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<span id="MultipleTables"></span>
=Multiple Tables=
Most modern programs, influenced by [[Fruit]], use two sets of tables. One for the [[Opening|opening]] of the game and another for the [[Endgame|endgame]]. The final evaluation is them then [[Tapered Eval|interpolated]] between these two based on [[Game Phases|game stage]] (often [[Material|material]] on the board). This allows for changes in material as well, since the material part of the evaluation can also be stored in these tables. Using two tables also lets pieces change in evaluation as the game proceeds. For example, [[Pawn|pawns]] can gain in value in the endgame using this method.
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=Pre-processing=
With today's search depth this approach seems to be impractical, since the difference between the root and leaf position may be very big. There also might be a problem with re-using hash scores from the previous entries. About the only recent chess program that sticks with pre-processing for good or bad is [[RomiChess]] <ref>[https://www.stmintz.com/ccc/index.php?id=18203 Re: What is "pre-processing"] by [[Ulrich Türke]], [[CCC]], May 08, 1998</ref> <ref>[https://www.stmintz.com/ccc/index.php?id=18213 Re: What is "pre-processing"] by [[Amir Ban]], [[CCC]], May 08, 1998</ref>.
=ExampleExamples= Material and piece-square tables alone are enough for a program to play a semi-decent game of chess. Indeed, [[Tomasz Michniewski]] advocated a method of testing requiring all the tested programs to have identical, simplistic evaluation function, so that only search and efficiency issues would influence the result. One such tournament has been carried out in Poland.[[Ronald Friederich]] improved this approach using a [[Tapered Eval]] and [[Texel's Tuning Method|Texel's tuning method]] as applied in [[RofChade]] and [[PeSTO]].
* [[Simplified Evaluation Function]]
* [[PeSTO's Evaluation Function]]
=See also=
* [[Oracle]]
* [[Space]]
* [[Tapered Eval]]
=Publications=
* [http://www.talkchess.com/forum/viewtopic.php?t=51518 SEE logic] by [[Youri Matiounine]], [[CCC]], March 08, 2014 » [[Static Exchange Evaluation]]
* [http://www.talkchess.com/forum/viewtopic.php?t=52861 multi-dimensional piece/square tables] by [[Pawel Koziol]], [[CCC]], July 04, 2014
: [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=52861&start=8 7 Re: multi-dimensional piece/square tables] by Tony P., [[CCC]], January 28, 2020» [[Automated Tuning]]
==2015 ...==
* [http://www.talkchess.com/forum/viewtopic.php?t=57384 about pst] by [[Daniel Anulliero]], [[CCC]], August 26, 2015
* [http://www.talkchess.com/forum/viewtopic.php?t=66588 Learning piece-square table] by [[Mathieu Pagé]], [[CCC]], February 13, 2018 » [[Automated Tuning]]
* [http://www.talkchess.com/forum/viewtopic.php?t=66966 'ab-initio' piece values] by [[Harm Geert Muller]], [[CCC]], March 30, 2018 » [[Point Value]]
* [http://www.talkchess.com/forum3/viewtopic.php?f=2&t=68311&start=19 Re: New uci engine: Rofchade] by [[Ronald Friederich]], [[CCC]], August 28, 2018 » [[RofChade]], [[Tapered Eval]]
==2020 ...==
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=73865 PST for FRC] by [[Vivien Clauzon]], [[CCC]], May 07, 2020 » [[Chess960]]
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=74752 Using piece-square table score for move ordering] by [[Maksim Korzh]], [[CCC]], August 11, 2020 » [[Move Ordering]]
* [https://prodeo.actieforum.com/t120-engine-choosing-between-sets-of-piece-square-tables Engine choosing between sets of piece/square tables] by [[Pawel Koziol|nescitus]], [[Computer Chess Forums|ProDeo Forum]], December 05, 2020
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=76256 Piece square tables] by [[Elias Nilsson]], [[CCC]], January 08, 2021
* [https://prodeo.actieforum.com/t252-little-fun-with-tscp little fun with TSCP] by [[Pawel Koziol|nescitus]], [[Computer Chess Forums|ProDeo Forum]], February 12, 2021 » [[TSCP]], [[PeSTO's Evaluation Function]]
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=76831 The PSTs of Carnivor] by [[Michael Sherwin|Mike Sherwin]], [[CCC]], March 10, 2021
* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=77089 PST-only Evaluation for MinimalChess 0.4] by [[Thomas Jahn]], [[CCC]], April 15, 2021 » [[MinimalChess]]
=External Links=
* [http://home.hccnet.nl/h.g.muller/pcsqr.html Evaluation: Piece-Square Tables] from [[Micro-Max]] by [[Harm Geert Muller]]
* Cage. Music, art, chess - Film by Brian Brandt with [https://en.wikipedia.org/wiki/Margaret_Leng_Tan Margaret Leng Tan] and [https://www.linkedin.com/in/larry-list-937b888 Larry List], [https://en.wikipedia.org/wiki/Noguchi_Museum Noguchi Museum] <ref>[https://shop.noguchi.org/imofchre.html The Imagery of Chess Revisited]</ref> <ref>[https://www.youtube.com/watch?v=vegmCb9j4kE Discovering The Imagery of Chess featuring Larry List], 2017, [https://en.wikipedia.org/wiki/YouTube YouTube] Video </ref> <ref>[http://www.edochess.ca/batgirl/Imagery_of_Chess3.html The Imagery of Chess -Surrealism and Chess]</ref>, 2006, [https://en.wikipedia.org/wiki/YouTube YouTube] Video
: {{#evu:https://www.youtube.com/watch?v=Hva8WMcRyOE|alignment=left|valignment=top}}
