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Conspiracy Numbers

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=Conspiracy Theory=
Let δ be a number called the singular margin <ref>The term ''singular margin'' comes from the [[Singular Extensions|singular extension]] algorithm ([[Thomas Anantharaman|Anantharaman]] et al. 1990)</ref>. '''Conspiracy theory''' can be formulated using the following definition <ref>[[David McAllester]], [[Deniz Yuret]] ('''1993'''). ''[[Alpha-Beta Conspiracy Search]]''. [http://ttic.uchicago.edu/%7Edmcallester/abc.ps ps (draft)]</ref>:
'''Definition''': Let '''T''' be a search tree with min-max value '''<nowiki>V[T]</nowiki>'''. The [[Lower Bound|lower boand]] conspiracy number of '''T''', denoted '''C<sub><</sub><nowiki>[T]</nowiki>''', is the number of leaf static values that must be changed to bring the root min-max value down to '''<nowiki>V[T]</nowiki>-δ'''. The Upper Bound|upper boand]] conspiracy number of '''T''', denoted '''C<sub>></sub><nowiki>[T]</nowiki>''', is the number of leaves that must be changed to bring the root value up to '''<nowiki>V[T]</nowiki>+δ'''.
* [[Maarten van der Meulen]], [[Victor Allis]], [[Jaap van den Herik]] ('''1990'''). ''A Comment on `Conspiracy-Number Search''. [[ICGA Journal#13_2|ICCA Journal, Vol. 13, No. 2]]
* [[Victor Allis]], [[Maarten van der Meulen]], [[Jaap van den Herik]] ('''1991'''). ''Conspiracy-Number Search.'' [[Advances in Computer Chess 6]]
* [[David McAllester]], [[Deniz Yuret]] ('''1993'''). ''[[Alpha-Beta Conspiracy Search]]''. [http://ttic.uchicago.edu/%7Edmcallester/abc.ps ps (draft)]
* [[Lisa Lister]], [[Jonathan Schaeffer]] ('''1994'''). ''An Analysis of the Conspiracy Numbers Algorithm''. [https://en.wikipedia.org/wiki/Computers_and_Mathematics_with_Applications Computers & Mathematics with Applications] Vol. 27, No. 1, [https://en.wikipedia.org/wiki/Elsevier Elsevier], [http://webdocs.cs.ualberta.ca/%7Ejonathan/publications/ai_publications/icn.pdf pdf]
* [[Deniz Yuret]] ('''1994'''). ''[https://scholar.google.com/citations?view_op=view_citation&hl=en&user=EJurXJ4AAAAJ&cstart=40&citation_for_view=EJurXJ4AAAAJ:TQgYirikUcIC The Principle of Pressure in Chess]''. TAINN 1994

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