洗牌算法与随机性分析：扑克牌混合效果研究.pdfVIP

Introduction

Shufflingadeckofyingcardsisaveryimportantlifeskill.Thestandardriffleshufflegoeslikethis:you

takeastackofcards,splititintotwopi,holdonepileinyourlefthandandtheotherinyourright,and

dropcardsfromeachhandontoacommonpileonthetableinrandomorder.Afterrepeatingthisseveral

times,yourcarddeckishopefullyfairlywell-mixedandreadyforagameormaybeamagictrick.(Ofcourse,

inpractice,theeasiestwaytoperformtheriffleshuffleistoallowthecardstointerleavewithoutdropping

them,butthisismathematicallyequivalent.)

Peopleoftenperformonlythreeorfourriffleshuffinarowbeforeusingastandarddeckof52ying

cards.Onemightaskifthisisreallyenough.It’snothardtoseethatafteroneriffleshuffle,manyorderings

ofthecardsareimpossibletoreachandmanyothersaremuchmorelikelythantheyoughttobeina

uniformlyrandomprobabilitydistribution.Howmanyshuffinarowdoyoureallyneedtoapproximate

uniformrandomness?ThisPowerRoundbuildsupsomeofthebasicideasyouneedtoanswerthisquestion.

Inordertounderstandhowtomathematizeshuffling,wefirstdiscussthebasicconceptofapermutation

andsomespecificpropertiesthatwewillneed.Next,wegiveamathematicallyprecisedefinitionofthe

Gilbert-Shannon-Reedsriffleshuffle,whichhasbeenshowninexperimentstobeagoodmodelforhowreal

peopleshuffle,anddevelopthetheoryoftheprobabilitiesitgenerates.Unfortunately,actuallycomputing

thenecessarynumberofshuffforapproximateuniformrandomnessisbeyondthescopeofthistest,

buthopefullyyouwillcometobelievethatsuchanumberisindeedcomputable.Finally,wedevelopthe

mathematicsoftheperfectshuffle,adeterministicshuffleveryusefulinmagictrickstothoseabletoperform

it.Havefun!

介绍

洗一副