Brian Alspach Mathematics and Poker.pdf

(1075 KB) Pobierz
49265574 UNPDF
49265574.006.png 49265574.007.png 49265574.008.png 49265574.009.png 49265574.001.png 49265574.002.png 49265574.003.png 49265574.004.png 49265574.005.png
MathematicsandPoker
BrianAlspach
LetmebeginbycongratulatingRandyHewinesandDaveScharfforini-
tiatingaCanadianmagazinedevotedtopoker.WhyaCanadianmagazine,
youmayask,giventhatinsomesensethegameofpokerisunaliatedwith
anycountry,althoughtherestillaremanyplacesinwhichpopularlocalgames
areplayedwithareduceddeckinsteadofthestandard52-carddeck.Ibe-
lievetheexistenceofaCanadianpokermagazinespeakstothestrengthofthe
gameinCanada,especiallyintheprovincesofBC,AlbertaandSaskatchewan.
ThereisnowarespectablescheduleofmajorannualtournamentsinAlberta
andSaskatchewan.
Therulesofthegamearethesameessentiallyeverywhere,butthereare
issuessurroundingthegamethatariseincommonforCanadianvenues.Soit
seemstometherearesomecompellingreasonsforaCanadianpokermagazine.
Ofcourse,mostofthearticleswillbeofinteresttopeoplefrommanycoun-
tries.Ishallbewritingavarietyofarticlesaboutmathematicsandpoker.The
relationshipbetweenmathematicsandpokerisinterestingandmurky.
Frequently,Iamaskedabouttheperceivedadvantageamathematicianhas
inpoker.Thepeoplewhoaskmeaboutthisalmostalwaysarenotpokerplayers.
Iassurethemthatmathematicsplaysarole,buttherearemanyverysuccessful
playerswhohavealmostnoformalknowledgeofmathematics.
Ontheotherhand,anotherfeatureofthepeoplewhoaskthatquestionis
alackofunderstandingofwhatmathematicsis.Isuspectmostofthepeople
readingthisarticledonotsharemyviewofwhatmathematicsis.Athumbnail
descriptionofmyviewisthefollowing:Mathematicsistheattempttodiscover
andclassifypatterns.ThepointofthisisthattherearemanyquestionsIsee
asmathematics,whereas,mostpeoplewouldscrewuptheirbrowsandquery,
“That’smath?”
Purecuriositydrivesonetypeofmathematicalquestionthatarisesinpoker
—answeringthesequestionsisinteresting,but,intruth,willhavelittleimpact
uponhowweplaythegame.Thisisthekindofquestionthatamathematician
findsmuchmoreinterestingthandoesapokerplayer.Themathematician
willsmileandthinkthatproblemsoundsfunandthenattempttosolveit.
Meanwhile,atypicalpokerplayer,uponhearingthequestion,willsay,“Who
cares?”
HereiswheremyprofessionalbackgroundcomesintoplaybecauseIfind
suchproblemsamusing.Ishallwriteaboutavarietyofproblemsfallinginto
thatcategory.Hopefully,readerswillfindsuchquestionsfuntoo.
Anothercategoryofquestion,thoughmuchrarerthanthecuriositydriven
questions,consistsofthosethatgotothecoreofhowwethinkaboutplaying
poker.Questionsinthiscategoryarenormallydicultandthesubjectof
debate.Accurateresultssometimessurprisepeopleandcausepeopletoshift
theirapproachestothegame.
Onelastcategoryofquestionsconsistsofthosewithdirectapplicationsbut
1
norealimpactonhowweplaythegame.Atypicalquestioninthiscategory
wouldbe:Whatistheprobabilityofabad-beatjackpotoccurringunderthe
followingrules?Acasinousestheanswertoestablishbad-beatjackpotrules
fulfillingcertaincriteria,buttheanswertothequestionhaslittleimpacton
howanindividualplaysthegame.
TheabovediscussionprovidesanindicationofthekindsofquestionsIshall
beaddressingthroughoutthisseriesofarticles.
NowI’dliketodiscussmyapproach.MostofthepokerauthorsIhaveread
whoprovidenumericalresultsgivelittleornoinformationonhowthoseresults
areachieved.Istoodinfrontoftoomanyuniversitystudentsthroughouta33-
yearteachingcareertobesatisfiedwiththisapproach.Iamgoingtoprovide
somedetailsonhowIreachwhateverconclusionsarepresent.Myhopeindoing
soistoallowinterestedreaderstoderivealltheresultsthemselves.Normally,
Ishallnotcarryoutallthedetails,butwillattempttohavecompletedetails
atmywebsite(www.math.sfu.ca/ ~ alspach)underthefolderentitled“Poker
Computations.”
Mathematiciansreceivetrainingthatturnsthemintoarguablythemost
notoriousquestionersofall.Wealwaysareaskingwhy.Iwanttoinstillsome
ofthatattitudeinthereader.
Inaddition,Iwanttoprovidesomegeneralapproachestoproblemsolving
employedbymathematicians.Letmenowgiveapreviewofcomingattractions.
ThisistheproblemI’llsolveinmynextarticle.Someofyoumaywanttotake
awhackatitaheadoftimeortestyourintuition.Itisaperfectexampleofa
curiositydrivenquestion.
AfriendatCasinoRegina,callhimG,toldmethattwoofthemwere
discussingthesumofthethreecards,usingtheusualblackjackschemeinwhich
anacecounts1or11,appearingintheflopinhold’em.Theynoticed,orthought
theynoticed,thatthecardsfrequentlysumto21.Theymadeasmallwager
basedonintuitiveguessesabouttheprobabilityofthesumbeing21.
Justtomakecertainyouunderstandthequestion,I’llgivetwoexamples.If
theflopis4-J-A,thesumiseither15or25.Iftheflopis2-9-K,thesumis21.
Thequestionthenis:Whatistheprobabilitythesumoftheflopinhold’emis
21?Ifyoudon’twanttoworkouttheexactvalue,makeanintuitiveguess.
Bytheway,wearegoingtoworkoutthevalueundertheassumptionthat
theobservorknowsnoneofthecardsheldbyanyoftheplayers.
LetmefinishbywishingRandyandDavesuccesswiththismagazine.Ialso
wishtothankthemforaskingmetoplayapart.
2

Plik z chomika:

Inne pliki z tego folderu:

Inne foldery tego chomika:

Zgłoś jeśli naruszono regulamin