Acknowledgements（第1页）

Aents

IthaonVaughanWilliamsahforhelpfulinformatiodds，LesMillerfortheresultsofhissimulatioespins，IanMcHaleforhisdetailedexplanationofhowtoestimatethewinnihe32teamsinthefinalsofsoccer’sWorlddDerekRobinsonforhishelpwiththediagrams。Iamparticularlygratefultoananonymousreferee，whoseadstruentshavehelpedmeremoveambiguities，orderthematerialmoretly，aodrawoutthetralideasofthesubject。

Ibegfivehoseotherswhhemselvesastheunaowledgediion，opinioesinthisbook，butIhavereliedontoomaogiveindividualcrediteverytime。Thisisnotaise，witheveryassertiooitsroots，butaosharpenthereader’sappreofwhatthesubjectofprobabilityisabout，hoed，amightbeapplied。

Allerrorsahatremainareminealone。

JohnHaigh

August2011