odds of winning the lottery
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LouisBarclay
TheoddsofwinningtheNationalLotteryare14milliontoone.Whydo
peopleplay?
"AlotteryisaTaxation
UponalltheFoolsincreation"
HenryFielding,TheLottery,1792,sixteenyearsbeforetheUKLotterywasdenouncedbyparliamentasradicallyviciousandabolishedeighteenyearslater.
Theyliketowin,buttheydonotconsidertheirprobabilityofwinning.
Wagenaar,ParadoxesofGamblingBehaviour,1988,seventeenyearsbeforeCamelotannouncesthatitisthebiggestprogrammeofcivicregenerationsincethe
19thCentury
1.
ThirteenyearsonfromitsemergenceintoBritishconsciousness,theNationalLotteryisstrugglingtoattra
thelevelsofinterest,andmoreimportantly,demand,whichitexperiencedinitsopeningyears.Having
peakedin1997/82,justthreeyearsafterCamelotwasawardeditsfirstsevenyearlotterycontracttorun
thescheme,theNationalLotterybrandhasattemptedtogrowbymeansofinnovationinitsdiverse
portfolioofgames3.HoweverthebiweeklyLottodraw
4,whichconstitutesthelargestpartofNational
Lotteryrevenue,isexperiencingalongtermtrendofdecliningsales5.Thisisnottosaythatthegameis
unpopularaccordingtoCamelot,over65%ofUKadultsplayregularly,makingLottothemostpopular
formofgamblinginthiscountry.
Theeconomicside
Thelotteryisclassifiedassoftcoregambling,incontrasttomostcasinogames,whicharetermedhard
core.Thedistinctionisbasedontherelativesumsofmoneyspentonbothforms,andtheirpowertoturn
intoanaddiction(compulsivity).Thelotteryisalsodistinguishedbytherelativelyinfrequentopportunities
1 http://www.camelotgroup.co.uk/pressreleases/2005/november/HYResultsNov2005Final.pdf2 Mintel International Group, Lotteries [Leisure Intelligence], 2004, p23 For instance, Dream Numbers, a game introduced this yearhttp://www.camelotgroup.co.uk/pressreleases/2006/May/EndYearResults2006.pdf4 The draw to which this question refers. There are in fact many games under the name of the National Lottery, including thethree extra draws of Dream Number, Thunderball and Hotpicks, and a range of scratch-cards.
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toplay,andtherelativelylongdelaybetweenbetandoutcome.Also,thepayoutsareorganizedsothat
thereisonedisproportionatelylargeprize,withseveralsmaller,moreattainable,rewards.Whiletheodds
onwinningtheLottojackpotare13,983,815toone,thereisa51toonechanceofwinninganyofthe
prizes.Lastly,thesimplicityofalotteryisnoteworthyinthecaseofLotto,choosingsixnumbersfrom1t
49.
Theapproachusedwithinstandardeconomicstoevaluatedecisionsmadeinthefaceofriskand
uncertaintyistheexpectedvaluemodel6.Inthecontextofalottery,themodelisusedtocomparethe
priceofthetickettotheamountthelotteryplayercouldexpecttotakeasayield.Thislastpartiscalculate
astheaveragevalueofthepayoutmultipliedbytheprobabilityofoneticketwinning.Typicallyforlotterie
theexpectedvalueisnegative,andtendstorangefromabout 30%oftheticketpriceto 70%ormore.Th
iscurious,asmosthardcoregamblingfeaturesahigherexpectedvalue.Roulette,forexample,hasan
expectedvalueof5%7.InthespecificcaseoftheUKlottery,theLotto,ona1tickettheexpectedvaluei
about71pence.Inotherwords,thevaluefromplayingtheLotteryis29%lessthantheticketprice.
Therefore,theexpectedvaluemodelpredictsthatpeoplewillnotplayLotto.
Inpractice,peopledoplaythelotteryandthissuggeststhattheexpectedvaluemodelignoresother
utilitiesthataregainedfroma1lotteryticket,inadditiontothe71penceinexpectedvalue.Theseutiliti
include,firstly,theopportunitytotakepartinanaspectofpopularculturebanterwithfriendsandfamil
and
speculation
over
numbers
and
near
misses.
Secondly,
there
is
the
warm
glow
effect
of
having
indirectlydonatedmoneytocharity(29penceperticket).Finally,inthesmallscrapofpaperthereisthe
possibilityofwinningalifetransformingsumofmoney.Referredtoasbuyingadreamthisfactoris
consideredbymanytoconstitutethelargestutilityfromplayingtheLottery.
Theinsufficiencyoftheconventionaleconomicapproach
Doticket
buyers
weigh
up
these
utilities
and
consider
them
to
more
than
make
up
for
the
29
pence
gap?
Perhapssubconsciously,butthereisalsoatheorythatmanyofthosewhospendonlotteryticketssuffer
frompsychological misconceptionswhichmeanthatinfact,theydonotconsidertheLotteryinrational
terms.ThisisevidencedbythecaseofthecompetingDutchlotteriesinthe1980s:theStateLotteryandth
GiroLottery.Theformerhadanexpectedvalueof30%,with2millionplayers.TheGiroLotterywas
5 Lotteries [Leisure Intelligence], 2004, p26 As used in Willem Wagenaars Paradoxes of Gambling Behavior, 1988, and Stephen Creigh-Tyte and Lisa Farrells 1998 paperThe Economics of the National Lottery7 According to The Times, in The Lottery It Shouldnt Be You, January 27, 2006, Casinos typically pay out more than 97 per
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launchedwithanexpectedvalueof75%andthereforenorationalplayershouldhavepreferredtoplayit
ratherthantheStatelottery.Nonetheless,itwasabletoattract1.2millionplayers.Thissuggeststhatas
longasalotterykeepstotacitlyacceptedpropertiesofafairstructure8,suchasthelowcostofaticket,
andsufficientlylifetransformingpowerofthemainprize,itwillattractdemand.
Moreevidencetosuggestthat,ingeneral,Lottoplayersdonotthinkrationally,liesinthepriceelasticityo
demandforLottotickets,whichhasbeenshowntolieclosetounity9.Thismeansthata50%decreasein
thepriceofaLotteryticketwillresultinroughlya50%increaseinthequantitydemanded.However,the
expectedelasticityforrationalconsumerswouldleadtosignificantly,anddisproportionatelygreater
demandasthepricenearedtheexpectedvalueoftheLotteryticketandwentbelowit.Thisisbecausethe
moneyspentonaticketpricedatitsexpectedvalue(orless)wouldeffectivelybeaworthwhileinvestmen
Heuristicsandbiases
Thepsychologicalmisconceptionsthatmightmakeplayersmorelikelytobuyalotteryticketcanbedivide
intotwocategories: intuitivediscoveryprocesses,namedheuristics,andpartialitieswhichhinder
objectiveconsiderationofanissue,correctlytermedbiases10
.WillemWagenaarcallstheseabagof
tricks11
which,together,maygosomewaytoexplainingthemindsetoflotteryparticipants,andin
particularthefailureoffeedbackthatis,whycontinuedlossesdonotdisillusionplayers.
Therearetwomainbiases:
Confirmationbiashappenswhenapersonneglectstheprincipleofregressiontothemean.Thisistosay
thatapersonmightthinkthattheyareonawinningstreak,orgettingcloser,becausetheyhavehadtwo
nearmisseswiththeirnumbers.Someplayersbelievethatcertainnumbershaveahigherlikelihoodof
winning,asevidencedbysitessuchaslotterygen.co.ukwhichpresentstatisticsofhotnumbers.
Hindsightbiasoccursfromthinkingthatalosswaspredictedinotherwords,thatnotwinningwas
inevitable.Thisencouragesthepersontothinkthattheywillwinonthenextgamble,becausetheybelieve
thattheirpredictionsholdfast.
cent of money staked8 Paradoxes of Gambling Behavior p709 Farrell et al., 199610 Hogarth, 1981
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Fiveheuristicexplanationsareidentified:
Problemframingiswhenaplayerattributeslosingtoalackofskill,possiblysubconsciously.Thereforein
thecaseofthelottery,everynewselectionofnumbersisanewattempttorefinetechnique.Buyingticket
regularlyisimportantfortheprocessofimproving.
Similarly,flexibleattributionresultsfromplayersconsideringskilltohavehadahandinanearmiss,but
losingtobedowntootherfactorssuchasbuyingtheticketfromthewrongplace,oratthewrongtime.
Lotterycompaniesalongwiththemediapublicizethewinnersofthejackpot.Thisleadspeopletoconside
ahigheravailabilityoftheprizethanthatwhichactuallyexists.Itthereforecausesthemtooverestimate
theprobabilityandconsiderthelotterymoreworthwhile.Camelot,theownersoftheNationalLottery
contract,haveemphasizedavailabilityinpastadvertisingcampaignswithsloganssuchasitcouldbeyou.
Anticipatoryregretappliestohardcoreplayerswhokeepthesamenumbersforeverygametheyplay.
TheyfeelcompelledtobuyticketseveryWednesdayandSaturdayforfearthatonthedaytheydonotpla
thenumberswillcomeup.
Illusorycorrelationisthebeliefinluckaffectingthechanceofsuccessinagame.Forinstance,superstitiou
people
who
believe
in
lucky
days
might
consider
their
odds
improved,
and
thus
be
more
likely
to
buy
a
ticket.Thisissimilartothegamblersfallacyoffailingtounderstandthatsuccessinthelotteryis
independentofsuccessinotherevents.
Thesementalquirksareallmademorelikelybyanotherheuristic: reductionofcomplexity12
.Thisoccurs
whenlotteryplayersfailtorealizewhatreallydeterminestheoddsofwinningthejackpot,anddonot
considerthescaleofthegameincorrectproportion.Buteventhesepsychologicalmisconceptionsdonot
satisfactorilyaccount
for
regular
lottery
play.
They
may
explain
why
people
buy
impulsively,
such
as
in
the
caseofavailabilityorillusorycorrelation,andmayshowsomecharacteristicsofhardcoreplayers,asinth
caseofflexibleattributionandproblemframing,buttheydonotaccountfortheconstantdemandfor
lotteryticketsby27millionadultsintheUK.
ManycriticsandcertainnewspapersclaimthattheNationalLotteryencouragesgamblingamongthose
11 Paradoxes of Gambling Behavior p7612 Paradoxes of Gambling Behavior p81
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whocanleastaffordit13
.Itissometimessuggestedthatheuristicsandbiasesare,bytheirnature,afeatur
oflowerincomegroups,whicharemorepoorlyeducated.Thereforeifheuristicsandbiasesconstituteda
largepartofthereasonsforwhichpeopleplaythelotteryregularly,somecorrelationbetweenincomean
regularlotteryplaywouldbeobserved. ABRMB/Mintelstudyof964adultsgivesthefollowingdataonth
proportionofpeopleinthefivestandardsocioeconomicgroupswhoplayNationalLotterygamesregular
Saturday Wednesday
AB 61% 34%
C1 62% 33%
C2 73% 38%
D 64% 40%
E 52% 33%
FromParticipationinNLgamesoverthepast12months,bygender,age,andsocioeconomicgroup,May
2004(MintelInternationalGroup,Lotteries[LeisureIntelligence],2004,p32).
Thesedataquestiontheviewthatlowersocioeconomicgroupsplaythelotterymore.Themiddling
C2groupismostdedicatedtotheNationalLottery,butothersdonotlagfarbehind.Anexplanationis
neededtoaccountforthefactthat61%ofthe(relativelywelleducated)ABdemographicplaythe
Saturday
Lotto
on
a
regular
basis.
ProspectTheory
Perhaps,then,wemustreturntoseekanexplanationforwhypeopleplayingthelotterymayactuallybe
behavingrationally.Theheuristicsandbiasesdescribedabovesuggestthatthehumanmindsetwhen
buyinglotteryticketsissignificantlymoreliabletoinconsistenciesthaningeneral,thatis,theyseekto
explainlottery
playing
behaviour
as
adeviation
from
rationality.
Normative
theories
of
gambling,
accounts
whichattempttoexplainlotterygamblingwithoutessentiallychangingthenatureofthegame14
usethe
rationalmindasthepointofreference.ProspectTheory(KahnemanandTversky1979)isthekeynormativ
theorythatcanbeappliedtolotteryplay.
ToexplainProspectTheory,itisnecessarytoconsidertheconditionunderwhichlotteryplayis
13 The Times puts forward such views in The Lottery It Shouldnt Be You, January 27, 2006.14 Paradoxes of Gambling Behavior p71
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economicallyrational(discardingthevalueofutilitiessuchasthosedescribedabove).Thisconditioncome
intheformofthefollowinginequality:
Expectedvalue C
TheconstantCrepresentsthepriceofaticket.Theinequalityisnotflexible,butProspectTheorysuggests
thattheactualvalueofCtoapersonis.Thepriceofaticketisconsideredwithreferencetoapersons
financialstatusquo;Hence,ifthepersoniscomfortableenoughthattheamounttheyspendonthelottery
everyweekisirrelevanttothem,Ccanbediscarded(replacedbyavalueof0),satisfyingtheinequalityan
makinglotteryplaynotionallyrational.
ProspectTheoryquestionstheideaintraditionaleconomicsthattherationalpersonseekstotakecareof
everypennyheownsinordertomaximizehisutility.Insteadtheargumentisthatthevaluesplacedon
winningandlosingarenotdirectlyrelatedtotheprobabilityofsucheventsoccurring.Ofcourse,onecould
stillarguethatthisisanirrationalconceit andthatitisabsurdforasocalled'rational'persontoconsider
weekly415
sumofmoneyirrelevantinthelongrun,seeingasthepossiblesavingsovertheyearswould
havesometransformingpower,evenifthelittlepoundcoinsgoingonebyonedidnot.
ProspectTheorycombinesforcefullywiththepowerofsocialpressurestoconvincepeopletoplaythe
Lottery.
If
one's
friends
all
believe
that
the
weekly
'charge'
for
being
a
participant
in
the
Lotto
draw
is
so
smallastobenegligible,thesentimentislikelytoextendtooneself.
TheLottohasalsospawnedlotterysyndicates,wheretheindividualcontributesandthesyndicateselects
numberssothat,forinstance,theindividualonlyneedstogettwocorrectnumbersinordertowinafair
amountofmoney.Here,inasimilarwayasthesocialpressuresabove,ProspectTheorycancombinewith
conveniencetomaketheLottodrawmoreappealing.Thesesyndicates,whichhavewonaquarterofall
Lotteryjackpots
16
,have
anumber
of
ways
to
make
the
Lottery
more
appealing
to
those
put
off
by
the
overwhelminglyweakoddsforthesingleplayer.Ultimately,though,therewardsareproportionaltothe
amountofmoneyputin.Certainlyintermsofexpectedreturnthereisnoadvantagetoplayingina
syndicate.
15 4 is roughly the average weekly spending on lottery tickets by a regular player.http://www.natlotcomm.gov.uk/UploadDocs/Contents/Documents/social_research_2003_pdf(3).pdf16 http://www.national-lottery.co.uk/player/information.do?info=newsandinfo
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TheroleofCamelot
Camelot,theUKlotteryprovidernowayearintoitsthirdcontract,isabletoalterdemandfortheLotto
drawtosomeextent,althoughitsinfluencecertainlydoesnotprovidethemotivationsforlotteryplay.Its
innovationshavebeenmanyandfrequent(althoughoccasionallywithdireresults).Ithasexploitedthelac
ofrestrictionsonadvertisingthatwouldnormallyapplytogamblingcompanies,startingoffwithhigh
profileTVandradiocampaignsbackin1994,andprogressingswiftlyonthrougharangeofslogans,logos
andaffiliations.Hiccups,suchastheflopwhichwasthe'dontlivealittle,liveLottocampaignwithBilly
Connolly,andLotto'sunfortunatelinktotheMillenniumDome,werenoticeableinslowingsales.Successe
suchasthe'fingerscrossed'logo(which,asaresultofCamelotsinfluence,nowmustbecarriedbyall
NationalLotteryfundedcharities)andtheproliferationofthe'itcouldbeyou'catchphrasehave
contributedtocreatingarecognizablebrand.Camelothaveastrongincentivetoincreaserevenueofthe
NationalLottery halfapencefromeachpoundticketgoesdirectlytothefirm'sprofit.Furthermore,the
priceofatickethasstayedconstantsincethelotterybegan,meaningthatCamelot'sprofitshavetotryan
conquerbothinflationandthereductioninCamelotstakefrom1%profitto0.5%profitthatwasmadea
fewyearsagoafterpressurefromOFLOT,theregulatoryboardthatoverseeslotteries.
The
role
of
a
technologically
advanced
and
widespread
retail
network
is
important
in
maximizing
revenue.Afterall,withouttheopportunitytobuythehighlynonessentialtickets,therewouldbelittleeffective
demand.Asitstands,Camelotcanboastthatmorethan96%ofUKhouseholdsarewithintwomilesofa
Lotteryterminal17
.Also,in2002aprogramwasundertakentooverhaulthesemachines,triplingthe
numberoflotteryticketsavailableperminute(thisnumbercontinuestorise).Moreover,ticketshavebee
availableonline,onmobilephone,andeven(throughadealwithBSkyB)ondigitalTVsincefouryearsago
Allthisgoestosuggestthattheeasewithwhichonecanplaywithoutanyapparentdisruptiontoone's
lifestyleisafactor
in
determining
demand,
Camelotaimstomakethiseasenotjustaquestionoflifestyle,butalsooffinancialaffordability,withits
stubbornrefusaltoraisetheLottoticketprice.Equallyimportantly,especiallywiththegrowthincharitabl
awarenessintheWest,Camelotstartedin2002tomakeplayingLottoeasyonone'sconscienceaswell,by
emphasizingthebenefitstosocietyfromthe29penceperLottopoundthatgoestogoodcauses.Thisis
17 Lotteries [Leisure Intelligence], 2004, p24
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evidencedbytheadvertisingcampaignofthatyearwhichfeaturedbeneficiariesofNationalLottery
'fingerscrossed'charitiessayingatelevised'Thankyou'toNLplayers,accompaniedbytheslogan'You
played,thenationwon'.NodoubtthisfeedsintotheutilityofthewarmglowfrombuyingaLottoticket,
hencegivingpeopleajustificationtospendthemoney.Thetrendoffocusingoncharitycontinues aquic
lookattheprominentpositionofthe'GoodCauseCounter'onCamelot'swebsiteconfirmsthis.
Thedecisivefactor
Ultimately,theideasbehindProspectTheoryform,inmyopinion,thelargestpartoftheanswertothe
question'WhydopeopleplayLotto?ItisnoticeablethatLotteryplayersveryrarelyconsiderthemselvest
bewastingmoneythissupportsthenotionthatLottobuyingmoneyismarginal,suitableforexpenditure
onnonessentialgoodsandrarelyexperienceaddiction.Theutilities,aslaidoutabove,playasupporting
roletheexcitement,thedream,andthedeliberationanddiscussionovernumberseveniftheseutilitie
are,andarerecognizedbyplayerstobepetty,cheapthrills.
ToquoteDianeThompson,theCEOofCamelot,theLottodrawisa'harmlessflutter'18
.Thisisaneaterand
lesscircumspectwayofarticulatingProspectTheory.Itisaphrasewhichcomesclosertowhattheregular
Lottoticketbuyermightthinktohimselfandthat,afterall,isthekeytounderstandingwhypeopleplay.
18 From her letter to The Times, 9 September 2007
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Bibliography
BrunoBernard,LotteriesinEurope(1994)
StephenCreighTyteandLisaFarrell,TheEconomicsoftheNationalLottery(1998)
DKahnermanandATversky,ProspectTheory:AnAnalysisofDecisionUnderRisk(1979)
MintelInternationalGroup,Lotteries(LeisureIntelligence)(2004)
PRogers,TheCognitivePsychologyofLotteryGambling:ATheoreticalReview,publishedintheJournalof
GamblingStudies(1998)
KerrySproston,ReportonParticipation,ExpenditureandAttitudes,conductedfortheNationalLottery
Commission(2003)availableat
http://www.natlotcomm.gov.uk/UploadDocs/Contents/Documents/social_research_2003_pdf(3).pdf)
WillemWagenaar,ParadoxesofGamblingBehaviour,1988
Online
http://freespace.virgin.net/john.hewitt1/pg_gloss.htmforguidanceonthedefinitionofaheuristicinthe
psychologicalcontext
http://wordnet.princeton.edu/perl/webwn?s=biaslikewise,forthedefinitionofbiasinthepsychological
context
Note:becauseoftheoutdatednatureofmanyofthereportsavailableattheBritishLibraryontheNationa
Lottery(duetocopyrightlaw),someofthequotedfiguresabovemayhavechangedinthelastfewyears.
http://www.natlotcomm.gov.uk/UploadDocs/Contents/Documents/social_research_2003_pdf(3).pdf)http://www.natlotcomm.gov.uk/UploadDocs/Contents/Documents/social_research_2003_pdf(3).pdf)http://freespace.virgin.net/john.hewitt1/pg_gloss.htmhttp://wordnet.princeton.edu/perl/webwn?s=biashttp://wordnet.princeton.edu/perl/webwn?s=biashttp://freespace.virgin.net/john.hewitt1/pg_gloss.htmhttp://www.natlotcomm.gov.uk/UploadDocs/Contents/Documents/social_research_2003_pdf(3).pdf)
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