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KRK
,Created page with "'''Home * Evaluation * Game Phases * Endgame * KRK''' {| |- style="vertical-align:top;" | rowspan="2" | '''KRK''',<br/> the King and Rook ve..."
'''[[Main Page|Home]] * [[Evaluation]] * [[Game Phases]] * [[Endgame]] * KRK'''
{|
|- style="vertical-align:top;"
| rowspan="2" | '''KRK''',<br/>
the [[King]] and [[Rook]] versus King endgame is beside KQR the most elementary endgame with three pieces. If the rook can not be captured immediately - or the losing king isn't [[Stalemate|stalemated]], [[Checkmate|checkmate]] can be forced by driving the losing king to the edge or corner of the board, the rook giving mate similar to the [[Mate at a Glance##MatesWithSlidingPieces|back-rank mate]], the winning king locking all escape squares, often initiated by a rook [[Tempo|tempo]] move to force the king into [[Opposition|opposition]].
| <fentt border="double" style="font-size:24pt">4k3/8/3K4/5R2/8/8/8/8</fentt>
|-
| KRK Mate in Two
|}
=Heuristics=
Simple heuristics of a [[Mop-up Evaluation|mop-up evaluation]] <ref>[[David Slate]], [[Larry Atkin]] ('''1977'''). ''CHESS 4.5 - The Northwestern University Chess Program.'' [[Chess Skill in Man and Machine]], reprinted ('''1988''') in [[Computer Chess Compendium]]</ref>, only considering [[Center Manhattan-Distance|Center Manhattan-distance]] of the losing king, and [[Distance|Chebyshev distance]] and/or [[Manhattan-Distance|Manhattan distance]] between both kings, along with a tiny [[Search|search]], should be sufficient to execute the mate. Further, the rook may receive a bonus to maximize the absolute difference of its [[Ranks#RankDistance|rank-]] and [[Files#FileDistance|file-distances]] to the losing king, to confine the king without becoming attacked.
Despite todays engines have no difficulty to win this easily even without [[Endgame Tablebases|tablebases]], deviation from optimal tablebase play, in particular in games with short time control, and most compact and efficient code considering symptoms of [[Search Pathology|search pathology]] remain interesting issues <ref>[http://www.talkchess.com/forum/viewtopic.php?t=54295 Why minimax is fundamentally flawed] by [[Harm Geert Muller]], [[CCC]], November 09, 2014</ref>.
=Testbed=
First implemented by [[Leonardo Torres y Quevedo]] in [[Timeline#1912|1912]] within his electro-mechanical KRK solver [[El Ajedrecista]], KRK was and still is [https://en.wikipedia.org/wiki/Testbed testbed] and subject of research on [[Evaluation|evaluation]] and [[Search|search]] heuristics and strategies, [[Oracle|oracle approaches]], [[Mate Search|mate search]], [[Search Pathology|search pathology]], [[Knowledge|search versus knowledge]], [[Space-Time Tradeoff|space-time tradeoff]], [[Retrograde Analysis|retrograde analysis]] and [[Endgame Tablebases|tablebase generation]] <ref>[[Thomas Ströhlein]] ('''1970'''). ''Untersuchungen über kombinatorische Spiele.'' Ph.D. Thesis, [[Technical University of Munich]] (German)</ref>, [https://en.wikipedia.org/wiki/Knowledge_extraction knowledge extraction] and [https://en.wikipedia.org/wiki/Data_compression compression], feature detection and [[Automated Tuning|tuning]], [[Learning|learning]] <ref>[[Michael Bain]] ('''1994'''). ''Learning Logical Exceptions in Chess''. Ph.D. thesis, [https://en.wikipedia.org/wiki/University_of_Strathclyde University of Strathclyde]</ref>, [[Genetic Programming|genetic programming]], [[Pattern Recognition|pattern recognition]], [https://en.wikipedia.org/wiki/Decision_tree decision trees], [https://en.wikipedia.org/wiki/Logic logic] and [https://en.wikipedia.org/wiki/Logic_programming logic programming] <ref>[[Ivan Bratko]] ('''2001,2010'''). ''[http://www.worldcat.org/search?qt=wikipedia&q=isbn%3A0201403757 Prolog programming for artificial intelligence]''. Harlow England, [https://en.wikipedia.org/wiki/Addison-Wesley Addison Wesley]</ref>, [https://en.wikipedia.org/wiki/Inductive_reasoning inductive] and [https://en.wikipedia.org/wiki/Deductive_reasoning deductive reasoning], [https://en.wikipedia.org/wiki/Rule-based_modeling rule-based modeling], [https://en.wikipedia.org/wiki/Problem_solving problem solving] and [https://en.wikipedia.org/wiki/Boolean_satisfiability_problem SAT] <ref> [[Marko Maliković]], [[Predrag Janičić]] ('''2013'''). ''Proving Correctness of a KRK Chess Endgame Strategy by SAT-based Constraint Solving''. [[ICGA Journal#36_2|ICGA Journal, Vol. 36, No. 2]]</ref>. In 1977, [[Donald Michie]] addressed KRK and the [[Infinite Board|infinite board]] <ref>[[Donald Michie]] ('''1977'''). ''King and Rook Against King: Historical Background and a Problem on the Infinite Board''. [[Advances in Computer Chess 1]]</ref>.
=See also=
* [[Center Manhattan-Distance]]
* [[El Ajedrecista]]
* [[Distance]]
* [[Endgame Tablebases]]
* [[Huberman|Huberman's program]]
* [[Infinite Board]]
* [[Interior Node Recognizer]]
* [[KPK]]
* [[Knowledge]]
* [[Michael Bain#LearningKRK|Learning KRK]]
* [[Manhattan-Distance]]
* [[Mate Search]]
* [[Mop-up Evaluation]]
* [[Oracle]]
* [[Retrograde Analysis]]
* [[Rook Endgame]]
* [[Search Pathology]]
* [[Space-Time Tradeoff]]
* [[Tempo]]
* [[Triangulation]]
* [[Zugzwang]]
=Selected Publications=
==1914==
* [[Henri Vigneron]] ('''1914'''). ''Les Automates''. [https://en.wikipedia.org/wiki/La_Nature La Nature], [http://cyberneticzoo.com/wp-content/uploads/2011/01/Automates-La-Nature-Torres-1914.pdf pdf] from [http://cyberneticzoo.com/ cyberneticzoo.com], Translation by [[David Levy]] as ''Robots'' in [[David Levy]], [[Monroe Newborn]] ('''1982'''). ''All About Chess and Computers''. [https://en.wikipedia.org/wiki/Springer_Science%2BBusiness_Media Springer], pp. 14-23, also in [[David Levy]] (ed.) ('''1988'''). ''[[Computer Chess Compendium]]'', pp. 273-278.
==1960 ...==
* [[Barbara Liskov|Barbara J. Huberman]] ('''1968'''). ''A Program to Play Chess End Games''. Technical Report no. CS-106, Ph.D. thesis. [[Stanford University]], Computer Science Department
==1970 ...==
* [[Thomas Ströhlein]] ('''1970'''). ''Untersuchungen über kombinatorische Spiele.'' Ph.D. Thesis, [[Technical University of Munich]] (German)
* [[Soei Tan|Soei T. Tan]] ('''1972'''). ''Representation of Knowledge for Very simple Endings in Chess.'' Memorandum MIP-R-98, School of Artificial Intelligence, [[University of Edinburgh]]
* [[Coen Zuidema]] ('''1974'''). ''Chess: How to Program the Exceptions?'' Technical Report IW21/74, Department of Informatics, [https://en.wikipedia.org/wiki/Centrum_Wiskunde_%26_Informatica Mathematical Center Amdsterdam]. [http://oai.cwi.nl/oai/asset/9480/9480A.pdf pdf]
* [[Donald Michie]] ('''1977'''). ''King and Rook Against King: Historical Background and a Problem on the Infinite Board''. [[Advances in Computer Chess 1]]
* [[David Slate]], [[Larry Atkin]] ('''1977'''). ''CHESS 4.5 - The Northwestern University Chess Program.'' [[Chess Skill in Man and Machine]], reprinted ('''1988''') in [[Computer Chess Compendium]]
* [[Ivan Bratko]] ('''1978'''). ''Proving Correctness of Strategies in the AL1 Assertional Language''. Information Processing Letters, Vol. 7, No. 5, pp. 223-230. <ref>[[Donald Michie]] ('''1976'''). ''[http://portal.acm.org/citation.cfm?id=1045272 AL1: a package for generating strategies from tables]''. ACM SIGART Bulletin, Issue 59</ref>
* [[Thomas Ströhlein]], [[Ludwig Zagler]] ('''1978'''). ''Ergebnisse einer vollstandigen Analyse von Schachendspielen: König und Turm gegen König, König und Turm gegen König und Läufer.'' Report, Institut für Informatik, [[Technical University of Munich]] (German)
==1980 ...==
* [[Ross Quinlan]] ('''1983, 1985'''). ''Learning efficient classification procedures and their application to chess end games''. Machine Learning: An Artificial Intelligence Approach
* [[David Slate]] ('''1984'''). ''Interior-node Score Bounds in a Brute-force Chess Program.'' [[ICGA Journal#7_4|ICCA Journal, Vol. 7, No. 4]]
* [[Reiner Seidel]] ('''1986'''). ''Deriving Correct Pattern Descriptions and Rules for the KRK Endgame by Deductive Methods''. [[Advances in Computer Chess 4]]
* [[Stephen Muggleton]] ('''1987'''). ''Duce, an oracle-based approach to constructive induction''. Proceedings of the 10th IJCAI Conference, Milano, Italy. [http://www.doc.ic.ac.uk/%7Eshm/Papers/ijcai87.pdf pdf]
* [[Stephen Muggleton]], [[Michael Bain]], [[Jean Hayes Michie]], [[Donald Michie]] ('''1989'''). ''An Experimental Comparison of Human and Machine Learning Formalisms''. [http://www.informatik.uni-trier.de/~ley/db/conf/icml/ml1989.html#MuggletonBMM89 6. ML 1989], [http://www.doc.ic.ac.uk/~shm/Papers/ml6paper.pdf pdf]
==1990 ...==
* [[Stephen Muggleton]] ('''1991'''). ''Inductive Logic Programming''. [http://www.springer.com/computer/ai/journal/354 New Generation Computing], Vol. 8, pp. 295-318. ISSN 0228-3635.
* [[Michael Bain]] ('''1992'''). ''Learning optimal chess strategies.'' [http://www.cs.york.ac.uk/ILP-events/ILP-1992/ ILP92]
* [[Ashwin Srinivasan]], [[Stephen Muggleton]], [[Michael Bain]] ('''1992'''). ''Distinguishing Noise from Exceptions in Non-monotonic Learning''. [http://www.cs.york.ac.uk/ILP-events/ILP-1992/ ILP92]
* [[Michael Bain]] ('''1994'''). ''Learning Logical Exceptions in Chess''. Ph.D. thesis, [https://en.wikipedia.org/wiki/University_of_Strathclyde University of Strathclyde], [http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.54.729 CitySeerX]
* [[Ulrich Thiemonds]] ('''1999'''). ''Ein regelbasiertes Spielprogramm für Schachendspiele''. [https://en.wikipedia.org/wiki/University_of_Bonn University of Bonn], [https://en.wikipedia.org/wiki/Diplom Diplom] thesis, [http://www.iai.uni-bonn.de/~idb/diplomarbeiten/thiemonds99.ps.gz zipped ps], [http://idb.informatik.uni-bonn.de/publications/da/da_thiemonds_1999.pdf pdf] (German) <ref>[http://idb.informatik.uni-bonn.de/publications/DA Diploma Theses — IDB]</ref> <ref>[http://www.iai.uni-bonn.de/~idb/ehemaligedipl.html Uni Bonn - AG Intelligente Datenbanken - Was sind intelligente Datenbanken?]</ref>
==2000 ...==
* [[Ivan Bratko]] ('''2001,2010'''). ''[http://www.worldcat.org/search?qt=wikipedia&q=isbn%3A0201403757 Prolog programming for artificial intelligence]''. Harlow England, [https://en.wikipedia.org/wiki/Addison-Wesley Addison Wesley]
* [[David Gleich]] ('''2003'''). ''Machine Learning in Computer Chess: Genetic Programming and KRK''. [https://en.wikipedia.org/wiki/Harvey_Mudd_College Harvey Mudd College], [http://www.cs.purdue.edu/homes/dgleich/publications/Gleich%202003%20-%20Machine%20Learning%20in%20Computer%20Chess.pdf pdf]
* [[Aleksander Sadikov]], [[Ivan Bratko]], [[Igor Kononenko]] ('''2003'''). ''Search versus Knowledge: An Empirical Study of Minimax on KRK''. [[Advances in Computer Games 10]], [http://www.ailab.si/sasha/acg2003.pdf pdf]
* [[Aleksander Sadikov]], [[Ivan Bratko]], [[Igor Kononenko]] ('''2005'''). ''[http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V1G-4HCN79X-1&_user=10&_coverDate=12%2F14%2F2005&_rdoc=1&_fmt=high&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=79f966215bea9b7461b6877c9373b0bf Bias and pathology in minimax search]''. Theoretical Computer Science, Volume 349, Issue 2, [http://lkm.fri.uni-lj.si/xaigor/slo/clanki/Sadikov_final.pdf pdf]
* [[Gabriel Breda]] ('''2006'''). ''KRK Chess Endgame Database Knowledge Extraction and Compression''. Diploma thesis, [[Darmstadt University of Technology]]
* [[Nicolas Lassabe]], [[Stéphane Sanchez]], [[Hervé Luga]], [[Yves Duthen]] ('''2006'''). ''[http://www.sciweavers.org/publications/genetically-programmed-strategies-chess-endgame Genetically Programmed Strategies For Chess Endgame]''. [http://www.sigevo.org/gecco-2006/ GECCO 2006], [http://www.cs.york.ac.uk/rts/docs/GECCO_2006/docs/p831.pdf pdf]
==2010 ...==
* [[Marko Maliković]], [[Mirko Čubrilo]], [[Predrag Janičić]] ('''2012'''). ''Formal Analysis of Correctness of a Strategy for the KRK Chess Endgame''. [http://argo.matf.bg.ac.rs/events/2012/fatpa2012/fatpa2012.html Fifth Workshop on Formal and Automated Theorem Proving and Applications], [https://en.wikipedia.org/wiki/Belgrade Belgrade], [https://en.wikipedia.org/wiki/Serbia Serbia], [http://argo.matf.bg.ac.rs/events/2012/fatpa2012/slides/MarkoMalikovic.pdf slides as pdf]
* [[Marko Maliković]], [[Predrag Janičić]] ('''2013'''). ''Proving Correctness of a KRK Chess Endgame Strategy by SAT-based Constraint Solving''. [[ICGA Journal#36_2|ICGA Journal, Vol. 36, No. 2]]
=Forum Posts=
* [http://www.talkchess.com/forum/viewtopic.php?t=47477 My program can't mate KQK or KRK!] by [[Rasjid Chan]], [[CCC]], March 11, 2013
* [http://stackoverflow.com/questions/15988069/chess-task-king-rook-vs-king algorithm - Chess task - King, Rook Vs King] by [http://stackoverflow.com/users/1448316/sreekanth-karumanaghat Sreekanth Karumanaghat], [https://en.wikipedia.org/wiki/Stack_Overflow Stack Overflow], April 13, 2013
* [http://www.talkchess.com/forum/viewtopic.php?t=54295 Why minimax is fundamentally flawed] by [[Harm Geert Muller]], [[CCC]], November 09, 2014 » [[Minimax]]
=External Links=
* [http://www.gilith.com/chess/endgames/kr_k.html Longest mate in King and Rook versus King endgame] by [[Joe Leslie-Hurd]], February 16, 2005
* [http://archive.ics.uci.edu/ml/datasets/Chess+%28King-Rook+vs.+King%29 UCI Machine Learning Repository: Chess (King-Rook vs. King) Data Set] by [[Michael Bain]]
* [https://en.wikipedia.org/wiki/Checkmate#King_and_rook Checkmate - King and rook - Wikipedia]
* [http://www.wikihow.com/Mate-With-King-and-Rook-Vs-King How to Mate With King and Rook Vs King: 19 Steps - wikiHow]
* [http://www.chesscorner.com/tutorial/basic/r_k_mate/r_k_mate.htm Chess Corner - Chess Tutorial - Checkmating with Lone Rook]
=References=
<references />
'''[[Endgame|Up one Level]]'''
{|
|- style="vertical-align:top;"
| rowspan="2" | '''KRK''',<br/>
the [[King]] and [[Rook]] versus King endgame is beside KQR the most elementary endgame with three pieces. If the rook can not be captured immediately - or the losing king isn't [[Stalemate|stalemated]], [[Checkmate|checkmate]] can be forced by driving the losing king to the edge or corner of the board, the rook giving mate similar to the [[Mate at a Glance##MatesWithSlidingPieces|back-rank mate]], the winning king locking all escape squares, often initiated by a rook [[Tempo|tempo]] move to force the king into [[Opposition|opposition]].
| <fentt border="double" style="font-size:24pt">4k3/8/3K4/5R2/8/8/8/8</fentt>
|-
| KRK Mate in Two
|}
=Heuristics=
Simple heuristics of a [[Mop-up Evaluation|mop-up evaluation]] <ref>[[David Slate]], [[Larry Atkin]] ('''1977'''). ''CHESS 4.5 - The Northwestern University Chess Program.'' [[Chess Skill in Man and Machine]], reprinted ('''1988''') in [[Computer Chess Compendium]]</ref>, only considering [[Center Manhattan-Distance|Center Manhattan-distance]] of the losing king, and [[Distance|Chebyshev distance]] and/or [[Manhattan-Distance|Manhattan distance]] between both kings, along with a tiny [[Search|search]], should be sufficient to execute the mate. Further, the rook may receive a bonus to maximize the absolute difference of its [[Ranks#RankDistance|rank-]] and [[Files#FileDistance|file-distances]] to the losing king, to confine the king without becoming attacked.
Despite todays engines have no difficulty to win this easily even without [[Endgame Tablebases|tablebases]], deviation from optimal tablebase play, in particular in games with short time control, and most compact and efficient code considering symptoms of [[Search Pathology|search pathology]] remain interesting issues <ref>[http://www.talkchess.com/forum/viewtopic.php?t=54295 Why minimax is fundamentally flawed] by [[Harm Geert Muller]], [[CCC]], November 09, 2014</ref>.
=Testbed=
First implemented by [[Leonardo Torres y Quevedo]] in [[Timeline#1912|1912]] within his electro-mechanical KRK solver [[El Ajedrecista]], KRK was and still is [https://en.wikipedia.org/wiki/Testbed testbed] and subject of research on [[Evaluation|evaluation]] and [[Search|search]] heuristics and strategies, [[Oracle|oracle approaches]], [[Mate Search|mate search]], [[Search Pathology|search pathology]], [[Knowledge|search versus knowledge]], [[Space-Time Tradeoff|space-time tradeoff]], [[Retrograde Analysis|retrograde analysis]] and [[Endgame Tablebases|tablebase generation]] <ref>[[Thomas Ströhlein]] ('''1970'''). ''Untersuchungen über kombinatorische Spiele.'' Ph.D. Thesis, [[Technical University of Munich]] (German)</ref>, [https://en.wikipedia.org/wiki/Knowledge_extraction knowledge extraction] and [https://en.wikipedia.org/wiki/Data_compression compression], feature detection and [[Automated Tuning|tuning]], [[Learning|learning]] <ref>[[Michael Bain]] ('''1994'''). ''Learning Logical Exceptions in Chess''. Ph.D. thesis, [https://en.wikipedia.org/wiki/University_of_Strathclyde University of Strathclyde]</ref>, [[Genetic Programming|genetic programming]], [[Pattern Recognition|pattern recognition]], [https://en.wikipedia.org/wiki/Decision_tree decision trees], [https://en.wikipedia.org/wiki/Logic logic] and [https://en.wikipedia.org/wiki/Logic_programming logic programming] <ref>[[Ivan Bratko]] ('''2001,2010'''). ''[http://www.worldcat.org/search?qt=wikipedia&q=isbn%3A0201403757 Prolog programming for artificial intelligence]''. Harlow England, [https://en.wikipedia.org/wiki/Addison-Wesley Addison Wesley]</ref>, [https://en.wikipedia.org/wiki/Inductive_reasoning inductive] and [https://en.wikipedia.org/wiki/Deductive_reasoning deductive reasoning], [https://en.wikipedia.org/wiki/Rule-based_modeling rule-based modeling], [https://en.wikipedia.org/wiki/Problem_solving problem solving] and [https://en.wikipedia.org/wiki/Boolean_satisfiability_problem SAT] <ref> [[Marko Maliković]], [[Predrag Janičić]] ('''2013'''). ''Proving Correctness of a KRK Chess Endgame Strategy by SAT-based Constraint Solving''. [[ICGA Journal#36_2|ICGA Journal, Vol. 36, No. 2]]</ref>. In 1977, [[Donald Michie]] addressed KRK and the [[Infinite Board|infinite board]] <ref>[[Donald Michie]] ('''1977'''). ''King and Rook Against King: Historical Background and a Problem on the Infinite Board''. [[Advances in Computer Chess 1]]</ref>.
=See also=
* [[Center Manhattan-Distance]]
* [[El Ajedrecista]]
* [[Distance]]
* [[Endgame Tablebases]]
* [[Huberman|Huberman's program]]
* [[Infinite Board]]
* [[Interior Node Recognizer]]
* [[KPK]]
* [[Knowledge]]
* [[Michael Bain#LearningKRK|Learning KRK]]
* [[Manhattan-Distance]]
* [[Mate Search]]
* [[Mop-up Evaluation]]
* [[Oracle]]
* [[Retrograde Analysis]]
* [[Rook Endgame]]
* [[Search Pathology]]
* [[Space-Time Tradeoff]]
* [[Tempo]]
* [[Triangulation]]
* [[Zugzwang]]
=Selected Publications=
==1914==
* [[Henri Vigneron]] ('''1914'''). ''Les Automates''. [https://en.wikipedia.org/wiki/La_Nature La Nature], [http://cyberneticzoo.com/wp-content/uploads/2011/01/Automates-La-Nature-Torres-1914.pdf pdf] from [http://cyberneticzoo.com/ cyberneticzoo.com], Translation by [[David Levy]] as ''Robots'' in [[David Levy]], [[Monroe Newborn]] ('''1982'''). ''All About Chess and Computers''. [https://en.wikipedia.org/wiki/Springer_Science%2BBusiness_Media Springer], pp. 14-23, also in [[David Levy]] (ed.) ('''1988'''). ''[[Computer Chess Compendium]]'', pp. 273-278.
==1960 ...==
* [[Barbara Liskov|Barbara J. Huberman]] ('''1968'''). ''A Program to Play Chess End Games''. Technical Report no. CS-106, Ph.D. thesis. [[Stanford University]], Computer Science Department
==1970 ...==
* [[Thomas Ströhlein]] ('''1970'''). ''Untersuchungen über kombinatorische Spiele.'' Ph.D. Thesis, [[Technical University of Munich]] (German)
* [[Soei Tan|Soei T. Tan]] ('''1972'''). ''Representation of Knowledge for Very simple Endings in Chess.'' Memorandum MIP-R-98, School of Artificial Intelligence, [[University of Edinburgh]]
* [[Coen Zuidema]] ('''1974'''). ''Chess: How to Program the Exceptions?'' Technical Report IW21/74, Department of Informatics, [https://en.wikipedia.org/wiki/Centrum_Wiskunde_%26_Informatica Mathematical Center Amdsterdam]. [http://oai.cwi.nl/oai/asset/9480/9480A.pdf pdf]
* [[Donald Michie]] ('''1977'''). ''King and Rook Against King: Historical Background and a Problem on the Infinite Board''. [[Advances in Computer Chess 1]]
* [[David Slate]], [[Larry Atkin]] ('''1977'''). ''CHESS 4.5 - The Northwestern University Chess Program.'' [[Chess Skill in Man and Machine]], reprinted ('''1988''') in [[Computer Chess Compendium]]
* [[Ivan Bratko]] ('''1978'''). ''Proving Correctness of Strategies in the AL1 Assertional Language''. Information Processing Letters, Vol. 7, No. 5, pp. 223-230. <ref>[[Donald Michie]] ('''1976'''). ''[http://portal.acm.org/citation.cfm?id=1045272 AL1: a package for generating strategies from tables]''. ACM SIGART Bulletin, Issue 59</ref>
* [[Thomas Ströhlein]], [[Ludwig Zagler]] ('''1978'''). ''Ergebnisse einer vollstandigen Analyse von Schachendspielen: König und Turm gegen König, König und Turm gegen König und Läufer.'' Report, Institut für Informatik, [[Technical University of Munich]] (German)
==1980 ...==
* [[Ross Quinlan]] ('''1983, 1985'''). ''Learning efficient classification procedures and their application to chess end games''. Machine Learning: An Artificial Intelligence Approach
* [[David Slate]] ('''1984'''). ''Interior-node Score Bounds in a Brute-force Chess Program.'' [[ICGA Journal#7_4|ICCA Journal, Vol. 7, No. 4]]
* [[Reiner Seidel]] ('''1986'''). ''Deriving Correct Pattern Descriptions and Rules for the KRK Endgame by Deductive Methods''. [[Advances in Computer Chess 4]]
* [[Stephen Muggleton]] ('''1987'''). ''Duce, an oracle-based approach to constructive induction''. Proceedings of the 10th IJCAI Conference, Milano, Italy. [http://www.doc.ic.ac.uk/%7Eshm/Papers/ijcai87.pdf pdf]
* [[Stephen Muggleton]], [[Michael Bain]], [[Jean Hayes Michie]], [[Donald Michie]] ('''1989'''). ''An Experimental Comparison of Human and Machine Learning Formalisms''. [http://www.informatik.uni-trier.de/~ley/db/conf/icml/ml1989.html#MuggletonBMM89 6. ML 1989], [http://www.doc.ic.ac.uk/~shm/Papers/ml6paper.pdf pdf]
==1990 ...==
* [[Stephen Muggleton]] ('''1991'''). ''Inductive Logic Programming''. [http://www.springer.com/computer/ai/journal/354 New Generation Computing], Vol. 8, pp. 295-318. ISSN 0228-3635.
* [[Michael Bain]] ('''1992'''). ''Learning optimal chess strategies.'' [http://www.cs.york.ac.uk/ILP-events/ILP-1992/ ILP92]
* [[Ashwin Srinivasan]], [[Stephen Muggleton]], [[Michael Bain]] ('''1992'''). ''Distinguishing Noise from Exceptions in Non-monotonic Learning''. [http://www.cs.york.ac.uk/ILP-events/ILP-1992/ ILP92]
* [[Michael Bain]] ('''1994'''). ''Learning Logical Exceptions in Chess''. Ph.D. thesis, [https://en.wikipedia.org/wiki/University_of_Strathclyde University of Strathclyde], [http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.54.729 CitySeerX]
* [[Ulrich Thiemonds]] ('''1999'''). ''Ein regelbasiertes Spielprogramm für Schachendspiele''. [https://en.wikipedia.org/wiki/University_of_Bonn University of Bonn], [https://en.wikipedia.org/wiki/Diplom Diplom] thesis, [http://www.iai.uni-bonn.de/~idb/diplomarbeiten/thiemonds99.ps.gz zipped ps], [http://idb.informatik.uni-bonn.de/publications/da/da_thiemonds_1999.pdf pdf] (German) <ref>[http://idb.informatik.uni-bonn.de/publications/DA Diploma Theses — IDB]</ref> <ref>[http://www.iai.uni-bonn.de/~idb/ehemaligedipl.html Uni Bonn - AG Intelligente Datenbanken - Was sind intelligente Datenbanken?]</ref>
==2000 ...==
* [[Ivan Bratko]] ('''2001,2010'''). ''[http://www.worldcat.org/search?qt=wikipedia&q=isbn%3A0201403757 Prolog programming for artificial intelligence]''. Harlow England, [https://en.wikipedia.org/wiki/Addison-Wesley Addison Wesley]
* [[David Gleich]] ('''2003'''). ''Machine Learning in Computer Chess: Genetic Programming and KRK''. [https://en.wikipedia.org/wiki/Harvey_Mudd_College Harvey Mudd College], [http://www.cs.purdue.edu/homes/dgleich/publications/Gleich%202003%20-%20Machine%20Learning%20in%20Computer%20Chess.pdf pdf]
* [[Aleksander Sadikov]], [[Ivan Bratko]], [[Igor Kononenko]] ('''2003'''). ''Search versus Knowledge: An Empirical Study of Minimax on KRK''. [[Advances in Computer Games 10]], [http://www.ailab.si/sasha/acg2003.pdf pdf]
* [[Aleksander Sadikov]], [[Ivan Bratko]], [[Igor Kononenko]] ('''2005'''). ''[http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V1G-4HCN79X-1&_user=10&_coverDate=12%2F14%2F2005&_rdoc=1&_fmt=high&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=79f966215bea9b7461b6877c9373b0bf Bias and pathology in minimax search]''. Theoretical Computer Science, Volume 349, Issue 2, [http://lkm.fri.uni-lj.si/xaigor/slo/clanki/Sadikov_final.pdf pdf]
* [[Gabriel Breda]] ('''2006'''). ''KRK Chess Endgame Database Knowledge Extraction and Compression''. Diploma thesis, [[Darmstadt University of Technology]]
* [[Nicolas Lassabe]], [[Stéphane Sanchez]], [[Hervé Luga]], [[Yves Duthen]] ('''2006'''). ''[http://www.sciweavers.org/publications/genetically-programmed-strategies-chess-endgame Genetically Programmed Strategies For Chess Endgame]''. [http://www.sigevo.org/gecco-2006/ GECCO 2006], [http://www.cs.york.ac.uk/rts/docs/GECCO_2006/docs/p831.pdf pdf]
==2010 ...==
* [[Marko Maliković]], [[Mirko Čubrilo]], [[Predrag Janičić]] ('''2012'''). ''Formal Analysis of Correctness of a Strategy for the KRK Chess Endgame''. [http://argo.matf.bg.ac.rs/events/2012/fatpa2012/fatpa2012.html Fifth Workshop on Formal and Automated Theorem Proving and Applications], [https://en.wikipedia.org/wiki/Belgrade Belgrade], [https://en.wikipedia.org/wiki/Serbia Serbia], [http://argo.matf.bg.ac.rs/events/2012/fatpa2012/slides/MarkoMalikovic.pdf slides as pdf]
* [[Marko Maliković]], [[Predrag Janičić]] ('''2013'''). ''Proving Correctness of a KRK Chess Endgame Strategy by SAT-based Constraint Solving''. [[ICGA Journal#36_2|ICGA Journal, Vol. 36, No. 2]]
=Forum Posts=
* [http://www.talkchess.com/forum/viewtopic.php?t=47477 My program can't mate KQK or KRK!] by [[Rasjid Chan]], [[CCC]], March 11, 2013
* [http://stackoverflow.com/questions/15988069/chess-task-king-rook-vs-king algorithm - Chess task - King, Rook Vs King] by [http://stackoverflow.com/users/1448316/sreekanth-karumanaghat Sreekanth Karumanaghat], [https://en.wikipedia.org/wiki/Stack_Overflow Stack Overflow], April 13, 2013
* [http://www.talkchess.com/forum/viewtopic.php?t=54295 Why minimax is fundamentally flawed] by [[Harm Geert Muller]], [[CCC]], November 09, 2014 » [[Minimax]]
=External Links=
* [http://www.gilith.com/chess/endgames/kr_k.html Longest mate in King and Rook versus King endgame] by [[Joe Leslie-Hurd]], February 16, 2005
* [http://archive.ics.uci.edu/ml/datasets/Chess+%28King-Rook+vs.+King%29 UCI Machine Learning Repository: Chess (King-Rook vs. King) Data Set] by [[Michael Bain]]
* [https://en.wikipedia.org/wiki/Checkmate#King_and_rook Checkmate - King and rook - Wikipedia]
* [http://www.wikihow.com/Mate-With-King-and-Rook-Vs-King How to Mate With King and Rook Vs King: 19 Steps - wikiHow]
* [http://www.chesscorner.com/tutorial/basic/r_k_mate/r_k_mate.htm Chess Corner - Chess Tutorial - Checkmating with Lone Rook]
=References=
<references />
'''[[Endgame|Up one Level]]'''
