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Created page with "'''Home * Search * Pathology''' FILE:Membranous nephropathy - mpas - very high mag.jpg|border|right|thumb|Micrograph of membranous nephropathy <ref>Very h..."
'''[[Main Page|Home]] * [[Search]] * Pathology'''
[[FILE:Membranous nephropathy - mpas - very high mag.jpg|border|right|thumb|Micrograph of membranous nephropathy <ref>Very high magnification [https://en.wikipedia.org/wiki/Micrograph micrograph] of [https://en.wikipedia.org/wiki/Membranous_nephropathy membranous nephropathy], abbreviated MN. MN may also be referred to as membranous glomerulonephritis, abbreviated MGN. [https://en.wikipedia.org/wiki/Kidney_biopsy Kidney biopsy]. [https://en.wikipedia.org/wiki/Jones_stain Jones stain], [https://en.wikipedia.org/wiki/Pathology Pathology from Wikipedia]</ref> ]]
'''Pathology''' in game-trees is a counterintuitive phenomenon where a [[Depth|deeper]] [[Minimax|minimax]] search results in worse play. It was discovered by [[Don Beal]] <ref>[[Don Beal]] ('''1980'''). ''An analysis of minimax''. [[Advances in Computer Chess 2]]</ref>, who constructed a simple mathematical model to analyze the minimax algorithm. To his surprise, the analysis of the model showed that the backed-up values were actually somewhat less trustworthy than the heuristic values themselves.
=Decision vs Evaluation=
Independently, pathology in game trees was coined by [[Dana Nau]], who discovered pathology to exist in a large class of games <ref>[[Dana Nau]] ('''1982'''). ''An Investigation of the Causes of Pathology in Games.'' [https://en.wikipedia.org/wiki/Artificial_Intelligence_%28journal%29 Artificial Intelligence], Vol. 19, 257–278, [https://en.wikipedia.org/wiki/University_of_Maryland,_College_Park University of Maryland, College Park], Recommended by [[Judea Pearl]], [http://www.cs.umd.edu/%7Enau/papers/nau82investigation.pdf pdf]</ref> under the assumption of independence of sibling values of trees with low branching factor (i.e. binary trees) with game theoretic leaf values of win and loss {1, -1}. In a simulation, Nau introduced strong dependencies between sibling nodes and discovered that this can cause search-depth pathology to disappear. While Nau was primarily concerned with decision accuracy, Beal <ref>[[Don Beal]] ('''1982'''). ''Benefits of minimax search''. [[Advances in Computer Chess 3]]</ref>, as well as [[Ivan Bratko|Bratko]] and [[Matjaž Gams|Gams]] <ref>[[Ivan Bratko]], [[Matjaž Gams]] ('''1982'''). ''Error Analysis of the Minimax Principle''. [[Advances in Computer Chess 3]]</ref> were concerned with evaluation accuracy.
<span id="RandomEvaluations"></span>
=Random Evaluations=
Quite contrary to pathology in chess, Beal and others demonstrated <ref>[[Don Beal]], [[Martin C. Smith]] ('''1994'''). ''Random Evaluations in Chess''. [[ICGA Journal#17_1|ICCA Journal, Vol. 17, No. 1]]</ref>, that deeper [[Search with Random Leaf Values|search with random leaf values]] yields to better play. As a quintessence, [[Dana Nau]] et al. suggested an ''Error minimizing minimax search'' in their recent paper <ref>[[Brandon Wilson]], [[Austin Parker]], [[Dana Nau]] ('''2009'''). ''Error Minimizing Minimax: Avoiding Search Pathology in Game Trees''. [http://www.cs.umd.edu/~nau/papers/wilson2009error.pdf pdf]</ref> .
=See also=
* [[Conspiracy Numbers]]
* [[Depth]]
* [[Depth#DiminishingReturns|Diminishing Returns]]
* [[Score#Grain|Score Granularity]]
* [[Search Instability]]
* [[Search with Random Leaf Values]]
* [[Singular Extensions#SingularityAndPathology|Singularity and Pathology]]
=Publications=
==1979==
* [[Dana Nau]] ('''1979'''). ''Quality of Decision Versus Depth of Search on Game Trees.'' Ph.D. dissertation, [[Duke University]]
* [[Dana Nau]] ('''1979'''). ''Preliminary results regarding quality of play versus depth of search in game playing.'' First Internat. Symposium on Policy Analysis and Information Systems, pp. 210–217, [http://www.cs.umd.edu/%7Enau/papers/nau79preliminary.pdf pdf]
==1980 ...==
* [[Don Beal]] ('''1980'''). ''An analysis of minimax''. [[Advances in Computer Chess 2]]
* [[Dana Nau]] ('''1980'''). ''Pathology on game trees: A summary of results.'' In Proceedings of the National Conference on Artificial Intelligence (AAAI), pp. 102–104, [http://www.cs.umd.edu/%7Enau/papers/pathology-aaai80.pdf pdf]
* [[Dana Nau]] ('''1982'''). ''An Investigation of the Causes of Pathology in Games.'' [https://en.wikipedia.org/wiki/Artificial_Intelligence_%28journal%29 Artificial Intelligence], Vol. 19, 257–278, [https://en.wikipedia.org/wiki/University_of_Maryland,_College_Park University of Maryland, College Park], Recommended by [[Judea Pearl]], [http://www.cs.umd.edu/%7Enau/papers/nau82investigation.pdf pdf]
* [[Ivan Bratko]], [[Matjaž Gams]] ('''1982'''). ''Error Analysis of the Minimax Principle''. [[Advances in Computer Chess 3]]
* [[Don Beal]] ('''1982'''). ''Benefits of minimax search''. [[Advances in Computer Chess 3]]
* [[Dana Nau]] ('''1983'''). ''Decision quality as a function of search depth on game trees.'' Journal of the ACM 30(4):687–708, [http://www.cs.umd.edu/%7Enau/papers/nau83decision.pdf pdf]
* [[Dana Nau]] ('''1983'''). ''Pathology on game trees revisited, and an alternative to minimaxing.'' [https://en.wikipedia.org/wiki/Artificial_Intelligence_%28journal%29 Artificial Intelligence], Vol. 21, No. 1-2, Reprinted in [[Judea Pearl]] (ed.), Search and Heuristics, North-Holland Publishing Company, Amsterdam, [http://www.cs.umd.edu/%7Enau/papers/nau83pathology.pdf pdf]
* [[Judea Pearl]] ('''1983'''). ''On the Nature of Pathology in Game Searching''. [https://en.wikipedia.org/wiki/Artificial_Intelligence_%28journal%29 Artificial Intelligence], Vol. 20, 427-453.
==1985 ...==
* [[Bruce Abramson]] ('''1985'''). ''A Cure for Pathological Behavior in Games that Use Minimax.'' Proceedings of the Workshop on Uncertainty in Artificial Intelligence, 1985, 225-231.
* [[Agata Muszycka-Jones|Agata Muszycka]] ('''1985'''). ''Game Trees: Searching Techniques and Pathological Phenomenon''. Master of Computer Science, Department of Computer Science, [https://en.wikipedia.org/wiki/Concordia_University Concordia University], [https://en.wikipedia.org/wiki/Montreal Montreal]
* [[Bruce Abramson]] ('''1986'''). ''An Explanation of and Cure for Minimax Pathology.'' Uncertainty in Artificial Intelligence, [[Laveen Kanal]] and John Lemmer, eds. (Amsterdam: North Holland, 1986), 495-504.
* [[Günther Schrüfer]] ('''1986'''). ''Presence and Absence of Pathology on Game Trees''. [[Advances in Computer Chess 4]]
* [[Ingo Althöfer]] ('''1988'''). ''Root Evaluation Errors: How they Arise and Propagate''. [[ICGA Journal#11_23|ICCA Journal, Vol. 11, Nos. 2/3]]
* [[Liwu Li]] ('''1989'''). ''[https://doi.org/10.7939/R3VX06F26 Probabilistic Analysis of Search]''. Ph.D. thesis, [[University of Alberta]], advisor [[Tony Marsland]]
==1990 ...==
* [[Liwu Li]], [[Tony Marsland]] ('''1990'''). ''On Minimax Game Tree Search Pathology and Node-value Dependence''. TR90-24, [[University of Alberta]], [https://webdocs.cs.ualberta.ca/~tony/TechnicalReports/TR90-24.pdf pdf]
* [[Ingo Althöfer]] ('''1991'''). ''On Pathology in Game Tree and other Recursion Tree Models'', Habilitation Thesis (June 1991), Faculty of Mathematics, [https://en.wikipedia.org/wiki/University_of_Bielefeld University of Bielefeld]
* [[Don Beal]], [[Martin C. Smith]] ('''1994'''). ''Random Evaluations in Chess''. [[ICGA Journal#17_1|ICCA Journal, Vol. 17, No. 1]]
* [[Don Beal]], [[Martin C. Smith]] ('''1994'''). ''Random Evaluations in Chess''. [[Advances in Computer Chess 7]]
==1995 ...==
* [[Mark Levene]], [[Trevor Fenner]] ('''1995'''). ''A Partial Analysis of Minimaxing Game Trees with Random Leaf Values''. [[ICGA Journal#18_1|ICCA Journal, Vol. 18, No. 1]]
* [[Ingo Althöfer]], [[Mathematician#ImreLeader|Imre Leader]] ('''1995'''). ''[http://epubs.siam.org/doi/abs/10.1137/S0895480192240470 Correlation of Boolean Functions and Pathology in Recursion Trees]''. [https://en.wikipedia.org/wiki/SIAM_Journal_on_Discrete_Mathematics SIAM Journal on Discrete Mathematics], Vol. 8, No. 4
* [[Don Beal]] ('''1999'''). ''The Nature of MINIMAX Search''. Ph.D. thesis, IKAT, ISBN 90-62-16-6348
==2000 ...==
* [[Mark Levene]], [[Trevor Fenner]] ('''2001'''). ''The Effect of Mobility on Minimaxing of Game Trees with Random Leaf Values''. [https://en.wikipedia.org/wiki/Artificial_Intelligence_%28journal%29 Artificial Intelligence], Vol. 130, No. 1, Review in [[ICGA Journal#18_1|ICGA Journal, Vol. 24, No. 4]]
==2005 ...==
* [[Mitja Luštrek]], [[Matjaž Gams]], [[Ivan Bratko]] ('''2005'''). ''[http://dl.acm.org/citation.cfm?id=1642327 Why Minimax Works: An Alternative Explanation]''. [http://www.informatik.uni-trier.de/~ley/db/conf/ijcai/ijcai2005.html#LustrekGB05 IJCAI 2005]
* [[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]''. [https://en.wikipedia.org/wiki/Theoretical_Computer_Science_%28journal%29 Theoretical Computer Science],, Vol. 349, 2, [http://lkm.fri.uni-lj.si/xaigor/slo/clanki/Sadikov_final.pdf pdf]
* [[Mitja Luštrek]], [[Matjaž Gams]], [[Ivan Bratko]] ('''2006'''). ''Is Real-Valued Minimax Pathological''? [https://en.wikipedia.org/wiki/Artificial_Intelligence_%28journal%29 Artificial Intelligence], Vol. 170, [http://dis.ijs.si/MitjaL/documents/Is_Real-Valued_Minimax_Pathological-AIJ-06.pdf pdf]
* [[Brandon Wilson]], [[Austin Parker]], [[Dana Nau]] ('''2009'''). ''Error Minimizing Minimax: Avoiding Search Pathology in Game Trees''. [http://www.cs.umd.edu/~nau/papers/wilson2009error.pdf pdf]
==2010 ...==
* [[Dana Nau|Dana S. Nau]], [[Mitja Luštrek]], [[Austin Parker]], [[Ivan Bratko]], [[Matjaž Gams]] ('''2010'''). ''[http://www.sciencedirect.com/science/article/pii/S0004370210001402 When is it better not to look ahead?]''. [https://en.wikipedia.org/wiki/Artificial_Intelligence_%28journal%29 Artificial Intelligence], Vol. 174, No. 16–17, [http://dis.ijs.si/mitjal/documents/Nau-When_is_it_better_not_to_look_ahead-AIJ-10.pdf preprint as pdf]
* [[Mitja Luštrek]], [[Ivan Bratko]], [[Matjaž Gams]] ('''2011'''). ''[http://www.sciencedirect.com/science/article/pii/S0304397511009522 Independent-valued minimax : Pathological or beneficial?]'' [https://en.wikipedia.org/wiki/Theoretical_Computer_Science_%28journal%29 Theoretical Computer Science], Vol. 422, [http://dis.ijs.si/MitjaL/documents/Independent-valued_minimax-Pathological_or_beneficial-TCS-12.pdf pdf]
=Forum Posts=
* [http://www.talkchess.com/forum/viewtopic.php?t=35538 Pathology on Game trees] by [[Gerd Isenberg]], [[CCC]], July 22, 2010
* [http://www.talkchess.com/forum/viewtopic.php?t=58527&start=10 Re: Null Move in Quiescent search] by [[Harm Geert Muller]], [[CCC]], December 10, 2015 » [[Null Move Pruning]], [[Quiescence Search]]
: [http://www.talkchess.com/forum/viewtopic.php?t=58527&start=11 Re: Null Move in Quiescent search] by [[Marcel van Kervinck]], [[CCC]], December 10, 2015 » [[Proof-number search#PDS|PDS]]
: [http://www.talkchess.com/forum/viewtopic.php?t=58527&start=16 Re: Null Move in Quiescent search] by [[Harm Geert Muller]], [[CCC]], December 12, 2015
* [http://www.talkchess.com/forum/viewtopic.php?t=63803 random evaluation perturbation factor] by [[Stuart Cracraft]], [[CCC]], April 24, 2017
=External Links=
* [https://en.wikipedia.org/wiki/Pathology_%28disambiguation%29 Pathology (disambiguation) from Wikipedia]
* [https://en.wikipedia.org/wiki/Pathological_%28mathematics%29 Pathological (mathematics) from Wikipedia]
* [https://en.wikipedia.org/wiki/Pathology Pathology from Wikipedia]
* [https://en.wikipedia.org/wiki/Pathological_science Pathological science from Wikipedia]
=References=
<references />
'''[[Search|Up one Level]]'''
[[FILE:Membranous nephropathy - mpas - very high mag.jpg|border|right|thumb|Micrograph of membranous nephropathy <ref>Very high magnification [https://en.wikipedia.org/wiki/Micrograph micrograph] of [https://en.wikipedia.org/wiki/Membranous_nephropathy membranous nephropathy], abbreviated MN. MN may also be referred to as membranous glomerulonephritis, abbreviated MGN. [https://en.wikipedia.org/wiki/Kidney_biopsy Kidney biopsy]. [https://en.wikipedia.org/wiki/Jones_stain Jones stain], [https://en.wikipedia.org/wiki/Pathology Pathology from Wikipedia]</ref> ]]
'''Pathology''' in game-trees is a counterintuitive phenomenon where a [[Depth|deeper]] [[Minimax|minimax]] search results in worse play. It was discovered by [[Don Beal]] <ref>[[Don Beal]] ('''1980'''). ''An analysis of minimax''. [[Advances in Computer Chess 2]]</ref>, who constructed a simple mathematical model to analyze the minimax algorithm. To his surprise, the analysis of the model showed that the backed-up values were actually somewhat less trustworthy than the heuristic values themselves.
=Decision vs Evaluation=
Independently, pathology in game trees was coined by [[Dana Nau]], who discovered pathology to exist in a large class of games <ref>[[Dana Nau]] ('''1982'''). ''An Investigation of the Causes of Pathology in Games.'' [https://en.wikipedia.org/wiki/Artificial_Intelligence_%28journal%29 Artificial Intelligence], Vol. 19, 257–278, [https://en.wikipedia.org/wiki/University_of_Maryland,_College_Park University of Maryland, College Park], Recommended by [[Judea Pearl]], [http://www.cs.umd.edu/%7Enau/papers/nau82investigation.pdf pdf]</ref> under the assumption of independence of sibling values of trees with low branching factor (i.e. binary trees) with game theoretic leaf values of win and loss {1, -1}. In a simulation, Nau introduced strong dependencies between sibling nodes and discovered that this can cause search-depth pathology to disappear. While Nau was primarily concerned with decision accuracy, Beal <ref>[[Don Beal]] ('''1982'''). ''Benefits of minimax search''. [[Advances in Computer Chess 3]]</ref>, as well as [[Ivan Bratko|Bratko]] and [[Matjaž Gams|Gams]] <ref>[[Ivan Bratko]], [[Matjaž Gams]] ('''1982'''). ''Error Analysis of the Minimax Principle''. [[Advances in Computer Chess 3]]</ref> were concerned with evaluation accuracy.
<span id="RandomEvaluations"></span>
=Random Evaluations=
Quite contrary to pathology in chess, Beal and others demonstrated <ref>[[Don Beal]], [[Martin C. Smith]] ('''1994'''). ''Random Evaluations in Chess''. [[ICGA Journal#17_1|ICCA Journal, Vol. 17, No. 1]]</ref>, that deeper [[Search with Random Leaf Values|search with random leaf values]] yields to better play. As a quintessence, [[Dana Nau]] et al. suggested an ''Error minimizing minimax search'' in their recent paper <ref>[[Brandon Wilson]], [[Austin Parker]], [[Dana Nau]] ('''2009'''). ''Error Minimizing Minimax: Avoiding Search Pathology in Game Trees''. [http://www.cs.umd.edu/~nau/papers/wilson2009error.pdf pdf]</ref> .
=See also=
* [[Conspiracy Numbers]]
* [[Depth]]
* [[Depth#DiminishingReturns|Diminishing Returns]]
* [[Score#Grain|Score Granularity]]
* [[Search Instability]]
* [[Search with Random Leaf Values]]
* [[Singular Extensions#SingularityAndPathology|Singularity and Pathology]]
=Publications=
==1979==
* [[Dana Nau]] ('''1979'''). ''Quality of Decision Versus Depth of Search on Game Trees.'' Ph.D. dissertation, [[Duke University]]
* [[Dana Nau]] ('''1979'''). ''Preliminary results regarding quality of play versus depth of search in game playing.'' First Internat. Symposium on Policy Analysis and Information Systems, pp. 210–217, [http://www.cs.umd.edu/%7Enau/papers/nau79preliminary.pdf pdf]
==1980 ...==
* [[Don Beal]] ('''1980'''). ''An analysis of minimax''. [[Advances in Computer Chess 2]]
* [[Dana Nau]] ('''1980'''). ''Pathology on game trees: A summary of results.'' In Proceedings of the National Conference on Artificial Intelligence (AAAI), pp. 102–104, [http://www.cs.umd.edu/%7Enau/papers/pathology-aaai80.pdf pdf]
* [[Dana Nau]] ('''1982'''). ''An Investigation of the Causes of Pathology in Games.'' [https://en.wikipedia.org/wiki/Artificial_Intelligence_%28journal%29 Artificial Intelligence], Vol. 19, 257–278, [https://en.wikipedia.org/wiki/University_of_Maryland,_College_Park University of Maryland, College Park], Recommended by [[Judea Pearl]], [http://www.cs.umd.edu/%7Enau/papers/nau82investigation.pdf pdf]
* [[Ivan Bratko]], [[Matjaž Gams]] ('''1982'''). ''Error Analysis of the Minimax Principle''. [[Advances in Computer Chess 3]]
* [[Don Beal]] ('''1982'''). ''Benefits of minimax search''. [[Advances in Computer Chess 3]]
* [[Dana Nau]] ('''1983'''). ''Decision quality as a function of search depth on game trees.'' Journal of the ACM 30(4):687–708, [http://www.cs.umd.edu/%7Enau/papers/nau83decision.pdf pdf]
* [[Dana Nau]] ('''1983'''). ''Pathology on game trees revisited, and an alternative to minimaxing.'' [https://en.wikipedia.org/wiki/Artificial_Intelligence_%28journal%29 Artificial Intelligence], Vol. 21, No. 1-2, Reprinted in [[Judea Pearl]] (ed.), Search and Heuristics, North-Holland Publishing Company, Amsterdam, [http://www.cs.umd.edu/%7Enau/papers/nau83pathology.pdf pdf]
* [[Judea Pearl]] ('''1983'''). ''On the Nature of Pathology in Game Searching''. [https://en.wikipedia.org/wiki/Artificial_Intelligence_%28journal%29 Artificial Intelligence], Vol. 20, 427-453.
==1985 ...==
* [[Bruce Abramson]] ('''1985'''). ''A Cure for Pathological Behavior in Games that Use Minimax.'' Proceedings of the Workshop on Uncertainty in Artificial Intelligence, 1985, 225-231.
* [[Agata Muszycka-Jones|Agata Muszycka]] ('''1985'''). ''Game Trees: Searching Techniques and Pathological Phenomenon''. Master of Computer Science, Department of Computer Science, [https://en.wikipedia.org/wiki/Concordia_University Concordia University], [https://en.wikipedia.org/wiki/Montreal Montreal]
* [[Bruce Abramson]] ('''1986'''). ''An Explanation of and Cure for Minimax Pathology.'' Uncertainty in Artificial Intelligence, [[Laveen Kanal]] and John Lemmer, eds. (Amsterdam: North Holland, 1986), 495-504.
* [[Günther Schrüfer]] ('''1986'''). ''Presence and Absence of Pathology on Game Trees''. [[Advances in Computer Chess 4]]
* [[Ingo Althöfer]] ('''1988'''). ''Root Evaluation Errors: How they Arise and Propagate''. [[ICGA Journal#11_23|ICCA Journal, Vol. 11, Nos. 2/3]]
* [[Liwu Li]] ('''1989'''). ''[https://doi.org/10.7939/R3VX06F26 Probabilistic Analysis of Search]''. Ph.D. thesis, [[University of Alberta]], advisor [[Tony Marsland]]
==1990 ...==
* [[Liwu Li]], [[Tony Marsland]] ('''1990'''). ''On Minimax Game Tree Search Pathology and Node-value Dependence''. TR90-24, [[University of Alberta]], [https://webdocs.cs.ualberta.ca/~tony/TechnicalReports/TR90-24.pdf pdf]
* [[Ingo Althöfer]] ('''1991'''). ''On Pathology in Game Tree and other Recursion Tree Models'', Habilitation Thesis (June 1991), Faculty of Mathematics, [https://en.wikipedia.org/wiki/University_of_Bielefeld University of Bielefeld]
* [[Don Beal]], [[Martin C. Smith]] ('''1994'''). ''Random Evaluations in Chess''. [[ICGA Journal#17_1|ICCA Journal, Vol. 17, No. 1]]
* [[Don Beal]], [[Martin C. Smith]] ('''1994'''). ''Random Evaluations in Chess''. [[Advances in Computer Chess 7]]
==1995 ...==
* [[Mark Levene]], [[Trevor Fenner]] ('''1995'''). ''A Partial Analysis of Minimaxing Game Trees with Random Leaf Values''. [[ICGA Journal#18_1|ICCA Journal, Vol. 18, No. 1]]
* [[Ingo Althöfer]], [[Mathematician#ImreLeader|Imre Leader]] ('''1995'''). ''[http://epubs.siam.org/doi/abs/10.1137/S0895480192240470 Correlation of Boolean Functions and Pathology in Recursion Trees]''. [https://en.wikipedia.org/wiki/SIAM_Journal_on_Discrete_Mathematics SIAM Journal on Discrete Mathematics], Vol. 8, No. 4
* [[Don Beal]] ('''1999'''). ''The Nature of MINIMAX Search''. Ph.D. thesis, IKAT, ISBN 90-62-16-6348
==2000 ...==
* [[Mark Levene]], [[Trevor Fenner]] ('''2001'''). ''The Effect of Mobility on Minimaxing of Game Trees with Random Leaf Values''. [https://en.wikipedia.org/wiki/Artificial_Intelligence_%28journal%29 Artificial Intelligence], Vol. 130, No. 1, Review in [[ICGA Journal#18_1|ICGA Journal, Vol. 24, No. 4]]
==2005 ...==
* [[Mitja Luštrek]], [[Matjaž Gams]], [[Ivan Bratko]] ('''2005'''). ''[http://dl.acm.org/citation.cfm?id=1642327 Why Minimax Works: An Alternative Explanation]''. [http://www.informatik.uni-trier.de/~ley/db/conf/ijcai/ijcai2005.html#LustrekGB05 IJCAI 2005]
* [[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]''. [https://en.wikipedia.org/wiki/Theoretical_Computer_Science_%28journal%29 Theoretical Computer Science],, Vol. 349, 2, [http://lkm.fri.uni-lj.si/xaigor/slo/clanki/Sadikov_final.pdf pdf]
* [[Mitja Luštrek]], [[Matjaž Gams]], [[Ivan Bratko]] ('''2006'''). ''Is Real-Valued Minimax Pathological''? [https://en.wikipedia.org/wiki/Artificial_Intelligence_%28journal%29 Artificial Intelligence], Vol. 170, [http://dis.ijs.si/MitjaL/documents/Is_Real-Valued_Minimax_Pathological-AIJ-06.pdf pdf]
* [[Brandon Wilson]], [[Austin Parker]], [[Dana Nau]] ('''2009'''). ''Error Minimizing Minimax: Avoiding Search Pathology in Game Trees''. [http://www.cs.umd.edu/~nau/papers/wilson2009error.pdf pdf]
==2010 ...==
* [[Dana Nau|Dana S. Nau]], [[Mitja Luštrek]], [[Austin Parker]], [[Ivan Bratko]], [[Matjaž Gams]] ('''2010'''). ''[http://www.sciencedirect.com/science/article/pii/S0004370210001402 When is it better not to look ahead?]''. [https://en.wikipedia.org/wiki/Artificial_Intelligence_%28journal%29 Artificial Intelligence], Vol. 174, No. 16–17, [http://dis.ijs.si/mitjal/documents/Nau-When_is_it_better_not_to_look_ahead-AIJ-10.pdf preprint as pdf]
* [[Mitja Luštrek]], [[Ivan Bratko]], [[Matjaž Gams]] ('''2011'''). ''[http://www.sciencedirect.com/science/article/pii/S0304397511009522 Independent-valued minimax : Pathological or beneficial?]'' [https://en.wikipedia.org/wiki/Theoretical_Computer_Science_%28journal%29 Theoretical Computer Science], Vol. 422, [http://dis.ijs.si/MitjaL/documents/Independent-valued_minimax-Pathological_or_beneficial-TCS-12.pdf pdf]
=Forum Posts=
* [http://www.talkchess.com/forum/viewtopic.php?t=35538 Pathology on Game trees] by [[Gerd Isenberg]], [[CCC]], July 22, 2010
* [http://www.talkchess.com/forum/viewtopic.php?t=58527&start=10 Re: Null Move in Quiescent search] by [[Harm Geert Muller]], [[CCC]], December 10, 2015 » [[Null Move Pruning]], [[Quiescence Search]]
: [http://www.talkchess.com/forum/viewtopic.php?t=58527&start=11 Re: Null Move in Quiescent search] by [[Marcel van Kervinck]], [[CCC]], December 10, 2015 » [[Proof-number search#PDS|PDS]]
: [http://www.talkchess.com/forum/viewtopic.php?t=58527&start=16 Re: Null Move in Quiescent search] by [[Harm Geert Muller]], [[CCC]], December 12, 2015
* [http://www.talkchess.com/forum/viewtopic.php?t=63803 random evaluation perturbation factor] by [[Stuart Cracraft]], [[CCC]], April 24, 2017
=External Links=
* [https://en.wikipedia.org/wiki/Pathology_%28disambiguation%29 Pathology (disambiguation) from Wikipedia]
* [https://en.wikipedia.org/wiki/Pathological_%28mathematics%29 Pathological (mathematics) from Wikipedia]
* [https://en.wikipedia.org/wiki/Pathology Pathology from Wikipedia]
* [https://en.wikipedia.org/wiki/Pathological_science Pathological science from Wikipedia]
=References=
<references />
'''[[Search|Up one Level]]'''
