced in November 2015 along with his [[Gull|Gull 3]] release <ref>[http://www.talkchess.com/forum/viewtopic.php?t=58299 Gull 3 Linux+Syzygy and Fathom released] by [[Basil Falcinelli]], [[CCC]], November 20, 2015</ref> . Unlike the original tbprobe code, Fathom does not necessarily require the callee to provide [[Move Generation|move generation]] functionality. The new modifications and extensions to Ronald de Man's original code which can be "redistributed and/or modified without restrictions", are released under the permissive [[Massachusetts Institute of Technology#License|MIT License]]. The API consists of three functions <ref>[https://github.com/basil00/Fathom GitHub - basil00/Fathom: Syzygy TB probe tool] by [[Basil Falcinelli]]</ref> :
* tb_init initializes the tablebase
[[Jon Dart]] has a fork of Fathom with some bug fixes and enhancements <ref>[https://github.com/jdart1/Fathom jdart1/Fathom · GitHub] by [[Jon Dart]]</ref>, also supporting 7-man <ref>[http://www.talkchess.com/forum3/viewtopic.php?f=7&t=70568 7-man Syzygy support in Fathom] by [[Jon Dart]], [[CCC]], April 23, 2019</ref>.
==Pyrrhic=='''Pyrrhic''' is a cleaned up Fathom by [[Andrew Grant]], introduced in August 2020 <ref>[http://www.talkchess.com/forum3/viewtopic.php?f=7&t=74809 Pyrrhic, Fathom for Humanoids] by [[Andrew Grant]], [[CCC]], August 16, 2020</ref> <ref>[https://github.com/AndyGrant/Pyrrhic/ GitHub - AndyGrant/Pyrrhic: Fathom, for Humanoids]</ref>. =Elo gain=[[Stockfish#Fishtest|Fishtest]] team revealed a test with [[Stockfish]] (SF10dev) at 10+0.1, with all Syzygy WDL files on RAM, testing using none(0), 4, 5, and 6 man TB in a round-robin tournament<ref>https://github.com/glinscott/fishtest/wiki/UsefulData Collection of useful data concerning SF</ref>. {| class="wikitable"|-! Rank! Name ! Elo ! +/-! Games! Score! Draws|-! 1 | style="text-align:right;" | syzygy6 | style="text-align:right;" | 13 | style="text-align:right;" | 2| style="text-align:right;" | 82591| style="text-align:right;" | 51.8%| style="text-align:right;" | 59.5%|-! 2 | style="text-align:right;" | syzygy5 | style="text-align:right;" | 2 | style="text-align:right;" | 2| style="text-align:right;" | 82590| style="text-align:right;" | 50.3%| style="text-align:right;" | 59.4%|-! 3 | style="text-align:right;" | syzygy4| style="text-align:right;" | -7 | style="text-align:right;" | 2| style="text-align:right;" | 82591| style="text-align:right;" | 49.0%| style="text-align:right;" | 59.3%|-! 4| style="text-align:right;" | syzygy4| style="text-align:right;" | -7| style="text-align:right;" | 2| style="text-align:right;" | 82592| style="text-align:right;" | 48.9%| style="text-align:right;" | 59.4%|} =Quotes=by [[Ronald de Man]] in a reply to [[Guy Haworth]], April 06, 2013 <ref>[http://kirill-kryukov.com/chess/discussion-board/viewtopic.php?f=6&t=6971&start=6 Re: New 6-piece tablebase generator] by [[Ronald de Man|syzygy]], [[Computer Chess Forums|CCRL Discussion Board]], April 06, 2013</ref> : I create both WDL and DTZ in one go, so I don't use WDL in the creation of DTZ. The algorithm used is the [[Retrograde Analysis#Algorithm|grandfather algorithm]] with 2 plies per iteration (I think [[Harm Geert Muller|HGM]] calls this leapfrogging, but I might be wrong). I tried the outcounting method, but it didn't seem to be competitive (and it makes things more complicated). <ref>[http://www.open-chess.org/viewtopic.php?f=5&t=779 Retrograde tablebase methods] by [[Mark Watkins|BB+]], [[Computer Chess Forums|OpenChess Forum]], November 26, 2010</ref> <ref>[http://home.hccnet.nl/h.g.muller/EGT7/retro.html Leapfrog: Retrograde Analysis] from [http://home.hccnet.nl/h.g.muller/EGT7/7-men.html Leapfrog tablebase generator] by [[Harm Geert Muller]]</ref> A pure WDL/DTZ pair is not of much use for creating WDL50+/DTZ50+. I create tables in RAM that have all the information necessary for WDL50+ and DTZ50+, then permute them to different indexing schemes and compress. I do test runs on subsets of the data to find good permutations. (The idea to try permutations is from [[Jesper Torp Kristensen|Jesper Torp Kristensen's]] master thesis.) <ref>[[Jesper Torp Kristensen]] ('''2005'''). ''[https://issuu.com/jespertk/docs/master_thesis Generation and compression of endgame tables in chess with fast random access using OBDDs]''. Master thesis, supervisor [[Mathematician#Miltersen|Peter Bro Miltersen]], [https://en.wikipedia.org/wiki/Aarhus_University Aarhus University]</ref> <ref>[https://en.wikipedia.org/wiki/Binary_decision_diagram OBDD - Ordered Binary Decision Diagram from Wikipedia]</ref> [[Ronald de Man]] in a reply to [[Pham Hong Nguyen|Nguyen Pham]], April 15, 2020 <ref>[http://talkchess.com/forum3/viewtopic.php?f=7&t=73598 Re: Almost perfect DTM tablebase] by [[Dann Corbit]], [[Computer Chess Forums|CCRL Discussion Board]], April 15, 2020</ref> : Syzygy WDL is double sided, DTZ is single sided. So to know whether a 7-piece position is winning, losing or drawn (or cursed), the engine needs to do only a single probe of a 7-piece WDL table. (It may in addition have to do some probes of 6-piece WDL tables if any direct captures are available.) If the engine needs to know the DTZ value (which is only necessary when a TB root position has been reached), the probing code may have to do a 1-ply search to get to the "right" side of the DTZ table. For 6-piece TBs, DTZ is 81.9GB when storing only the smaller side of each table. Storing both sides might require perhaps 240GB. =Endgame News= In his 2014 ''Chess Endgame News'' in [[ICGA Journal#37_2|ICGA Journal, Vol. 37, No. 2]] <ref>[[Guy Haworth]] ('''2014'''). ''Chess Endgame News''. [[ICGA Journal#37_2|ICGA Journal, Vol. 37, No. 2]]</ref> , [[Guy Haworth]] classified Syzygy Bases as '''new''' data in '''three''' ways:# 5-valued scale for evaluating positions in the context of the [[FIDE]] [[Fifty-move Rule|50-move rule]] (50mr) which constrains the length of phases of play## +2 ≡ unconditional win for the side to move## +1 ≡ ‘win’ which can be frustrated by best play and a 50mr draw-claim## <span style="color: #ffffff;">_</span>0 ≡ unconditional draw## -1 ≡ ‘loss’ saved by a 50mr draw-claim## -2 ≡ unconditional loss# depths for ‘50mr draw’ positions with value ±1# depths in symmetric, information-preserving ply ‘p’ and further gives some news about early software bugs and glitches concerning [[ChessBase]] products, and the importance of [https://en.wikipedia.org/wiki/MD5 MD5] to check the EGT integrity.
=See also=
* [http://www.talkchess.com/forum/viewtopic.php?t=60312&start=240 Natural TB (take 2)] by [[Marco Costalba]], [[CCC]], August 22, 2017 » [[Stockfish]]
* [http://www.talkchess.com/forum/viewtopic.php?t=65284 Probing tablebases through USB 3.0] by [[Jon Fredrik Åsvang]], [[CCC]], September 25, 2017 » [[Memory#USB3|USB 3.0]]
* [http://www.talkchess.com/forum/viewtopic.php?t=65390 understanding DTZ] by [[Alexandru Mosoi]], [[CCC]], October 06, 2017 » [[Endgame Tablebases#DTZ|DTZ]], [[Syzygy Bases#Fathom|Fathom]]
* [http://www.talkchess.com/forum/viewtopic.php?t=65713 Is there now coming changes to syzygy databases?] by [[Jouni Uski]], [[CCC]], November 13, 2017 » [[Endgame Tablebases#DTM|DTM]], [[CFish]]
* [http://www.talkchess.com/forum/viewtopic.php?t=66096 How to Download Syzygy Endgame Tablebase Files] by Daniel Johnson, [[CCC]], December 23, 2017
: [http://talkchess.com/forum3/viewtopic.php?f=7&t=66797&start=472 Re: 7-men Syzygy attempt] by [[Bojun Guo]], [[CCC]], August 19, 2018
* [http://www.talkchess.com/forum/viewtopic.php?t=66830 Syzygy implementations of top engines] by [[Kai Laskos]], [[CCC]], March 14, 2018
* [http://www.talkchess.com/forum/viewtopic.php?t=67122 Probing the Syzygy tablebase - beginners question] by [[Andreas Matthies]], [[CCC]], April 16, 2018
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=67536 DTM50] by [[Ronald de Man]], [[CCC]], May 22, 2018
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=68236 Re-Pair compression questions] by [[Rein Halbersma]], [[CCC]], August 17, 2018
'''2019'''
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=70074 Testing the implementation of Syzygy] by [[Vincent Tang]], [[CCC]], March 02, 2019
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=70568 7-man Syzygy support in Fathom] by [[Jon Dart]], [[CCC]], April 23, 2019» [[#Fathom|Fathom]]
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=71397 Simplest use of syzygy table] by [[Vivien Clauzon]], [[CCC]], July 28, 2019
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=71512 SYZYGY question] by [[Robert Hyatt]], [[CCC]], August 11, 2019 » [[Crafty]], [[En passant]]
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=71625 Syzygy 7 man advice please] by Barry Clements, [[CCC]], August 21, 2019
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=71896 Syzygy DTZ data explaination?] by [[Pham Hong Nguyen|Nguyen Pham]], [[CCC]], September 23, 2019
==2020 ...==
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=73598 Almost perfect DTM tablebase] by [[Dann Corbit]], [[CCC]], April 08, 2020
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=74809 Pyrrhic, Fathom for Humanoids] by [[Andrew Grant]], [[CCC]], August 16, 2020 » [[#Pyrrhic|Pyrrhic]]
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=75396 EGTB compression] by [[Dann Corbit]], [[CCC]], October 14, 2020 <ref>[https://en.wikipedia.org/wiki/LZ4_(compression_algorithm) LZ4 (compression algorithm) from Wikipedia]</ref> <ref>[https://en.wikipedia.org/wiki/Zstandard Zstandard from Wikipedia]</ref>
* [http://www.talkchess.com/forum3/viewtopic.php?f=2&t=75487 Syzygy bases ... question to "Syzygy Probe Depth"] by [[Frank Quisinsky]], [[CCC]], October 21, 2020
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=75906 Fathom and 7-men] by [[Joshua Shriver]], [[CCC]], November 24, 2020 » [[#Fathom|Fathom]]
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=75973 Problem with Syzygy tablebase] by [[Elias Nilsson]], [[CCC]], December 03, 2020
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=76010 Can EGTB storage requirements be reduced using this scheme?] by mmt, [[CCC]], December 07, 2020
=External Links=
* [https://github.com/jdart1/Fathom jdart1/Fathom · GitHub] by [[Jon Dart]] (with some bug fixes and enhancements)
* [https://github.com/ljgw/syzygy-bridge GitHub - ljgw/syzygy-bridge: Java bridge to use the Syzygy Tablebases via JNI] by [[Laurens Winkelhagen]] » [[FrankWalter]]
==Pyrrhic==
* [https://github.com/AndyGrant/Pyrrhic/ GitHub - AndyGrant/Pyrrhic: Fathom, for Humanoids] by [[Andrew Grant]]
==Online Lookup==
* [https://www.chessdb.cn/queryc_en/ Chess Cloud Database Query Interface] by [[Bojun Guo|noobpwnftw]] <ref>[http://www.talkchess.com/forum3/viewtopic.php?f=2&t=71764 ChessDBCN] by [[Bojun Guo|noobpwnftw]], [[CCC]], September 09, 2019</ref>
* [https://syzygy-tables.info/ Syzygy endgame tablebases Web Interface]
==ChessBase==
* [https://en.wikipedia.org/wiki/Syzygy_%28mathematics%29 Syzygy (mathematics) from Wikipedia]
* [https://en.wikipedia.org/wiki/Caledonian_Antisyzygy Caledonian Antisyzygy from Wikipedia]
* [[:Category:Michael Brecker|Michael Brecker Band]] - [https://en.wikipedia.org/wiki/Michael_Brecker_(album) Syzygy], August 16[https://www.bjd.sk/archiv-1979-2001#1987 BJD 1987], 1987 at [https://en.wikipedia.org/wiki/Newport_Jazz_Festival Newport Jazz FestivalBratislava Bratislava], [https://en.wikipedia.org/wiki/YouTube YouTube] VideoVideos: [[:Category:Michael Brecker|Michael Brecker]], [[:Category:Mike Stern|Mike Stern]], [https://de-de.facebook.com/JeffAndrewsBassPage/ Jeff Andrews], [https[:Category://en.wikipedia.org/wiki/Adam_Nussbaum Adam Nussbaum|Adam Nussbaum]], [https://en.wikipedia.org/wiki/Joey_Calderazzo Joey Calderazzo]: {{#evu:https://www.youtube.com/watch?v=lgVxFM7cONQcU9aDLOG89o|alignment=left|valignment=top}}: {{#evu:https://www.youtube.com/watch?v=BUcz1YD0Nr8|alignment=left|valignment=top}}
=References=
[[Category:Quotes]]
[[Category:Michael Brecker]]
[[Category:Adam Nussbaum]]
[[Category:Mike Stern]]
