25,161
edits
Changes
no edit summary
'''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==Syzygy Bases consist of two sets of files, '''WDL''' files (extension .rtbw) storing win/draw/loss information considering the [[Fifty-move Rule|fifty-move rule]] for access during [[Search|search]], and '''DTZ''' files (extension .rtbz) with [[Endgame Tablebases#DTZ50|distance-to-zero]] information for access at the [[Root|root]]. WDL has full data for two sides but DTZ50 omitted data of one side to save space. Each endgame has a pair of those types. ==File Sizes==
{| class="wikitable"
|-
|}
=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?fComparision=6&t=7396#p83338 Re: Syzygy tb generator for windows] by EGTB is significantly smaller than any [[Ronald de ManEndgame Tablebases#DTM|syzygyDTM]]EGTB. It is 7 times as small as Gaviota for 5 men, [[Computer Chess Forums|CCRL Discussion Board]]8 times as small as Nalimov for 6 men, June 018 times as small as Lomonosov for 7 men. However, 2014</ref> . Ronald de Man wasn't initially interested in creation when all DTM EGTBs have full data of 7-men two sides, Syzygy Based <ref>[http://kirill-kryukov.com/chess/discussion-board/viewtopicEGTB omits data of one side for DTZ data to save space.php?f=6&t=7618#p83771 Re: 7-piece syzygy] by [[Ronald de Man|syzygy]]estimated if keep them all, [[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 the Syzygy attempt] by [[Bojun Guo]], [[CCC]], March 10, 2018</ref>. In August of 2018 their creation was completed<ref>[https://syzygy-tables.info/ Powered by Ronald de Man's Syzygy endgame tablebases6 men size may increase 158 GB, 7-piece tables generated by Bojun Guo and a public API hosted by lichess.org], August 19become 307 GB in total, 2018</ref><ref>[http://tablebase.lichess.ovh/tables/standard/7/ Index of /tables/standard/7/ double on lichess]size, August 19, 2018</ref>4 times as small as Nalimov 6 men.
=During the SearchGeneration= During the [[Search|search]], with the WDL tables stored on [https://en.wikipedia.org/wiki/Solid==Up to 6-state_drive SSD] <ref>[http://www.talkchess.com/forum/viewtopic.php?tman=47931&start=2 Re: SSD and On the use of Tablebases] by [[Ronald de Man]], [[CCC]], May 08first release (Apr 01, 2013</ref> ) 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 is possible to probe the tables requires a system with at all [[Depth|depths]] without much slowdown. They have been tested least 32 GB of RAM and may run in Ronald de Man's engine [[Sjaak]] 5 days (playing on [[FICS]] as TrojanKnight(C)) the period was measured with a couple of months quite successfullycomputer 6-core i3930K @ 4.2Ghz, don't probing in [[Quiescence Search|quiescence search]]64 GB).
=At the Root=7-man== At Ronald de Man wasn't initially interested in the creation of 7-men Syzygy Based <ref>[[Root|root]], since pure DTZ50http://kirill-optimal play (ikryukov.ecom/chess/discussion-board/viewtopic. minimaxing the number of moves to the next php?f=6&t=7618#p83771 Re: 7-piece syzygy] by [[CapturesRonald de Man|capturesyzygy]] or , [[Pawn PushComputer Chess Forums|pawn moveCCRL Discussion Board]] by either side) can be very unnatural, it might be desirable to let July 03, 2014</ref> since the engine search on the winning moves until it becomes clear generation would require about 1 TB of RAM, too expensive at that insufficient progress is being made and only then switch to DTZtime. Generation time would be about 64 x per table, which means around 175 x time total <ref>[http://kirill-optimal play (ekryukov.gcom/chess/discussion-board/viewtopic. php?f=6&t=7396#p83338 Re: Syzygy tb generator for windows] by detecting [[RepetitionsRonald de Man|repetitionssyzygy]] and monitoring the , [[Halfmove ClockComputer Chess Forums|halfmove clockCCRL Discussion Board]]) , June 01, 2014</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://www.talkchess.com/forum/viewtopic.php?t=47681&start=8 Re: New 666797 7-piece tablebasesmen Syzygy attempt] by [[Ronald de ManBojun Guo]], [[CCC]], April 05March 10, 2018</ref>. His hardware was estimated at over US$ 90K. In August of 2018 their creation was completed <ref>[https://syzygy-tables.info/ Powered by Ronald de Man'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, 20132018</ref> .
=Quotes= by [[Ronald de Man]] in a reply to [[Guy Haworth]], April 06, 2013 <ref>[http://kirill-kryukov.com/chess/discussion-board/viewtopic.php?fChecksums=6&t=6971&start=6 Re: New 6Syzygy endgame files may contain 128-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 bit checksum keys at the creation end of DTZthose files. The algorithm used is the [[Retrograde Analysis#Algorithm|grandfather algorithm]] with 2 plies per iteration It also has its own code for checksums (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 based on subsets of the data to find good permutations. (The idea to try permutations is from [[Jesper Torp Kristensen|Jesper Torp KristensenGoogle's]] master thesis.) <ref>[[Jesper Torp Kristensen]] ('''2005'''cityhash library). ''[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>
=Endgame NewsSearch= In his 2014 ''Chess Endgame News'' in ==During the Search== During the [[ICGA Journal#37_2Search|ICGA Journalsearch]], Volwith the WDL tables stored on [https://en. 37, Nowikipedia. 2]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 [[Guy HaworthRonald de Man]] ('''2014'''). ''Chess Endgame News''. , [[ICGA Journal#37_2|ICGA JournalCCC]], Vol. 37May 08, No. 2]]2013</ref> , it is possible to probe the tables at all [[Guy HaworthDepth|depths]] classified Syzygy Bases as '''new''' data without much slowdown. They have been tested in Ronald de Man'''three''' ways:# 5-valued scale for evaluating positions in the context of the s engine [[FIDESjaak]] (playing on [[Fifty-move Rule|50-move ruleFICS]] as TrojanKnight(50mrC) which constrains the length ) a couple 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 months quite successfully, don't probing in symmetric, information-preserving ply ‘p’[[Quiescence Search|quiescence search]].
==At the Root== 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 further gives some news about early software bugs and glitches concerning only then switch to DTZ-optimal play (e.g. by detecting [[ChessBaseRepetitions|repetitions]] products, and monitoring the importance of [https[Halfmove Clock|halfmove clock]]) <ref>[http://enwww.wikipediatalkchess.orgcom/wikiforum/MD5 MD5] to check the EGT integrityviewtopic.<span idphp?t=47681&start="Fathom">8 Re: New 6-piece tablebases] by [[Ronald de Man]], [[CCC]], April 05, 2013</spanref>.
=Pros& Cons===Pros==* 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 is much easier to create, store and , provide it much easier , download than other EGTBs
* Free and more popular (than other EGTBs) to find on the Internet
* Support [[Endgame Tablebases#DTZ50|DTZ50]] metric. That metric can help engines to have better results than [[Endgame Tablebases#DTM|DTM]] which is supported widely by other EGTBs
==Cons==* Hard to integrate with chess engines. [[Ronald de Man]] has not provided probing code as an independent library. Instead, he provided it but as a part of [[Stockfish]] chess engines. The probe code has integrated too deeply with that chess engine code and it requires a lot of effort to de-integrate. All make the reuse of the code for , modify and integrate with other chess engines become hard jobsprojects* Hard to understand and contribute to the project. ETGB itself is a hard topic. Syzygy EGTB has also integrated with many advance advanced techniques/tricks. It is written in old-style C language. All make it become very hard to understand and/or modify to improve or for other purposes* [[Endgame Tablebases#DTZ50|DTZ50]] metric may lead the engines to win in much longer and ugly ways, compared with [[Endgame Tablebases#DTM|DTM]] one
=Endgame DownloadData publish=[[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 via DVD or online via . ==DVD==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>. ==Free Download==There are some free FTP servers for downloading such as FTP server of [[Bojun Guo]], and [[Lichess]] serverservers. ===3-6 men===The sizes of those men are small enough to download and store on modern computers. Users should download them in full sets (3, 4, 5, 6 men).
===7 men===
All 7 men files' size is over 16.7 TiB, over storages of normal typical modern computers. They also require a long time to download too. Thus some users choose to download one or a few endgames only, based on their statistics of use in endgames. Bellow is the top 20 of those endgames by their order. The first one, KRPPvKRP, has a significantly higher frequency of use than the others.and should be always downloaded:
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 =Checksums= Syzygy endgame files may contain 128-bit checksum keys at the end of those files. It also has its own code for checksums (based on Google's cityhash library).
=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://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
* [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
* [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
=External Links=
==Tablebase==
* [https://github.com/syzygy1/tb syzygy1/tb · GitHub] by [[Ronald de Man]]
* [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/Caledonian_Antisyzygy Caledonian Antisyzygy from Wikipedia]
* [[:Category:Michael Brecker|Michael Brecker Band]] - [https://en.wikipedia.org/wiki/Michael_Brecker_(album) Syzygy], August 16, 1987 at [https://en.wikipedia.org/wiki/Newport_Jazz_Festival Newport Jazz Festival], [https://en.wikipedia.org/wiki/YouTube YouTube] Video
: [[:Category:Michael Brecker|Michael Brecker]], [[:Category:Mike Stern|Mike Stern]], [https://de-de.facebook.com/JeffAndrewsBassPage/ Jeff Andrews], [https[://en.wikipedia.org/wiki/Adam_Nussbaum Category:Adam Nussbaum|Adam Nussbaum]], [https://en.wikipedia.org/wiki/Joey_Calderazzo Joey Calderazzo]
: {{#evu:https://www.youtube.com/watch?v=lgVxFM7cONQ|alignment=left|valignment=top}}
[[Category:Quotes]]
[[Category:Michael Brecker]]
[[Category:Adam Nussbaum]]
[[Category:Mike Stern]]
