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Acknowledgements（第1页）

Aents

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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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