Odds of Winning the Lottery

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<ul><li><p>7/28/2019 Odds of Winning the Lottery</p><p> 1/9</p><p>LouisBarclay</p><p>TheoddsofwinningtheNationalLotteryare14milliontoone.Whydo</p><p>peopleplay?</p><p>"AlotteryisaTaxation</p><p>UponalltheFoolsincreation"</p><p>HenryFielding,TheLottery,1792,sixteenyearsbeforetheUKLotterywasdenouncedbyparliamentasradicallyviciousandabolishedeighteenyearslater.</p><p>Theyliketowin,buttheydonotconsidertheirprobabilityofwinning.</p><p>Wagenaar,ParadoxesofGamblingBehaviour,1988,seventeenyearsbeforeCamelotannouncesthatitisthebiggestprogrammeofcivicregenerationsincethe</p><p>19thCentury</p><p>1.</p><p>ThirteenyearsonfromitsemergenceintoBritishconsciousness,theNationalLotteryisstrugglingtoattra</p><p>thelevelsofinterest,andmoreimportantly,demand,whichitexperiencedinitsopeningyears.Having</p><p>peakedin1997/82,justthreeyearsafterCamelotwasawardeditsfirstsevenyearlotterycontracttorun</p><p>thescheme,theNationalLotterybrandhasattemptedtogrowbymeansofinnovationinitsdiverse</p><p>portfolioofgames3.HoweverthebiweeklyLottodraw</p><p>4,whichconstitutesthelargestpartofNational</p><p>Lotteryrevenue,isexperiencingalongtermtrendofdecliningsales5.Thisisnottosaythatthegameis</p><p>unpopularaccordingtoCamelot,over65%ofUKadultsplayregularly,makingLottothemostpopular</p><p>formofgamblinginthiscountry.</p><p>Theeconomicside</p><p>Thelotteryisclassifiedassoftcoregambling,incontrasttomostcasinogames,whicharetermedhard</p><p>core.Thedistinctionisbasedontherelativesumsofmoneyspentonbothforms,andtheirpowertoturn</p><p>intoanaddiction(compulsivity).Thelotteryisalsodistinguishedbytherelativelyinfrequentopportunities</p><p>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.</p></li><li><p>7/28/2019 Odds of Winning the Lottery</p><p> 2/9</p><p>toplay,andtherelativelylongdelaybetweenbetandoutcome.Also,thepayoutsareorganizedsothat</p><p>thereisonedisproportionatelylargeprize,withseveralsmaller,moreattainable,rewards.Whiletheodds</p><p>onwinningtheLottojackpotare13,983,815toone,thereisa51toonechanceofwinninganyofthe</p><p>prizes.Lastly,thesimplicityofalotteryisnoteworthyinthecaseofLotto,choosingsixnumbersfrom1t</p><p>49.</p><p>Theapproachusedwithinstandardeconomicstoevaluatedecisionsmadeinthefaceofriskand</p><p>uncertaintyistheexpectedvaluemodel6.Inthecontextofalottery,themodelisusedtocomparethe</p><p>priceofthetickettotheamountthelotteryplayercouldexpecttotakeasayield.Thislastpartiscalculate</p><p>astheaveragevalueofthepayoutmultipliedbytheprobabilityofoneticketwinning.Typicallyforlotterie</p><p>theexpectedvalueisnegative,andtendstorangefromabout 30%oftheticketpriceto 70%ormore.Th</p><p>iscurious,asmosthardcoregamblingfeaturesahigherexpectedvalue.Roulette,forexample,hasan</p><p>expectedvalueof5%7.InthespecificcaseoftheUKlottery,theLotto,ona1tickettheexpectedvaluei</p><p>about71pence.Inotherwords,thevaluefromplayingtheLotteryis29%lessthantheticketprice.</p><p>Therefore,theexpectedvaluemodelpredictsthatpeoplewillnotplayLotto.</p><p>Inpractice,peopledoplaythelotteryandthissuggeststhattheexpectedvaluemodelignoresother</p><p>utilitiesthataregainedfroma1lotteryticket,inadditiontothe71penceinexpectedvalue.Theseutiliti</p><p>include,firstly,theopportunitytotakepartinanaspectofpopularculturebanterwithfriendsandfamil</p><p>and</p><p>speculation</p><p>over</p><p>numbers</p><p>and</p><p>near</p><p>misses.</p><p>Secondly,</p><p>there</p><p>is</p><p>the</p><p>warm</p><p>glow</p><p>effect</p><p>of</p><p>having</p><p>indirectlydonatedmoneytocharity(29penceperticket).Finally,inthesmallscrapofpaperthereisthe</p><p>possibilityofwinningalifetransformingsumofmoney.Referredtoasbuyingadreamthisfactoris</p><p>consideredbymanytoconstitutethelargestutilityfromplayingtheLottery.</p><p>Theinsufficiencyoftheconventionaleconomicapproach</p><p>Doticket</p><p>buyers</p><p>weigh</p><p>up</p><p>these</p><p>utilities</p><p>and</p><p>consider</p><p>them</p><p>to</p><p>more</p><p>than</p><p>make</p><p>up</p><p>for</p><p>the</p><p>29</p><p>pence</p><p>gap?</p><p>Perhapssubconsciously,butthereisalsoatheorythatmanyofthosewhospendonlotteryticketssuffer</p><p>frompsychological misconceptionswhichmeanthatinfact,theydonotconsidertheLotteryinrational</p><p>terms.ThisisevidencedbythecaseofthecompetingDutchlotteriesinthe1980s:theStateLotteryandth</p><p>GiroLottery.Theformerhadanexpectedvalueof30%,with2millionplayers.TheGiroLotterywas</p><p>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</p></li><li><p>7/28/2019 Odds of Winning the Lottery</p><p> 3/9</p><p>launchedwithanexpectedvalueof75%andthereforenorationalplayershouldhavepreferredtoplayit</p><p>ratherthantheStatelottery.Nonetheless,itwasabletoattract1.2millionplayers.Thissuggeststhatas</p><p>longasalotterykeepstotacitlyacceptedpropertiesofafairstructure8,suchasthelowcostofaticket,</p><p>andsufficientlylifetransformingpowerofthemainprize,itwillattractdemand.</p><p>Moreevidencetosuggestthat,ingeneral,Lottoplayersdonotthinkrationally,liesinthepriceelasticityo</p><p>demandforLottotickets,whichhasbeenshowntolieclosetounity9.Thismeansthata50%decreasein</p><p>thepriceofaLotteryticketwillresultinroughlya50%increaseinthequantitydemanded.However,the</p><p>expectedelasticityforrationalconsumerswouldleadtosignificantly,anddisproportionatelygreater</p><p>demandasthepricenearedtheexpectedvalueoftheLotteryticketandwentbelowit.Thisisbecausethe</p><p>moneyspentonaticketpricedatitsexpectedvalue(orless)wouldeffectivelybeaworthwhileinvestmen</p><p>Heuristicsandbiases</p><p>Thepsychologicalmisconceptionsthatmightmakeplayersmorelikelytobuyalotteryticketcanbedivide</p><p>intotwocategories: intuitivediscoveryprocesses,namedheuristics,andpartialitieswhichhinder</p><p>objectiveconsiderationofanissue,correctlytermedbiases10</p><p>.WillemWagenaarcallstheseabagof</p><p>tricks11</p><p>which,together,maygosomewaytoexplainingthemindsetoflotteryparticipants,andin</p><p>particularthefailureoffeedbackthatis,whycontinuedlossesdonotdisillusionplayers.</p><p>Therearetwomainbiases:</p><p>Confirmationbiashappenswhenapersonneglectstheprincipleofregressiontothemean.Thisistosay</p><p>thatapersonmightthinkthattheyareonawinningstreak,orgettingcloser,becausetheyhavehadtwo</p><p>nearmisseswiththeirnumbers.Someplayersbelievethatcertainnumbershaveahigherlikelihoodof</p><p>winning,asevidencedbysitessuchaslotterygen.co.ukwhichpresentstatisticsofhotnumbers.</p><p>Hindsightbiasoccursfromthinkingthatalosswaspredictedinotherwords,thatnotwinningwas</p><p>inevitable.Thisencouragesthepersontothinkthattheywillwinonthenextgamble,becausetheybelieve</p><p>thattheirpredictionsholdfast.</p><p>cent of money staked8 Paradoxes of Gambling Behavior p709 Farrell et al., 199610 Hogarth, 1981</p></li><li><p>7/28/2019 Odds of Winning the Lottery</p><p> 4/9</p><p>Fiveheuristicexplanationsareidentified:</p><p>Problemframingiswhenaplayerattributeslosingtoalackofskill,possiblysubconsciously.Thereforein</p><p>thecaseofthelottery,everynewselectionofnumbersisanewattempttorefinetechnique.Buyingticket</p><p>regularlyisimportantfortheprocessofimproving.</p><p>Similarly,flexibleattributionresultsfromplayersconsideringskilltohavehadahandinanearmiss,but</p><p>losingtobedowntootherfactorssuchasbuyingtheticketfromthewrongplace,oratthewrongtime.</p><p>Lotterycompaniesalongwiththemediapublicizethewinnersofthejackpot.Thisleadspeopletoconside</p><p>ahigheravailabilityoftheprizethanthatwhichactuallyexists.Itthereforecausesthemtooverestimate</p><p>theprobabilityandconsiderthelotterymoreworthwhile.Camelot,theownersoftheNationalLottery</p><p>contract,haveemphasizedavailabilityinpastadvertisingcampaignswithsloganssuchasitcouldbeyou.</p><p>Anticipatoryregretappliestohardcoreplayerswhokeepthesamenumbersforeverygametheyplay.</p><p>TheyfeelcompelledtobuyticketseveryWednesdayandSaturdayforfearthatonthedaytheydonotpla</p><p>thenumberswillcomeup.</p><p>Illusorycorrelationisthebeliefinluckaffectingthechanceofsuccessinagame.Forinstance,superstitiou</p><p>people</p><p>who</p><p>believe</p><p>in</p><p>lucky</p><p>days</p><p>might</p><p>consider</p><p>their</p><p>odds</p><p>improved,</p><p>and</p><p>thus</p><p>be</p><p>more</p><p>likely</p><p>to</p><p>buy</p><p>a</p><p>ticket.Thisissimilartothegamblersfallacyoffailingtounderstandthatsuccessinthelotteryis</p><p>independentofsuccessinotherevents.</p><p>Thesementalquirksareallmademorelikelybyanotherheuristic: reductionofcomplexity12</p><p>.Thisoccurs</p><p>whenlotteryplayersfailtorealizewhatreallydeterminestheoddsofwinningthejackpot,anddonot</p><p>considerthescaleofthegameincorrectproportion.Buteventhesepsychologicalmisconceptionsdonot</p><p>satisfactorilyaccount</p><p>for</p><p>regular</p><p>lottery</p><p>play.</p><p>They</p><p>may</p><p>explain</p><p>why</p><p>people</p><p>buy</p><p>impulsively,</p><p>such</p><p>as</p><p>in</p><p>the</p><p>caseofavailabilityorillusorycorrelation,andmayshowsomecharacteristicsofhardcoreplayers,asinth</p><p>caseofflexibleattributionandproblemframing,buttheydonotaccountfortheconstantdemandfor</p><p>lotteryticketsby27millionadultsintheUK.</p><p>ManycriticsandcertainnewspapersclaimthattheNationalLotteryencouragesgamblingamongthose</p><p>11 Paradoxes of Gambling Behavior p7612 Paradoxes of Gambling Behavior p81</p></li><li><p>7/28/2019 Odds of Winning the Lottery</p><p> 5/9</p><p>whocanleastaffordit13</p><p>.Itissometimessuggestedthatheuristicsandbiasesare,bytheirnature,afeatur</p><p>oflowerincomegroups,whicharemorepoorlyeducated.Thereforeifheuristicsandbiasesconstituteda</p><p>largepartofthereasonsforwhichpeopleplaythelotteryregularly,somecorrelationbetweenincomean</p><p>regularlotteryplaywouldbeobserved. ABRMB/Mintelstudyof964adultsgivesthefollowingdataonth</p><p>proportionofpeopleinthefivestandardsocioeconomicgroupswhoplayNationalLotterygamesregular</p><p>Saturday Wednesday</p><p>AB 61% 34%</p><p>C1 62% 33%</p><p>C2 73% 38%</p><p>D 64% 40%</p><p>E 52% 33%</p><p>FromParticipationinNLgamesoverthepast12months,bygender,age,andsocioeconomicgroup,May</p><p>2004(MintelInternationalGroup,Lotteries[LeisureIntelligence],2004,p32).</p><p>Thesedataquestiontheviewthatlowersocioeconomicgroupsplaythelotterymore.Themiddling</p><p>C2groupismostdedicatedtotheNationalLottery,butothersdonotlagfarbehind.Anexplanationis</p><p>neededtoaccountforthefactthat61%ofthe(relativelywelleducated)ABdemographicplaythe</p><p>Saturday</p><p>Lotto</p><p>on</p><p>a</p><p>regular</p><p>basis.</p><p>ProspectTheory</p><p>Perhaps,then,wemustreturntoseekanexplanationforwhypeopleplayingthelotterymayactuallybe</p><p>behavingrationally.Theheuristicsandbiasesdescribedabovesuggestthatthehumanmindsetwhen</p><p>buyinglotteryticketsissignificantlymoreliabletoinconsistenciesthaningeneral,thatis,theyseekto</p><p>explainlottery</p><p>playing</p><p>behaviour</p><p>as</p><p>adeviation</p><p>from</p><p>rationality.</p><p>Normative</p><p>theories</p><p>of</p><p>gambling,</p><p>accounts</p><p>whichattempttoexplainlotterygamblingwithoutessentiallychangingthenatureofthegame14</p><p>usethe</p><p>rationalmindasthepointofreference.ProspectTheory(KahnemanandTversky1979)isthekeynormativ</p><p>theorythatcanbeappliedtolotteryplay.</p><p>ToexplainProspectTheory,itisnecessarytoconsidertheconditionunderwhichlotteryplayis</p><p>13 The Times puts forward such views in The Lottery It Shouldnt Be You, January 27, 2006.14 Paradoxes of Gambling Behavior p71</p></li><li><p>7/28/2019 Odds of Winning the Lottery</p><p> 6/9</p><p>economicallyrational(discardingthevalueofutilitiessuchasthosedescribedabove).Thisconditioncome</p><p>intheformofthefollowinginequality:</p><p>Expectedvalue C</p><p>TheconstantCrepresentsthepriceofaticket.Theinequalityisnotflexible,butProspectTheorysuggests</p><p>thattheactualvalueofCtoapersonis.Thepriceofaticketisconsideredwithreferencetoapersons</p><p>financialstatusquo;Hence,ifthepersoniscomfortableenoughthattheamounttheyspendonthelottery</p><p>everyweekisirrelevanttothem,Ccanbediscarded(replacedbyavalueof0),satisfyingtheinequalityan</p><p>makinglotteryplaynotionallyrational.</p><p>ProspectTheoryquestionstheideaintraditionaleconomicsthattherationalpersonseekstotakecareof</p><p>everypennyheownsinordertomaximizehisutility.Insteadtheargumentisthatthevaluesplacedon</p><p>winningandlosingarenotdirectlyrelatedtotheprobabilityofsucheventsoccurring.Ofcourse,onecould</p><p>stillarguethatthisisanirrationalconceit andthatitisabsurdforasocalled'rational'persontoconsider</p><p>weekly415</p><p>sumofmoneyirrelevantinthelongrun,seeingasthepossiblesavingsovertheyearswould</p><p>havesometransformingpower,evenifthelittlepoundcoinsgoingonebyonedidnot.</p><p>ProspectTheorycombinesforcefullywiththepowerofsocialpressurestoconvincepeopletoplaythe</p><p>Lottery.</p><p>If</p><p>one's</p><p>friends</p><p>all</p><p>believe</p><p>that</p><p>the</p><p>weekly</p><p>'charge'</p><p>for</p><p>being</p><p>a</p><p>participant</p><p>in</p><p>the</p><p>Lotto</p><p>draw</p><p>is</p><p>so</p><p>smallastobenegligible,thesentimentislikelytoextendtooneself.</p><p>TheLottohasalsospawnedlotterysyndicates,wheretheindividualcontributesandthesyndicateselects</p><p>numberssothat,forinstance,theindividualonlyneedstogettwocorrectnumbersinordertowinafair</p><p>amountofmoney.Here,inasimilarwayasthesocialpressuresabove,ProspectTheorycancombinewith</p><p>conveniencetomaketheLottodrawmoreappealing.Thesesyndicates,whichhavewonaquarterofall</p><p>Lotteryjackpots</p><p>16</p><p>,have</p><p>anumber</p><p>of</p><p>ways</p><p>to</p><p>make</p><p>the</p><p>Lottery</p><p>more</p><p>appealing</p><p>to</p><p>those</p><p>put</p><p>off</p><p>by</p><p>the</p><p>overwhelminglyweakoddsforthesingleplayer.Ultimately,though,therewardsareproportionaltothe</p><p>amountofmoneyputin.Certainlyintermsofexpectedreturnthereisnoadvantagetoplayingina</p><p>syndicate.</p><p>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</p></li><li><p>7/28/2019 Odds of Winning the Lottery</p><p> 7/9</p><p>TheroleofCamelot</p><p>Camelot,theUKlotteryprovidernowayearintoitsthirdcontract,isabletoalterdemandfortheLotto</p><p>drawtosomeextent,althoughitsinfluencecertainlydoesnotprovidethemotivationsforlotteryplay.Its</p><p>innovationshavebeenmanyandfrequent(althoughoccasionallywithdireresults).Ithasexploitedthelac</p><p>ofrestrictionsonadvertisingthatwouldnormallyapplytogamblingcompanies,startingoffwithhigh</p><p>profileTVandradiocampaignsbackin1994,andprogressingswiftlyonthrougharangeofslogans,logos</p><p>andaffiliations.Hiccups,suchastheflopwhichwasthe'dontlivealittle,liveLottocampaignwithBilly</p><p>Connolly,andLotto'sunfortunatelinktotheMillenniumDome,werenoticeableinslowingsales.Successe</p><p>suchasthe'fingerscrossed'logo(which,asaresultofCamelotsinfluence,nowmustbecarriedbyall</p><p>NationalLotteryfundedcharities)andtheproliferationofthe'itcouldbeyou'catchphrasehave</p><p>contributedtocreatingarecognizablebrand.Camelothaveastrongincentivetoincreaserevenueofthe</p><p>NationalLottery halfapencefromeachpoundticketgoesdirectlytothefirm'sprofit.Furthermore,the</p><p>priceofatickethasstayedconstantsincethelotterybegan,meaningthatCamelot'sprofitshavetotryan</p><p>conquerbothinflationandthereductioninCamelotstakefrom1%profitto0.5%profitthatwasmadea</p><p>fewyearsagoafterpressurefromOFLOT,theregulatoryboardthatoverseeslotteries.</p><p>The</p><p>role</p><p>of</p><p>a</p><p>technologically</p><p>advanced</p><p>and</p><p>widespread</p><p>retail</p><p>network</p><p>is</p><p>important</p><p>in</p><p>maximizing</p><p>revenue.Afterall,withouttheopportunitytobuythehighlynonessentialtickets,therewouldbelittleeffective</p><p>demand.Asitstands,Camelotcanboastthatmorethan96%ofUKhouseholdsarewithintwomilesofa</p><p>Lotteryterminal17</p><p>.Also,in2002aprogramwasundertakentooverhaulthesemachines,triplingthe</p><p>numberoflotteryticketsavailableperminute(thisnumbercontinuestorise).Moreover,ticketshavebee</p><p>availableonline,onmobilephone,andeven(throughadealwithBSkyB)ondigitalTVsincefouryearsago</p><p>Allthisgoestosuggestthattheeasewithwhichonecanplaywithoutanyapparentdisruptiontoone's</p><p>lifestyleisafactor</p><p>in</p><p>determining</p><p>demand,</p><p>Camelotaimstomakethiseasenotjustaquestionoflifestyle,butalsooffinancialaffordability,withits</p><p>stubbornrefusaltoraisetheLottoticketprice.Equallyimportantly,especiallywiththegrowthincharitabl</p><p>awarenessint...</p></li></ul>

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