Hack 40. Play in the Black in Blackjack

BasicStrategy

Firstthingsfirst.Table4-12presentstheproperbasicblackjack

play,dependingonthetwo-cardhandyouaredealtandthe

dealer'supcard.Mostcasinosallowyoutosplityourhand(take

apairandsplititintotwodifferenthands)anddoubledown

(doubleyourbetinexchangeforthelimitationofreceivingjust

onemorecard).Whetheryoushouldstay,takeacard,split,or

doubledowndependsonthelikelihoodthatyouwillimproveor

hurtyourhandandthelikelihoodthatthedealerwillbust.

TableBasicblackjackstrategyagainstdealer'supcard



Yourhand

5-8

9

10-11

12

13-16

17-20

2,2

3,3

4,4

5,5

6,6

7,7

8,8

9,9

10,10

A,A

A,2

A,3orA,4

A,5

A,6



Hit

Always

2,7-A

10orA

2,3,7-A

7-A



8-A

2,8-A

2-5,7-A

10orA

7-A

8-A



2-6,8,9





2-5,7-A

2-4,7-A

2or3,7-A

2,7-A



Stay







4-6

2-6

Always

















Always













Doubledown



3-6

2-9













2-9













6

5or6

4-6

3-6



Split













2-7

3-7

6



2-6

2-7

Always

7,10,A



Always











A,7

A,8or9or10



9-A





2,7-A

Always



3-6











InTable4-12,"Yourhand"isthetwo-cardhandyouhavebeendealt.

Forexample,"5-8"meansyourtwocardstotaltoa5,6,7,or8."A"

meansAce.Ablanktablecellindicatesthatyoushouldneverchoose

thisoption,or,inthecaseofsplitting,thatitisnotevenallowed.



Theremainingfourcolumnspresentthetypicaloptionsand

whatthedealer'scardshouldbeforyoutochooseeachoption.

Asyoucansee,formosthandsthereareonlyacoupleof

optionsthatmakeanystatisticalsensetochoose.Thetable

showsthebestmove,butnotallcasinosallowyoutodoubledownonjustanyhand.Most,however,allowyoutosplitany

matchingpairofcards.



WhyItWorks

TheprobabilitiesassociatedwiththedecisionsinTable4-12are

generatedfromafewcentralrules:

Thedealerisrequiredtohituntilshemakesitto17or

higher.

Ifyoubust,youlose.

Ifthedealerbustsandyouhavenot,youwin.

Theprimarystrategy,then,istonotriskbustingifthedealeris



likelytobust.Conversely,ifthedealerislikelytohaveanice

hand,suchas20,youshouldtrytoimproveyourhand.The

optionthatgivesyouthegreatestchanceofwinningistheone

indicatedinTable4-12.



Therecommendationspresentedherearebasedonavarietyof

commonlyavailabletablesthathavecalculatedtheprobabilitiesof

certainoutcomesoccurring.Thestatisticshaveeitherbeengenerated

mathematicallyorhavebeenproducedbysimulatingmillionsof

blackjackhandswithacomputer.



Here'sasimpleexampleofhowtheprobabilitiesbattleeach

otherwhenthedealerhasa6showing.Thedealercouldhavea

10down.Thisisactuallythemostlikelypossibility,sinceface

cardscountas10.Ifthereisa10down,great,becauseifthe

dealerstartswitha16,shewillbustabout62percentofthe

time(aswillyouifyouhita16).

Sinceeightdifferentcardswillbusta16(6,7,8,9,10,Jack,

Queen,andKing),thecalculationslooklikethis:

8/13=.616

Ofcourse,eventhoughthesinglebestguessisthatthedealer

hasa10down,thereisactuallyabetterchancethatthedealer

doesnothavea10down.Alltheotherpossibilities(9/13)add

uptomorethanthechancesofa10(4/13).

AnycardotherthananAcewillresultinthedealerhitting.And

thechancesofthatnextcardbreakingthedealerdependson

theprobabilitiesassociatedwiththestartinghandthedealer

actuallyhas.Putitalltogetherandthedealerdoesnothavea

62percentchanceofbustingwitha6showing.Theactual

frequencywithwhichadealerbustswitha6showingiscloser

to42percent,meaningthereisa58percentchanceshewill



notbust.

Now,imaginethatyouhavea16againstthedealer'sdowncard

of6.Yourchanceofbustingwhenyoutakeacardis62

percent.Comparethat62percentchanceofanimmediateloss

tothedealer'schanceofbeatinga16,whichis58percent.

Becausethereisagreaterchancethatyouwilllosebyhitting

thanthatyouwilllosebynothitting(62isgreaterthan58),

youshouldstayagainstthe6,asTable4-12indicates.

Allthebranchingpossibilitiesforallthedifferentpermutations

ofstartinghandsversusdealers'upcardsresultinthe

recommendationsinTable4-12.



SuckerBet

Manycasinosofferachanceforyoutobuyinsuranceifthedealer'supcardisan

Ace.Insurancemeansthatyouwageruptohalfyouroriginalbet,andifthe

dealerhasablackjack(a10orfacecardasthedowncard),youwinthatside

betbutloseyouroriginalwager(unlessyou,too,haveablackjack,inwhichcase

it'satieandyougetyourwagerback).

Thechancesofthedealerhavinga10underneathare4/13,or31percent.You

willloseyourinsurancemoneymuchmoreoftenthenyouwillwinit.Unlessyou

arecountingcards,nevertakeinsurance.Yes,evenifyouhaveablackjack.



SimpleCard-CountingMethods

Thebasicstrategiesdescribedearlierinthishackassumethat

youhavenoideawhatcardsstillremaininthedeck.They

assumethattheoriginaldistributionofcardsstillremainsfora

singledeck,orsixdecks,orwhatevernumberofdecksisused

inaparticulargame.Themomentanycardshavebeendealt,

however,theactualoddschange,and,ifyouknowthenew

odds,youmightchoosedifferentoptionsforhowyouplayyour

hand.

Elaborateandverysound(statisticallyspeaking)methodsexist

forkeepingtrackofcardspreviouslydealt.Ifyouareserious

aboutlearningthesetechniquesanddedicatingyourselftothe

lifeofacardcounter,morepowertoyou.Idon'thavethe

spacetoofferacomplete,comprehensivesystemhere,though.

Fortherestofus,whowouldliketodabbleabitinwaysto

increaseourodds,thereareafewcountingproceduresthatwill

improveyourchanceswithoutyouhavingtoworkparticularly

hardormemorizemanychartsandtables.



Thebasicmethodforimprovingyourchancesagainstthecasino

istoincreaseyourwagerwhenthereisabetterchanceof

winning.Thewagermustbeplacedbeforeyougettoseeyour

cards,soyouneedtoknowaheadoftimewhenyouroddshave

improved.Thefollowingthreemethodsforknowingwhento

increaseyourbetarepresentedinorderofcomplexity.



CountingAces

Yougetevenmoneyforallwins,exceptwhenyouaredealta

blackjack.Yougeta3-to-2payout(e.g.,$15forevery$10bet)

whenablackjackcomesyourway.Consequently,whenthereis

abetter-than-averagechanceofgettingablackjack,youwould

liketohavealarger-than-averagewagerontheline.

Thechancesofgettingablackjack,allthingsbeingequal,is

calculatedbysummingtwoprobabilities:



Gettinga10-cardfirstandthenanAce

4/13x4/51=.0241



GettinganAcefirstandthena10-card

1/13x16/51=.0241

Addthetwoprobabilitiestogether,andyougeta.0482(about

5percent)probabilityofbeingdealtanatural21.

Obviously,youcan'tgetablackjackunlessthereareAcesinthe

deck.Whentheyaregone,youhavenochanceforablackjack.

Whentherearerelativelyfewofthem,youhavelessthanthe

normalchanceofablackjack.Withonedeck,apreviouslydealt



Acelowersyourchancesofhittingablackjackto.0362(about

3.6percent).DealingaquarterofthedeckwithnoAces

showingupincreasesyourchancesofablackjacktoabout6.5

percent.



Quicktipforthebuddingcardcounter:don'tmoveyourlips.



CountingAcesand10s

Ofcourse,justasyouneedanAcetohitablackjack,youalso

needa10-card,suchasa10,Jack,Queen,orKing.Whileyou

arecountingAces,youcouldalsocounthowmany10-cardsgo

by.

Thereisatotalof20Acesand10-cards,whichisabout38

percentofthetotalnumberofcards.Whenhalfthedeckis

gone,halfofthosecardsshouldhavebeenshown.Iffewerthan

10ofthesekeycardshavebeendealt,yourchancesofa

blackjackhaveincreased.Withall20stillremaininghalfway

throughadeck,yourchancesofseeingablackjackinfrontof

youskyrocketsto19.7percent.



Goingbythepointsystem

Becauseyouwantproportionatelymorehighcardsand

proportionatelyfewerlowcardswhenyouplay,asimplepoint

systemcanbeusedtokeeparunning"count"ofthedeckor

decks.Thisrequiresmorementalenergyandconcentration

thansimplycountingAcesorcountingAces,10s,andface

cards,butitprovidesamorepreciseindexofwhenadeckis



loadedwiththosemagichighcards.

Table4-13showsthepointvalueofeachcardinadeckunder

thispointsystem.

TableSimplecard-countingpointsystem



Card

10,Jack,Queen,King,Ace

7,8,9

2,3,4,5,6



Pointvalue

-1

0

+1



Anewdeckbeginswithacountof0,becausetherearean

equalnumberof-1cardsand+1cardsdealtinthedeck.

Seeinghighcardsisbad,becauseyourchancesofblackjacks

havedropped,soyouloseapointinyourcount.Spottinglow

cardsisgood,becausetherearenowproportionatelymorehigh

cardsinthedeck,soyougainapointthere.



Youcanlearntocountmorequicklyandeasilybylearningtorapidly

recognizethetotalpointvalueofcommonpairsofcards.Pairsofcards

withbothahighcardandalowcardcanceleachotherout,soyoucan

quicklyprocessandignorethosesortsofhands.Pairsthatarelow-low

areworthbigpoints(2),andpairsthatarehigh-higharetrouble,

meaningyoucansubtract2pointsforeachofthesedisappointing

combinations.



Youwillonlyoccasionallyseerunsofcardsthatdramatically

changethecountinthegooddirection.Thecountseldomgets

veryfarfrom0.Forexample,withasinglenewdeck,thefirst

sixcardswillbelowlessthan1percentofthetime,andthe

firsttencardswillbelowabout1/1000of1percentofthetime.

Thecountdoesn'thavetobeveryhigh,though,toimprove



youroddsenoughtosurpassthealmostevenchanceyouhave

justfollowingbasicstrategy.Withonedeck,countsof+2are

largeenoughtomeaningfullyimproveyourchancesofwinning.

Withmorethanonedeck,divideyourcountbythenumberof

decksthisisagoodestimationofthetruecount.

Sometimesyouwillseeveryhighcounts,evenwithsingle

decks.Whenyouseethatsortofstringofluck,don'thesitateto

raiseyourbet.Ifyougetverycomfortablewiththepoint

systemandhavereadmoreaboutsuchsystems,youcaneven

begintochangethedecisionsyoumakewhenhittingor

standingorsplittingordoublingdown.

Evenifyoujustusethesesimplesystems,youwillimprove

yourchancesofwinningmoneyattheblackjacktables.

Remember,though,thatevenwiththesesortsofsystems,

thereareotherpitfallsawaitingyouinthecasino,sobesureto

alwaysfollowothergoodgamblingadvice[Hack#35]aswell.



Hack41.PlaySmartWhenYouPlaytheLottery



Youroddsofwinningabigprizeinagiantlotteryare

really,reallysmall,nomatterhowyousliceit.Youdo

havesomecontroloveryourfate,however.Hereare

somewaystogiveyourselfanadvantage(albeitslight)

overalltheotherlottoplayerswhohaven'tboughtthis

book.

InOctoberof2005,thebiggestPowerballlotterywinnerever

wascrownedandawarded$340million.Itwasn'tme.Idon't

playthelotterybecause,asastatistician,Iknowthatplaying

onlyslightlyincreasesmychancesofwinning.It'snotworthit

tome.

Ofcourse,ifIdon'tplay,Ican'twin.Buyingalotteryticketisn't

necessarilyabadbet,andifyouaregoingtoplay,therearea

fewthingsyoucandotoincreasetheamountofmoneyyouwill

win(probably)andincreaseyourchancesofwinning(possibly).

Whoeverboughtthewinning$340millionticketinJacksonville,

Oregon,thatOctoberdaylikelyfollowedafewofthesewinning

strategies,andyoushouldtoo.

BecausePowerballisalotterygameplayedinmostU.S.states,

wewilluseitasourexample.Thishackwillworkforanylarge

lottery,though.



PowerballOdds

Powerball,likemostlotteries,asksplayerstochooseasetof

numbers.Randomnumbersarethendrawn,andifyoumatch

someorallofthenumbers,youwinmoney!Towinthebiggest



prizes,youhavetomatchlotsofnumbers.Becausesomany

peopleplayPowerball,manyticketsaresold,andtheprize

moneycangethuge.

Ofcourse,correctlypickingallthewinningnumbersishardto

do,butit'swhatyouneedtodotowinthejackpot.In

Powerball,youchoosefivenumbersandthenasixthnumber:

theredpowerball.Theregularwhitenumberscanrangefrom1

to55,andthepowerballcanrangefrom1to42.Table4-14

showsthedifferentcombinationsofmatchesthatresultina

prize,theamountoftheprize,andtheoddsandprobabilityof

winningtheprize.

TablePowerballpayoffs



Match

Powerballonly

1whiteballandthepowerball

3whiteballs

2whiteballsandthe

powerball

3whiteballsandthe

powerball

4whiteballs

4whiteballsandthe

powerball

5whiteballs

5whiteballsandthe

powerball



Cash



Odds



Percentage



$3

$4

$7



1in69

1in127

1in291



1.4percent

0.8percent

0.3percent



$7



1in745



0.1percent



$100



1in11,927



0.008percent



$100



1in14,254



0.007percent



$10,000



1in584,432



0.0002percent



$200,000

Grand

prize



1in3,563,609



0.00003percent



1in146,107,962 0.0000006percent



PowerballPayoff

Armedwithallthewisdomyoulikelynowhaveasastatistician

(unlessthisisthefirsthackyouturnedtointhisbook),you

mighthavealreadymadeafewinterestingobservationsabout

thispayoffschedule.