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[[FILE:ACC5Schaeffer.jpg|border|right|thumb|[[Jonathan Schaeffer]] on ''Conspiracy Numbers.'' <ref>Photo from [[Advances in Computer Chess 5]] by [[László Lindner]], [[ICGA Journal#10_3|ICCA Journal, Vol. 10, No. 3]], pp. 138</ref> ]]
'''Conspiracy Numbers''' of the [[Root|root]] or [[Interior Node|interior nodes]] of a [[Search Tree|search tree]] for some value '''vV''' are defined as the least number of conspirators, that are [[Leaf Node|leaves]] that must change their evaluation value to '''vV''' in order to change the minimax value of the interior node or root <ref>Definition, Sample, and Pseudo code taken from [[Maarten van der Meulen]] ('''1990'''). ''Conspiracy-Number Search''. [[ICGA Journal#13_1|ICCA Journal, Vol. 13, No. 1]]</ref>. Conspiracy Numbers and their possible application for [[Minimax]] search within a [[Best-First|best-first search]] algorithm was first described by [[David McAllester]] <ref>[[David McAllester]] ('''1988'''). ''Conspiracy Numbers for Min-Max Search''. [https://en.wikipedia.org/wiki/Artificial_Intelligence_(journal) Artificial Intelligence], Vol. 35, No. 1, pp. 287-310. ISSN 0004-3702</ref>.
=Sample=
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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'''.
'''C<sub><</sub><nowiki>[T]</nowiki>''' expresses the confidence that the lower bound [[Alpha|α]] will hold by further expansion of the search tree.
=Search Algorithms=
