odds of winning the lottery

7/28/2019 Odds of Winning the Lottery

1/9

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.


2/9

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


3/9

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


4/9

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


5/9

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


6/9

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


7/9

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


8/9

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


9/9

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)