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IthaonVaughanWilliamsahforhelpfulinformatiodds，LesMillerfortheresultsofhissimulatioespins，IanMcHaleforhisdetailedexplanationofhowtoestimatethewinnihe32teamsinthefinalsofsoccer’sWorlddDerekRobinsonforhishelpwiththediagrams.Iamparticularlygratefultoananonymousreferee，whoseadstruentshavehelpedmeremoveambiguities，orderthematerialmoretly，aodrawoutthetralideasofthesubject.
Ibegfivehoseotherswhhemselvesastheunaowledgediion，opinioesinthisbook，butIhavereliedontoomaogiveindividualcrediteverytime.Thisisnotaise，witheveryassertiooitsroots，butaosharpenthereader’sappreofwhatthesubjectofprobabilityisabout，hoed，amightbeapplied.
Allerrorsahatremainareminealone.
JohnHaigh
August2011
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