Insider Secrets to Playing Texas Hold'Em Online Poker by Theo Cage Poker eBook

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Insiders Secrets To Texas Holdem Poker Online by Theo Cage 1

INSIDERS SECRETS TO PLAYINGTEXAS HOLDEM POKERONLINE

2004

AllRightsReserved.

TheodoreCage2004Canada

AllrightsreservedunderInternationalCopyrightConventions.

PublishedinCanadabyCardSharkBooks.Unlessotherwisenoted,

allmaterialscontainedinthisdocumentarecopyrightedandmaynot

beusedexceptasprovidedunderthesetermsandconditions.This

documentisforpersonaluseonlyandisnottoberedistributed,soldorcopiedwithouttheauthorsexplicitpermission.


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AN INTRODUCTIONTO ONLINE POKERTHINKING ANDINSIDERS SECRETS

IdiscoveredthesecretrecipetoKFCChicken15yearsagoandI

havebeenhookedonInsidersSecretseversince.

aveyou everbeen to apartyor abarwhereyouvemetsomeoneforthefirsttimewhotoldyouaninsiderssecret

to theirbusinessorwork?Maybe Imjustagood listener

but this happens tome all the time.We all know these insider

kinds of details about our own littleworld. For example, ifwe

workedatCadbury,theCadburySecretwouldbeoneofthefirst

thingswewouldlearnaboutonthejob(evenifitwasntofficially

part of the training program). There are other kinds of insider

knowledge howsomething isreallymadeattheplantwework

at ho e tai odu t a e a keted he e a idea eally a e

H


4/209


price.

Dontyouwishyoucouldtalktoaninsiderattheplantwherethe

caryouareconsideringbuying ismade?Orsomeonewhoreally

knowsthescooponthemortgageindustrywhenitstimetogetre

financed?How about talking to the guywho programmed the

VLTmachineyouplayeverydayat lunch?Would thathelpyou

winmore?

EverybodywehavetalkedtoaboutTexasHoldemhassaidthatwhattheyreallywantismorethanjustabookthattellsthemthe

rules to thegame.Theywantsomethingnew.Somethingfresh

that will give them an edge over the other players. Something

exciting.

Sowetalkedtotheinsiders.Howdoesthesystemwork?Howare

the cards shuffled (whats the randomizing algorithm)? Hasanyonedoneanystudiesonwhatcardsreallypaythebest?What

tables play thebest?Are there systems thatwork onlinebetter

thanothers?Whatdotheinsidersknowaboutcardstoplay?Can

wereallymakemoneyatthisgame?

Fromthisfeedbackwedevelopthisbookconcept.Thenwehunted

down

the

facts.

In

the

end,

this

has

been

a

lot

of

fun

and

quite

profitable.WelovethegameofTexasHoldembutnowwehave

the tools towinmore games.As usual, if you have the insider

stuff,youarebetterarmedtosucceed.Prettymuchoneofthose

simplerulestoliveyourlifebyifyouaskme.

Ibelievethatwinninginlife,love,businessandsportsandyes,

poker,isallaboutthreedynamicsIliketocalltheCSIs.

Contingency (chance or luck)


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Intelligence(orstreetsmarts)

Wehavedivided thisbook into these threekeyareas foravery

goodreason.Whenyouplayonlinepokerforrealmoneyfor the

firsttimeyouwillfinditdifficultjusttosurvive.Yourstack(your

personal chips)willdisappear like anumbrella in a typhoon. If

youhavewhat it takes tostick itout through this initiation (and

theexpendablecashtolast),youwillnextdiscoverthatwhatyou

arelackingisrealtechnicalknowledge.Youwillsoonrealizethat

you need to play this game more with field intelligence thaninstinct.Thatis,ifyouwanttowinconsistently.

Finally,asyouprogressintolargerpotgames,therealtestwillbe

yourabilitytobementallytough,disciplinedandaggressive.Our

last section on selfawareness discusses the philosophy of great

pokerplayers.

Therearedozensofbooksavailabletodayonpoker.Ivereadmost

ofthem.Theytendtofocusononeormoreofthefollowingareas:

Analysisofoddsandstrategy

Historyandactualplayexamples

Techniquesontellsorhowtoreadtheotherplayers

Mental

preparation

for

the

game

itself

Noteventhebestbookscoveralloftheseareasorattempttobring

thesedifferentpracticestogetherinsomemeaningfulway.Thisis

ourgoalwithInsidersSecretsToPlayingTexasHoldemOnline;

to linkstrategyand intelligenceandmentalpreparation inaway

thatwill ramp you up tobe successful at thebest game in the

worldintheshortestpossibletime.

Whats new about this book? First unlike most of the books on the


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the traditional bricks andmortar game of Poker.Our focus is

specifictothenewonlineversionsofTexasHoldemPoker,played

by over 20,000,000 peopleworldwide over theNet every single

day.Anyonewhohasplayedonlinepokerknows this isquitea

differentanimalindeed.

Secondly,wepresenttheCageFoodChainTheory,anewsystem

of playbased on the results of three major research programs

carriedoutbycomputersimulationsonTexasHoldemPoker. If

you follow the system religiously, youwill find yourwinningsincreasing gradually at first, and then substantially. All the

researchshowsthataggressiveplayisthekeytowinningmonster

pots; aggression at the right time andbased on a solidbody of

knowledge.Wewillshowyoutheprocessandoutlinethestepsto

beingatruecardshark.Butyoumustfollowtherules.Whenwe

runlabsontheCageFoodChainTheorywefindthatplayersget

caughtup in thegameandbend the rulesof the system, lettingtheir emotions rule their play. Or they goby gut feeling on a

decisivehandinsteadofconsideringpotoddsandcardodds.The

online casinos love that kind of play itmakes them millions

everymonth.Itwonthoweverputanyextramoneyinyourbank

account.Youvegottostopplayingbygutfeel.

Of

the

three

dynamics,

we

start

with

the

intel

section

and

contingencydata first; this iswhere the rubberhits the road for

mostplayersandwewanted togetyoustartedwithanexciting

newsystemofplayingthatwillgiveyouafirsthandadvantage.

WhatsIntel?typical militaryspeakforfieldintelligence or

relevantknowledge.Whatyouneed toknow,now. In thecovert

worldofspiesandagents,havingtherightnuggetofinformation

availablewhen required can saveyour lifeor someoneelses. In

Poker it means making the win when others wouldnt and adding


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experience which you can only gain from playing the game

thousandsoftimes.

Fieldintelhelpsyouparachuteintoasituationandbecompetent

andsavvyinabighurry.

TheTheoCageFoodChainTheoryofPokercondensesdozensof

schoolsof thoughtonPoker intoaneasy todigestprogram that

youcanbeginusingimmediately.Thegoalofthistechniqueisto

get you out of the fish category and in to the shark categorybeforeyougeteatenalive.Pardonthefoodpunsbutthespeedand

aggressiveness of real money online poker can spin your head

around.Youwillneedtobearmedandready.

Inmanyareasof thisbookwedealwiththe latest inresearchon

contingency,anotherwordforodds.Whynotjustcallitluck?

Becausecontingencyisafarbroaderandmoreelegantterm.Luckis not a thing you canbuy or create and you certainly cannot

attractitorcaptureit(orchaseitaway).Whatweashumansseeas

luckisreallyjustchancecircumstanceplayingoutbeforeus.

Thebestway tovisualizecontingency is to imaginea fork in the

road.Which then leads to another fork.And still another. Each

requires

a

decision

and

each

decision

can

lead

to

very

different

conclusions.Thatswhat contingency isallabout.Sometimeswe

choosethepathwithoutknowingwhere itwilltakeusandother

timeswedontgettochooseatall.

InPoker,wecanusemathtobetterunderstandtheoddsofcertain

combinations occurring in your game.Really understanding the

odds inPoker is one of the keys to success;not onlybecause it

helps you to better understand the possibilities but because it

teaches us the expected monetary value of our hand as well


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Queen is1:7 ifwedontknowhow to translate that information

intoapracticalbettingdecision?

Recent computer simulations of Texas Holdem have taught us

quiteabitaboutrealgameoddsandstrategy.What theyvealso

shownusisthatittakesseverallifetimestoaverageouttheodds

betweenmatchedplayers. Soyouneedapowerfuladvantage to

win against others with similar skills and preparation. That

advantageisbetterselfawareness.

Assumethatyouandanotherplayerareperfectlymatchedincardskills.Youplay eachother everyweek.Butoneofyouhashad

lifetimewins of several times the otherbased on pullingbetter

cards.Howlongdoyouhavetokeepplayingbeforethewinnings

evenout?About250,000yearsaccordingtocomputerresearch.

Sohowdoesabetterplayergainadvantage if theydonthavea

few thousand lifetimes at their disposal? Bybeing significantlybetter than the otherplayers.Youneedhuge advantage tobe a

consistentwinner.Youneed toknow theotherplayers andyou

need togain this advantage asquickly aspossible.Youneed to

understandbettingoddsbetter.Youneed toknowyourself.And

youneedtobeveryaggressivewhenthetimeisright.

Thats

the

essence

of

a

shark.

Skilled.

Aggressive.

Knows

the

environment.Knowstheprey.Undaunted.

Havefunandbestofluckatthetables.

TheoCage

June2004


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TABLE OF CONTENTS

INTRODUCTION .............................................................................. 2

WHYISONLINEPOKERSODIFFERENT?................................... 9

GETTINGSTARTED......................................................................... 14

THECAGEFOODCHAINTHEORY!............................................ 15

ODDS,PERMUTATIONSANDROI............................................. 37

THERULES OFTEXASHOLDEM ............................................... 77

WINNINGBEFORE THEFIRSTCARDSDEALT..................... 83

THEIMPORTANCE OFTABLEPOSITION ............................ 103

PLAYERPROFILING ...................................................................... 108

PLAYINGLIMITTOURNAMENTS ............................................ 155

HOWTOPICKANONLINECASINO........................................ 168

POCKETCARDWINNINGODDS.............................................. 180

HOWTOTHINKLIKEASHARK................................................ 182

TEXASHOLDEMDICTIONARY................................................ 190


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WHY IS ONLINE TEXASHOLDEM POKER

SO DIFFERENT?

TexasHoldemPokerhasbecomethefastestgrow

ing game on the Internet. Play it a few times andyouwillunderstandwhy.Itsaddictive.Fast.Enter

taining. Colorful. And there you are, playing live

withpeoplefromallovertheglobe,agreatvirtual

casinoexperience andrealmoneyisbeingwonbypeoplejust

likeyouandme.Whatsnottolike?

Well,

you

say,

I

would

like

to

win

more

often

.

.

.

Lik h l h l l id k i l (VLT)


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They would love to win; they just arent prepared to do the

homework necessary to get really good at the game and win

consistently.Whohastimeforthat?

TheProsdo,thatswho!

And thePros likeOnlinepoker.UnlikeVLTs, theoddsarenot

stackedsomuch in favourof thehouseandplayerscanactually

makeconsistentprofits iftheyunderstandthegamewellenough.

Ihaveanunclewho is famous inourfamily.Hehasanunusual

career.Hehasmadeagreatlivingplayingprofessionalpokerfor

over 40 years. (Hewas known in the trade as a rounder for

detailsseethedictionaryattheendofthisbook.)Andhehasmade

morethanjustadecentlivinghehasseveralhomesandayacht

he moors in Florida. Hes an interesting character and he has

taughtme a lot.Much of thisbook isbased on his advice andteaching.

My uncle says there are two major differencesbetween casual

playersandprofessionals.

One Professionalsalwaysknowexactlywhomtheyareplaying

with.

Dontbe deceived. When you play poker you are not playing

againstthecardsyouareplayingagainsttheotherplayers.Great

pokerplayersnever forget this. Thegoalofourbook is to teach

youhow tobetterunderstand theguyorgal sittingacross from

you at the virtual poker table. A better understanding of the

dynamicsbetween humans at the table alone will dramatically

improveyourchancesofwinning.


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Thisbookwillteachyouhowtocalculateoddsusingactualgame

examples and give you shortcuts thatwill help you to increase

yourchancesofwinningeverytimeyouplay.

Oddsdonttellyouhowtoplay,theytellyouhowtobet.

Firstyouneedtounderstandwhyreadingabouttheconventional

brickandmortargameofTexasHoldem(thekindyouplayina

realcasino)certainlywonthurtbutitwilldefinitelynotprepare

youfortheuniqueexperienceofplayingthegameonline.

WHY IS ONLINE POKER SO DIFFERENT?

Online poker adds several interesting wrinkles to the game of

TexasHoldem. Somuchischangedinfact,thatthereareawhole

newsetofgamestrategies.Theoddsofwinningtheonlineversion

ofthisgamearenowstackedevenmoreinthefavourofthebettereducatedplayers.This isoneof thesecrets to realsuccessat the

virtualtable.

1.YOUCANWATCH.

Ifyouwalkintoabricksandmortarcasinotomorrowanddecide

you

would

like

to

just

watch

a

game

of

Texas

Hold

em

to

better

understandhow itsplayed, securitywillsoonhustleyououtof

thebuilding.Pokerisnotaspectatorsportatcasinos.Ifyouwant

tolearnthegame youneedtoplay.Andplayingwhenyourea

rookie (or as the pros call it a fish) canbe a very expensive

learningexperience.

On theotherhand,online,youcanwatcharealgameas longas

youwant,fornocostandfornorisk.Watchingatablecanteach

you a lot about the players and their betting style and the game in


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general.Watchingplayersforfreeisoneofthegreatadvantages

ofonlinepoker.

TakingnotesisanothergreatstrategyinOnlinePoker.

Thereisnothingwrongorunethicalaboutkeepingnotesonother

players. Some Online Poker rooms even provide a feature that

allows you to take notes online while you play. This feature

facilitates thebuildingofadatabasearound theplayingstylesof

consistentplayers.Our advice is to recordwhat kinds of hands

theyplay,howquicklytheyreact,andtorecorddetailonbetting

andraisingbehaviour.

In the heat of the game, you may not always have time to go

throughallof thedetails.Butoneday,aregularplayerwilljoin

your tablewith ahealthy stackof chipsandyouwillappreciate

knowing everything you can ahead of time about their playingstyle.

2.YOUKNOWEXACTLYWHATSINTHEPOT?

Ata regularcardgame,youneed todosomeroughguessingat

pot totals. (Theotherplayersrarelyencourageyou togodigging

throughthe

pot

to

come

up

with

atally).

Online,

the

total

is

calculated for you to the penny. Thismakes calculations about

howmuch tobetveryaccurate.Why is this important?Youwill

learnlaterthatoneofthekeystowinningisasystemusedbypros

fordecadescalledPotBetting.Themoreaccurateyourknowledge

ofthepot,thebetterableyouaretoknowexactlyhowmuchyou

shouldbebettingonagivenhand.OnlinePoker isaPotBetting

dreamcometrue.Sharpenupyourmathskillsabit,andyouare

ontheroadtomakingmoney.


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3.YOUHAVEMORETABLEANDBETTINGCHOICES!

Haveyoueverwalkedintoarealcasinolookingforaseatatacard

game?Youmaybe lucky to finda fewdozen.Whichone is the

best foryourplaying style?Youwontknowuntilyou sitdown

andplayanumberofhands.Andifyoudontlikeyourcompany

atthattable?Youmovetoanothertableandtryagain.

Therearethousandsofonlinecasinoswithdozensorhundredsof

tables at each one froyou to choose from.You canpick from a

widerange of betting options and from an infinite variety of

different player combinations combinations you will have

observedbeforeputtingdownyourhardearedmoney.Andyou

can do this in a matter of minutes right from your computer

screen.

Never have there been so many options for the poker playerwilling to learn.Remember,youarenotjustplayingagainst the

odds,youareplayingagainstotherplayersandinamathematical

sense, the tableasawhole.This is therealkey towinning.Look

for a tablewith thegreatestnumberofweakerplayers andyou

willhaveanautomaticadvantage.


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FOR THOSE OF YOUWHO JUST WANT TOGET STARTED NOW!

f you are anything likeme,youjustwant toget to thegood

stuff. So letsjump right into the game and theFood Chain

system.

Sure,therearerulestolearnandtechniquestounderstand and

all kinds of interesting tips on betting and odds. This book is

fullofstrategyandbackground.

But Ijustwant tojump into the game itself as a startingpoint.

Howcanyoubeawinner?OK!Letsstartwithanexampleofhowthissystemworks.Thenyou can learnabout thedetailsmoreat

I


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TheCageFoodChainTheoryofOnlineTexasHoldemPoker!

Fish,astheyarecalledinTexasHoldem,areprey.

Fisharethelosers andthebeginners andthesloppy

playerswhoget eaten everydayby thebigger fish. In

nature they are called prey. Thank goodness for the

fish.Theysustaintheentirepokerfoodchain.Withoutfish,there

wouldbenomonsterpotsorbigpaychecksandthegamewould

notbenearlyasinterestingnorasprofitable.

Dont getmewrong. Everyone is a fish in thebeginning and

thereisnowayaroundthisessentialtruth.Everyonegetsburned

and eaten repeatedly when they start to play poker. Everyonelosesoneventhebestnutshands.

This book is about how to get out of the fish category as

quicklyaspossibleandstarttakingmoneyhome.

Anoteabouttheresearchthatbacksthisbook.

The book you are reading, unlike most of the poker books


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guyswhohavespentdecades learning theropes; themajorityof

themplayingtheoldfashionedbricksandmortarversionofthe

game.

IamaComputerProgrammerwithanintenseloveforPoker(and

othergames)wherethereisastrongcomponentofskillinvolved.

InsiderSecrets2004isallaboutthescienceofPoker.

CardShark,ourresearchteam,hasgonethroughmillionsof lines

of code,data resultsandanalysisonbillionsofplayedhandsof

Poker.Agoodpercentageof this researchwas sourced from the

same online casinos you and I play at everyday. The rest came

fromreputablesourcessuchasCarnegieMelonUniversitywhere

grad students havebeen running computerized Texas Holdem

simulations for years. Our theories are based on solid

mathematics, proven odds calculations and the results of some

veryinterestingcomputerstudies.

At least three major research studies over the past three years

have generated over 5 billion virtual hands of Texas Holdem

poker.

Youwouldhavetoplaypokereverydayforseveralmillionyears

toexperience

that

many

hands.

(I

know

youre

trying

to

live

a

healthierlifestylebutImnotbettingonanyoneschancestomake

itthatfar!)

Mostof thestrategy in thisbook isbasedon thisnewexciting

research PLUS some good oldfashioned table sense based on

over20yearsofreadinggreatcardplayers.

Youmaybesurprisedbywhatthisnewresearchshows.IknowI

was


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The better the information you have about what is really

happeningwiththecardsandthetable,thefasteryouwillgetout

of the fishcategoryand intothewinningzone.Weopenup the

bigblackonlinepokerboxandshowyoutheinsides.Whatcould

bemorefun?

Heres the question we hear every day. How much money can

you make? Again,based on recent surveys, a good player can

make $40,000 to $50,000 per year playingmedium $3$10 stake

games.

A real expert, aSHARK,canmake$100,000or more peryear

andhundredsdo.

Letsstartwiththeresultsofarecentcomputeranalysis.

Imagine what we could learn about this game if we created avirtual10playerTexasHoldem table,programmed theplayers

indifferentwaysandthenjustletthemplayforafewthousand

years.

Withsomeof the testrunswewoulduseveryaggressiveplayer

behavioursjust to see how that type of combination of players

effectswinning

and

losing.

In

other

examples

we

would

use

avery

tightandconservativegroupofplayerstoseehowthataffectsthe

gameoveraperiodof time.Billionsofhandswere thenplayed

andanalyzedagainandagainoverseveralmonths. More than

manylifetimesofplay.

Here is thesimplest formof theresultsof thisresearchbasedon

yourchancesofwinningwiththefirsttwoholecards.


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Player Type If you are a beginner, you are fish. If

you aremore interested inplaying thanwinning,you

arefish.Ifyoudontdoyourhomeworkandcompletely

understandhowtheoddsaffectyourchancesthenyesVirginia,

youareafish.

Butevengoodplayerscanbecomefishduringplay.Tournament

play is a good example where the game can change radically

dependingonthenumberofplayersleftinthegame.Ifyoustartto panic or get shortstacked, youmayunintentionally revert to

fishtactics.Asabeginneryouwilltendto act likeafishyou

maystayinthepotlongerthanyourhandwouldjustify.Youmay

raisewhenyour cardsarenot that strong.Fishare typifiedbya

playingcharacteristiccalledloose.Loosenessimpliesadisregard

for card odds and a general lack of knowledge about the other

players.Combine

this

looseness

with

aggressive

behaviour

and

youhaveoneofthemostinterestingcreaturesataPokertablea

maniac.

Tosurviveandmakemoney,fishneedtoplayaverytightgame.

Asknowledgeand table smarts improve, they can increase their

aggressiveness,boldwithfreshwinnings.

Thebestguide tobeginnercardplay is touse theFishRuleas

t t d i th Pl T Ch t B d th l t t t


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research, fish should onlystay in thehand if they haveoneof

thetop24pocketcardsdealt.

Why?Because if theyhaveoneof thesehands, regardlessof the

type of talent at the table, theywillhave an excellent chanceof

winning. Theywill alsobegin to understand the discipline of a

tighterplaying style,which isbasedonknowing theoddsand

readingthetable.

Bettingtacticsshouldnotbeanissuehereandneithershouldthe

readingof tellsorevenplayerposition(whichwewilldiscussin

detaillater).

Here are the top 24 pocket hands in any Texas Holdem game

(outofapossible169).

Letsstartoffwiththetopofthehitparade.(Thesreferstocards

inthesamesuit.)

ThebigTop4AA,KK,QQ,JJareridiculouslyprofitableatany

table.Alwaysraiseandreraisewiththesecards.Theydontcome

alongoften,sotakeadvantage.Notraisingonthesecardsisasign

offoolishness.Beingaggressivehereisanobrainer.

The

top

16

ranked

starting

2

card

Hold

em

hands

(or

pocket

cards)arefundamentaltowinningplay.Theymakeuponly7%

f ll h d d lt it lik l th t ill t i h b


21/209


limitingyourplaytojustthesecardcombinations.Butyouneed

toknowwhattheyrepresentwhentheydocomealong.

IfyoucomparethischarttoolderbooksonPokeryoumaynotice

an obvious variation. The latest research has shown that the

overall power of AKs is slightly greater than that of KQs

especiallyingameswherefewplayersareleftaftertheriver.

Infact,withsixplayersaftertheriver,AKplaces10th,whileina

game with 6 players, it places 5th. This revelation was first

discovered in theR&Dbeingdoneusing the latestcomputerized

pokersimulationsinthelate90s.

JJisanotherexampleofholecardsthatvarygreatlydependingon

the typeofgame theyareplayed in.Theyhavebeenhighlighted

onthechartforthefollowingreason

Atalargetableof6ormoreplayers,JJisranked4thinpower.Ina

situationwheretherearefewerplayers,thepowerofthispairgoes

downto9th.

GamerankwithonlyTWOplayersaftertheriver(Top10)

GamerankwithSIXplayersaftertheriver(Top10)


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ThekeydecisionanyHoldemplayermakesiswhetherornotto

playthestarting2cardhandtheyaredealtwith.Andiftheydo

play,howdotheyplaysmartthroughthehand.

IyouareaFISH,neverbetonanythingbutthetop

ranked24pocketcards.

InsiderSecret

WewouldalsosuggestthatyouALWAYSraiseontheTop10.

Raise on the Top 16 unlessyou think the raise isnot likely to

driveoutotherplayersinaveryloosegame.

Underverytighttableconditions,onlytheTop5shouldberaised

beforetheflop.

However,ouradvicewouldbeifyoufindyourselfataverytight

table, you should probably get up and go find better playing

conditionselsewhere.

AK isagoodexampleofholecards thatonlydoreallywell ina

shorthanded game so you need to raise and drive out other

players right away. If you cant, youwill have lostmost of the

powerand

advantage

of

these

cards.


23/209


TT on the other hand drops dramatically in powerwith fewer

playerssoraisingtopushoutweakerhandsisapoorstrategy.

BarracudaThenextlevelupfromtheFishcategoryisBarracuda.Youre not thebiggest andmeanest fish in

the sea,butyouhaveexperienceandyouve survived.

Andyouremakingmoneywhenyouplay.

TheBarracudaPlayercansafelyplay theTop40pocketcardsas

listednext.

Youarenow in the landofthemediumsuitedconnectors KQs,

QJs,JTs,T9s whichdoverywellinsmallstakegamesaswellas

thebiggishoffsuitaces AQ,AJ.

BarracudaTip:

Pickyour10playertablecarefully.Lookforplayerswhoseem tobehavingfun,andwhereat leasthalf


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isamajordeterminantofhowwellyourhandswillholdupin

thelongrun.

When other players know what youre holding, you suffer

tremendousdisadvantage.Justplayinggoodcards isnotenough

asaBarracuda.RaisingAAandKKisclearlynotenough.

Youneedacarefullyplannedbuthardtoreadraisingstrategyas

well.At theBarracudastageyoubegin toexperimentwithmore

aggressive play.As youwill read later, timing your aggressive

strategy is the key. Being aggressive with a large number of

playersatthetable,unlesstheyareallveryconservative,willnot

workmostofthetime.Andnomatterhowaggressiveyouare,if

youaresurroundedbysharks,youwillbechum.

AsaFishyouwere focusedon the top1016pocket cardsdealt.

Youneedtoexpandthisnowintwoways.

One,youneed tobemoreaggressivebefore the floponawider

rangeofcards.

Two,youneed tomixupyourbetting strategy.Asyouwill see

later, the best player type is tightaggressive. This

characterizationis

based

more

on

how

the

other

players

see

you

andlessonyourownstrategy.Inpoker,perceptioniseverything.

Youneedtobeseenbyyouropponentassomeonewhosstyleis

slightlyhard to readandoccasionallyunpredictable.Thenwhen

youdoraiseaggressively,youropponentswilltakeyouseriously

andsurrenderthepot.

Be aware that in online Poker, because players come and go

constantly,itsmoredifficulttobuildareputationatthetable.Its

like performing on the stage you need to exaggerate your mo es a


25/209


tobeaggressiveonline,youraggressionneeds tobe clear that

meanspushingupthebetsmorethanyouwouldatarealtable.

Slowplaycanhave itsadvantageshere too. It tends tocatch the

attention of otherweaker players anxious to donate to the pot.

Evenifyouknowexactlyhowmuchyouplantoraise,slowdown.

Letthecounterclickoff.Thisisagreatattentiongettingdevice.If

afterstalling,youfold,youcommunicateindecision.Ontheother

hand,ifyouraiseheavy,youvemadethemovequiteclearand

youvegottheotherplayersthinking.

Mentaltoughnessisoneofthekeystosuccessasyoumoveupthe

pokerfoodchain.Beingmentallytoughmeansignoringtheother

playersconcernsabouthowfastyouplay.

Mr.SlowPlay

One of the toughest tournaments Iveplayed in had oneplayer

who constantly ranup to the last few secondsof their available

timeoneveryturn.Atfirstitlookedliketheyweredistracted,or

playinganothergameonlineatthesametime.Virtuallyeverytime

itcametotheirturn,theywouldstalluntilthecountdown.Soon,

other playersbegan chatting about the slow play.Namecalling

began.One

player

suggested

taking

aggressive

action

against

this

player as a group, simply because of the shared aggravation.

Which is exactly what happened. At one point, one playerbet

aggressivelyagainstMr.SlowPlayandwentallinandlost.

Whowon the tournament?Mr.SlowPlay.Whatagreatstrategy.

Herattledalmostalloftheotherplayerswithhisslowdetermined

pace.Hewent right down to the last few seconds on the clock

dozensoftimes.Themoretheotherplayerscomplained,themore

he hesitated


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Becausehewasslowoneveryplay,itwasverytoughtoreadhis

actual playing style. He was consistent. He also got a lot of

attention.Whenhewon,noonemissedit.Hemanagedtocontrol

thetableinaway.Tablecontrolisclearlyagoaloftheconsistent

winner.

The Shark Playerwillhave80hands in theirplay list (seechart

following)knowing that theyaregoodhands if the flop isgood

flop, that your opponentswill generally discount the likelihood

youllbeholdingthem,andthattheywillhavethewilltofoldon

asmanyroundsasittakeswhentheflopdoesntgointheirfavor.

Asagambler,withthesecards,therealmagicisgettingtheright

flopcards.

Based on using the Shark play list you would on average,

participate

in

about

1/3rd

of

all

pots

at

your

table.


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Again, if your goal is towin, please stay away from very tight

tablesbecausenomatterhowwellyouplay,onlythehousewins

wheneveryoneisgood.

AuthorsSklanskyandMalmuth(S&M)haveauthoredoneofthe

most popular pokerbook to date calledHoldemforAdvanced

Players.Ourprefloprecommendationsdifferinmanyways.

S&Mhas always advised raisingwithyour strongesthands and

limping (calling)withyourweakest. But thisamajormistake in

tightergames, sinceyour strongesthands areworthmuchmore

than theblinds,while yourweakesthands areworthmuch less

thantheblinds.Foldingisthewisestchoice.

Also, S&M advises not raisingwith hands like KT after several

looselimpers.Thenewestresearchhoweverindicatesyoushould

usuallyraisesinceyourhandislikelytobebestandwillwinmorethan your fair share of pots (though usually notmuchmoney).

S&Ms argument is that fish will call correctly with gutshots

(drawingonecardtoastraight)andpairsontheflopifyouraise

preflop,andyouwillsuckmoreplayersintothepot.Raisingwill

notgreatlyreduceyourchanceofyourwinningthepot,soifyou

willwinmore thanyour fairshareofpots,youshouldgenerally

raise.

StatsfromanumberofonlinecasinoshaverevealedanotherS&M

myth thatyoushould raisewithbabypairs like 33even ifyou

know theblindswillcall.Theoddsare thatyouwill flopa thrip

more then1 in9 timesbutyouwillwin thepot less than1 in9

times. Since youwillwin thepot less than your fair share, you

shouldnotraise.


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PLAYING THE PROGRAM STEP-BY-STEP

Letsstartwithanexamplehand.Iftherearetermshereyoudontunderstand, you can check the Dictionary in the back or the

IntroductionToTheGamechapter.

Ready?

The threebasicsyouneed tounderstandbeforeyoubetonecent

on

any

Texas

Holdem

game.

1) Ch k t th th l ! A h d l ? Ch k


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notesonthestrengthofeachplayer.Ihavesuppliedasystemyou

canusetodeterminetheirabilitytoplay.

2)Decideontherightspotatthetable.Veryimportant.Probably

oneof themost importantdecisionsyouwillmake in thegame.

YouwillfindalotoftipsinthechapteronTablePosition.

3) Make sure you have enough chips.Stack sizedoesmatter in

thisgame.Youwill find tipsonhow todecideonhowmuch to

playwiththislaterinthebook.

OK!Youreseated.Youhavereadthetableandtheotherplayers.

Youhaveenoughchipstowin.Nowwhat?

Fromthispointon,justfollowoursystem.

InthisexampleyouaredealtaKingandanine.

Yourfirstquestionwillbehowgoodismyhand?

Well,welltellyou.ReferfirstofalltotheOpeningOddsChartat

theendofthisbook.

Look up K9 from the chart (which youwill keepby your side

whenyouplay.)

The odds of winning with these two cards is 14%


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Now lookat thepot.What is the totalnow?This iseasybecause

thecomputerkeepstrackofthisforyoutothepenny.

Letssaythepottotalis$80.

14%of$80 is$11.20.(This isourPotOddscalculation.This tells

youhowmuchyoushouldbetbasedonwhatyouhave.)

Soyoumatch thebetof $10 andyouare in. (Tendollars is less

thanyour$11.20limit.Youunderpaidtostayinthegame.

Nowtheotherskeepbetting.Itgetsbacktoyouagainandthepot

isnow$120.

Whats14%of$120?Around$17.

Youve alreadybet $10. That leaves $7. (Your firstbet on thatroundplus$7)

Youneedanother$10tostayin.

Accordingtomyrulesthen,youshouldfold.

Nowthe$3differenceisnotmuch.Youmightdecidetogotothe$20 ifnecessary. But dont go any further.Theoddsareagainst

you and you are overpaying for the cardsyouhaveyet to see.

Nowyouareplayingscientificallyandbasedonwellunderstood

odds.This is how theprosplay.Theywatch the otherplayers.

Theywatchtheothercards.Andtheyknowthemath.

The

secret

to

winning

Texas

Holdem?

Beat

the

odds

by

knowingtheodds.


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You need tobeat the other playersby knowing the oddsbetter

than they do.Now lets learnmore about the secrets of online

poker.

Letsgetbacktoourtwopocketcards.

HerestheFLOP.

Now youre pretty excited. You just ended up with a pair of

Kings.IsapairofKingsgoodenoughtowin?Areyoureadyto

betthefarm?DoyouhavetheNuts?

50%ofTexasHoldempotsarewonwithapairof9s

orbetter.

InsiderTip

So that sounds good. Except there is a partial straight on the

table.

Atthispoint,aftertheFLOP,thereareTHREEthingstoconsider.


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Whatdotheotherplayershave(Tells)?

Whataremyoddsofgettingawinninghand?

Whatwillitcostmetoseethenextcard?

Backtothefirstpoint.

Whatdotheotherplayershave?Shortofthosexrayglassesthey

usedtoadvertiseinthecomicswhenyouwereakid,howwillyou

know?This is theartof the tellsevaluating theotherplayers

cards.

First,lookattheoddsfortheotherplayers.

Inourgame,thereisa2cardstraightonthetable.Anotherplayer

needstohavea56or69or9T inanysuitandtheyareclosetoastraight.(Lateronwewillshowyouexactlyhowtofigureoutthe

exactodds.)

It isvery likely that someone at the table is 1or2 cards froma

straight.Andtheystillhavetwomorecardstofillthatstraight.

Clearly, you need threeofakind to stay in the game. Another

King.

As far as you know there are 2 other Kings in the deck (you never


33/209


Theoddsaresimpletocalculate.

Thereare17 cardsdealt (basedon3downand7playerswith2

cardseach).

Youneed2outof17cards=11.7%odds.

Thebettingstartsandyoucanseethepot is$180when itgetsto

you.

Howmuchcanyoubet?

11.7%of$180=$20.

If you know that you need another King to win, the most you

shouldbettoseethenextcard(basedonwhatyouknow)is$20.

Youhaveoneotherveryvaluablebitofinformationatthispoint.

Youcanseehowothersarebetting.Thisshouldgiveyouagood

sense,combinedwithyourreadingofthetablebeforeyoustarted,

ofwhatkindofhandstheyhave.

LetsseethenextcardtheTURNcardasixofhearts.


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WHAT WOULD YOU DO AT THIS POINT IF YOU KNEW

THAT ONE OF THE OTHER PLAYERS ALREADY HAD A

STRAIGHT?

Youwouldfold.Right?Well neverbetonthecome.

Acardinalruleinpoker iftheyvegotyoubeatand

youknowit,foldnow.

InsiderTip

Yes,youmaygetacardtoimproveyourhandbutsocanthey,so

unlessyoucanseethenextcardforfree,dontwasteyourmoney.

Thequestionis,howdoyouknowwhattheotherplayerhas?Are

you making the determinationbased on how they arebetting?

Maybe

theyre

bluffing.

Youknowyoucantbeatastraightwithathrip(threeofakind).

Ontheotherhand,besidethePAIRofKINGS,youhavefourcards

inastraight6,7,8,9.

WhyyoushouldnotplayanythingbelowAToffsuit?Whyits

besttohaveA5sandbeloworATsandaboveoversomethingin

the middle like A8s?


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AnyAceunsuitedhandbelowATcanbebigtroubleinanykind

ofgame.

Somepeoplemighteven considerATandAJdifficulthands too

butforthegamesyouaregoingtobeplayingintheyareadequate

startinghands.

ThereasonA8,A7,A5allsuckisbecauseyoureallycanthitmuch

towin. TakeA8forexample.

Yourkickerisntthatgreat,the8,andyouhavenochanceof

hittinganystraightsorflushes. Theonlywayyoucanwinreally

istohopethattheyhaveaweakerAcethenyoudoandyoucatch

one.

Playingpokerislikeinvestinginthestockmarket.

Youwanttoputyourmoneyintogreatstockthathasachanceto

deliveragoodreturn.A8 isntthatkindofstock.

NowtoanswerthequestionofATsandaboveandA5sandbelow

versusA9sA8sA7sA6s.

The first onesworkbecause you can alsomake a straightwiththem I would take A5s over A8s because the A and the 5 can


36/209


WhenyouplayweakAcesthoughlikeA5s,youhavetobeextra

cautiousifyoucatchanAceontheflop.

Youwontbesure ifyourkicker isgoodornotsoyoullhave to

give the next step some thought. Playing these only in later

positionscanhelpyoumakebetterdecisionsbecausepeoplewill

checkmostlikelyiftheydonthavetheAorthathandbeat.

WhydohandslikeAA,KK,QQ,AK,AQworkbestatsmaller

tables?

Imagineascenariowhereeveryoneisinthehand,andyoulook

downandseetwogorgeousredAces?

Yourpulsestartstorace.Thenyoulookuptoseethateveryone

hasalreadycalled.Atthispointyouhavetoknowthatyour

chancesofwinningareslim.

Powerhandslikethisrarelywinwhentherearethatmanypeople

callingpreflop. Why?

Howdoyouimprovethishand?

Inbigallinpotstwopairrarelywinsagainstflushesandstraights.

Sowhatdoyoudo?

Theres only one tactic left You could check raise on the flop


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someoftheotherplayerstoleave.Limitingthefieldwould

increaseyourchancestowin.

WhyarehandslikeKTs,QJsJTs,89s,79s,and46sbetterwhen

youhaveafulltableofplayersin?

Youcanalmostnevergetintotroublewiththesekindsofpocket

cards.Ifyouhitsomething,itslikelytobequitestrong.Ifyou

dontgetthecardsyouwant,itseasyatthispointtofold.

TrythatwithapairofAces!Withthosekindsofcardsyouare

marriedtothepotusuallytothebitterend.AhandlikeJTsand

89sareidealforplayingagainstbigallinpots.Ouradviceisto

alwaysraisetobuildthepot.

Thereasonthesefavourbigpotsisbecausetheyarealways

drawingtoflushesandstraights.

Makeyourhand...andyouwillbehardtobeat.

SUMMARY FOR THE BEGINNER

Readthetable.

Play

very

tight,

especially

in

the

beginning.

Startwithenoughchips.

Betbasedonwhatthepotoddsare(neveroverbetthepot)

Watchtheoddsforupcomingcards.


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EVERYTHING YOU ALWAYS WANTEDTO KNOW (AND MAYBE DIDNT)ABOUT ODDS, PERMUTATIONS

AND RETURN ON INVESTMENT

WHATARECARDODDS?

Ifyouhaventalreadynoticed,probabilityisahugefactorinTexas

Hold em.Forexample,thereare2,598,960possiblehandsina52

carddeckbutonly4RoyalFlushes.Iftheaverageseriouspoker

player is dealt 100 000 hands in their lifetime they will never hold


39/209


(onthefirstfivecards)morethan4percentofallthepossible

hands.Andlikelyalotless.

Figuringoutstraightcardcombinationsforthepurposeofthistext

are called Card Odds (youwillbe introduced to other kindsof

odds later).CardOdds can reveal some quite interesting infor

mation.

For

example,

how

many

pat

straight

flushes

will

you

see

in

your

lifetime?Todeterminethatnumber,theexpectednumberofhands

that could be dealt during your lifetime is estimated by the

followingcalculation:

10completepokerhands/hr.x5hrs./game x 50games/yr.

x40yrs./pokerlife=l00,000handsofpokerperlifetime.

This is a pretty aggressive estimate, as most people will never

come close to thisnumberof completehands inTexasHoldem.

Based on this level ofplay, the number ofpat (on the first five

cards) poker hands that you should get during your lifetime is

calculatedfromthecardoddsandtabulatedasfollows:

CardsDealt NumberofPatHands

Nopair 50,000

Onepair 40,00

Twopair 5,000

Threeofakind 2,000

Straight 400

Flush 200

Fullhouse 170

Fourofakind 25Straight flush 1.4


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Sostatistically,youshouldseeapatstraightflushonyourfirst

fivecards

once

or

twice

during

your

lifetime.

Most

average

poker

playerswillneverseeevenone.

Cardplayersoftentalkabouthavingaluckystreakorarun.

Mathematically,streaksdontexist.Butsupposeyoudidhavean

amazingrunofcardsoneevening.Whatwouldtheoddsbeof

havingfiveconsecutivestraightflushesinarow?

Royal Flush 4 .0000015391

Other StraightFlush

36 .0000138517

Four of a kind 624 .0002400960

Full House 3,744 .0014405762

Flush 5,108 .0019654015

Straight 10,200 .0039246468

Three of akind

54,912 .0211284514

Two Pairs 123,552 .0475390156

One Pair 1,098,240 .4225690276

Nothing 1,302,540 .5011773940

Total 2,598,960 1.0000000000

In

every

1.7x1024

deals

.

.

.

or

once

in

every

700,000,000,000,000,000,000years. Youdhavetoreadthosecards

in thedark though,becauseoursunwillbelonggoneby that

time.

Playersusecardoddstomakeplayingdecisions.Adecisionmade

without taking into account card oddsmakes poker a guessing

game.Thechancesoffinishingaflushorastraight,theprobability

ofgettinganovercard(facecard),thepercentageoftimesyoure

going to flop a card to match your pocket pair are all extremely


41/209


Knowledgeofthesestatisticsiskeytowinning.

Herearesomeotherbasicprobabilitiesthatyoushouldknow

about:

Youneedonemorehearttomakeyourflushontheturn

orriver 35%

Probabilityofhittinganopenendedstraightdraw(i.e.4

straight

cards,

need

one

on

either

end

to

hit

on

turn

or

river) 31.5%

Probabilityofbeingdealtsuitedcards:23.5%

Probabilityofhittingathreeorfourofakindattheflop

whenyouholdapocketpair:11.8%

Probabilityyouwillmakeapairattheflop,holdingtwo

unpairedcardsinthehole:32.4%

Probabilityof

being

dealt

AA:

.45%

Probabilityofnooneholdingaspecificcard,bynumberof

players,assumingyoudonothavethatcard,bynumber

oftotalplayers.

2 84.5%

3 70.9%

459%

5 48.6%

6 39.7%

7 32.1%

8 25.6%

9 20.1%

10 15.6%

Probabilitysomeoneelsedoesnothaveanace,assuming


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2 88.2%

3 77.5%

4 67.6%

5 58.6%

6 50.4%

7 43%

8 36.4%

9 30.5%

10 25.3%

HOWARETHEODDSCALCULATED?

Letslookattheexampleofhaving4outs(fourcardsyouneedto

makeyourhand).Sayyoureholding6c7dandtheflopcomes9s

10hKc.Inthiscaseyouneedan8tomakethestraight.Sincethere

arefour8sinthedeck,youhave4outs.

YOURPOCKET

THEFLOP


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ODDSWITHONECARDTOCOME

Calculatingtheoddswithonecardtocomeisrelatively

straightforward.

Whenyoure looking tomake the inside straight,youhave four

outs.Thereareatotalof46unknowncards(52minusthe2cards

inyourhandminusthe3cardsfortheflopandthe1turncard).42

of

the

cards

don

t

make

your

hand

and

four

do.

42:4

or

10.5:1

=

about 9%. I prefer to use the percentage as it helps when

calculatingPotOdds(tocomelater).

ODDSWITHTWOTOCOME

To calculate the appropriate odds with two cards to come, you

must

first

determine

the

total

number

of

two

card

combinations

possibleaftertheflop.

Theeasiestway tocalculate this isbymultiplying thenumberof

cardsavailablefor the turn(47)bythenumberofcardsavailable

for the river (46)anddividing thatnumberby2 (becauseacard

cantmatchitself).47*46/2=1081.

Acertainnumberof these1081 twocardcombinationswillhave

eightsinthem.Todetermineoddsproperly,youneedtocalculate

twomorefigures.

EIGHTS ON BOTH THE TURN AND THE RIVER

Oneof the four eights can appearon the turn.And ifonedoes,

therewillbe three left for the river. If youmultiply 4by 3 and

di id b 2 (b d t t h it lf) th t th


44/209


EIGHTSONTHETURNORRIVER

Ifaneightcomesontheturn,thereare46unseencardsremaining.

Butyoureno longer interested in the three remainingeights, so

youcansubtractthose.Thisleaves43unseencardsthatwillmake

auniquepairwithoneoftheeights.Multiply4(thenumberof8s

inthedeck)by43(thenumberofunseencards)toarriveat172.

FINISH

THE

CALCULATION

172 plus 6 comes to 178 the total number of twocard

combination thathaveat leastoneeight in themandasmanyas

twoeights.

Outof1081possibletwocardcombinationsontheturnandriver,

178

of

those

combinations

help

us

make

our

hand.

Subtract

178

from1081tofindthenumberofcombinationsthatdontmakethe

straight(1081178=903).

The odds againstmaking a straightby the river are: 903:178, or

20%.

What

About

The

Cards

The

Other

Players

Are

Holding?

Everwonderwhyweneverfactortheopponents cardsorthe

burncardswhenfiguringouthowmanycardsareleft?

The reason is thatwe only consider unseen cards. If you saw

whattheburncardswere,oranopponentshowedyouhishand,

youwouldknowthat thosecardsarenotgoingtobedrawnand

coulduse that.We typicallydonotknowwhat theyhave,sowe

dont even think about it when talking about odds


45/209


Forinstance,takeastandarddeckof52cards,remove2Acesand

burn25ofthem.Ifyoudrewthenextcard,whatarethechancesof

itbeing anAce? Itwouldbe 2/50 (2Aces left out of 50unseen

cards). ItwouldNOTbe 2/25justbecause youburned half the

deck.Okay,dothesamethingagain,butthistimeyougettolook

attheburncards.Letssaythatofallthecardsyouburned,none

wereanace.Nowyouroddsare2/25becausetherearestill2Aces

andnowonly25 unseencards.

Youwill find that you can easily remember a few of themost

commonsituationsforoutssuchasthefourflushorstraightdraw

buttherehastobeaneasierwaythanmemorizingthefiguresfor

everynumberofouts.Thegoodnewsisthatthereisawaytogeta

goodestimationoftheoddswithouttheheavymathandyoucan

alsousehandyoddscharts.

WHATHANDSWILLWINTHEPOT?

The following are the most valuable starting hands in Texas

Holdem. This chart assumes a medium to loose $510 Texas

Holdemgame.Theresultsarebasedonacomputersimulationof

5,000,000 played hands. The percentage shown indicates how

manytimesintypicalgamethatthesehandswinthepot.

2Pair 31%

Pair 27%

Threeofakind 12%

Straight 9%

Flush 9%

Fullhouse 9%

Bust(nothing) 2%Fourofakind 1%


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Thisisinterestingdatabutheresthekickerlookatthepower

oftwopairsandsinglepairhands.Itsnotonlyhigherthanthe

WHATAREMYCHANCESOFWINNING?

Whataremychancesofwinningahandwithagivensetofpocket

cards?Whataretheoddsoffillingastraight?


47/209


Howmuchyoucanexpecttoprofitfromthesestartinghands?

Thestartinghandaveragewinforeachtimeplayedbasedon

mediumtolooseTexasHoldemPokergameswitha $5/$10limit.

AA $34.19

KK $24.13

QQ $17.36

JJ $12.08AKsuited $11.63

AKoffsuit $8.65

AQsuited $8.32

1010 $7.72

AJsuited $5.69

AQoffsuit $5.47

POCKETCARDODDS

Hole Cards Odds

Any Pair 16 : 1

Suited Cards 3 : 1

A-K 82 : 1

Suited Connecting Cards 24 : 1

A-A or K-K 110 : 1

A-anything 5.3 : 1

Any two cards J's or Higher 10:1

After the Flop

Pair J's or Higher 55 : 1


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Pair improving to 3 of a Kind 8 : 1

Flop being 3 of a Kind 391 : 1

The River (5th Street)

A-K hitting an A or K by the River 1:6 : 1

Q-Q vs A-K (A or K hitting) 1.5 : 1

Hitting 5th card to complete a Flush 1.6 : 1

Completing an Open Ended Straight 2.9 : 1

Three of a Kind improving to Full House 2.7 : 1

Pocket Pair improving to 3 of a Kind after the

Flop12 : 1

Hitting a Backdoor Flush 33 : 1

More Interesting Texas Hold'em Odds

5 Players, there's an A on the flop. Chances aplayer has an A in their hole.

1.7 : 1

4 Players, there's an A on the flop. Chances a

player has an A in their hole.2.1 : 1


player has an A in their hole.2.9 : 1


player has an A in their hole. 4.3 : 1

WHATAREPOTODDS?

Potoddsaretheoddsyougetwhenanalyzingthecurrentsizeof

the pot vs. your next call or bet. Pot Odds help you make

importantcall,raiseorfolddecisions.

Example 1: There is $200 in the pot and a final $10 bet coming at


49/209


one of four suits, the shortcut math is 1:4 chances or 25%.

Winning consistently is aboutbeating Pot Odds and not over

betting.IfyourCardOddsare25%(youhavefourheartsandneed

another towin) andyouonlyneed tobet5%of thepresentpot

($10 asapercentageof the$200) to see the last card,youare in

great shape. Based on Pot Odds for thishandyou couldgo as

highas25%ofthepotbasedonyouroddstopullaheartonthe

river.

Example 2: You are in a $5/$10 Holdem game with JackTen

pocketcards

and

one

opponent

left

on

the

turn.

Youhaveanoutside straightdrawwithaboardof259Q,and

only therivercard lefttomakeyourstraight.Any8oranyKing

willfinishthisstraightforyou,soyouhave8outs(four8sand4

Ksleftinthedeck)and46unseencardsleft.8/46givesyoua6:1

chance or a 17% chanceof getting thewin.Your opponentbets

$10.

6/1=17%PotOdds


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Ifyoutakea$10betyoucouldwin$100.Yourbetisthen10%of

thefinalpot.The10%betissmallerthanthe17%odds,soyouare

ingoodshapefromaninvestmentpointofview.

Wheneveryourcallorbet(in thiscase10%ofthepot) issmaller

thanyouroddsofgettingthewinninghand(17%)youarebuying

thenext card at adiscount.The key is looking at theoddsof a

winninghand,notbuildingapartofawinninghand.

Toomanybeginnersjustplaygoodcardsandjusttossbadones

oriftheyhavetheprospectofstraightoraflush theywilljust

drawanddrawwithlittleconsiderationtoanythingelse.

Unlessyouhave the NUTS (nuts= theverybestpossiblehand)

every time there is a certain degree of riskwhen you put your

moneyinthepot.

Intheheatofthebattleyoumaynotalwayshavetimetogetout

yourcalculatoranddothenumbercrunching.YoucanlookatPot

Oddsinamuchsimplerway justaskyourselfifthereisenough

moneyinthepottojustifytherisk?

If there is abig pot unless youjust know you arebeat, or it

simplycosts

too

much

too

call

(which

means

your

pot

odds

may

notbesogreatafteritsallsaidanddone) trytogetsomeaction.

Evenifyouknewyouwerealongshot wouldyoubet$25or$50

ona chance towin$500or$1000ormore?Whileyoumaybea

long shot itsnot abadbet if there is a reasonable chanceyou

couldwin.

On the flip side, and this is important, youmay have a decent

hand anditmayevenbethewinner,(useyouropponentortells

kno ledge) but if its going to cost you $250 to call and you stand


51/209


toonlywinafewhundredthenyourpotoddsarenotsogreatand

isprobablynotworththerisk.

Potoddsratiosareausefultooltoseehowoftenyouneedtowin

thehandtobreakeven.

Ifthereis$100inthepotandittakes$10tocall,youmustwinthis

hand1outof11 times inorder tobreakeven.The thinkinggoes

alongthelinesof:Ifyouplay11times,itllcostyou$110,butwhen

youwin,youget$110($100+your$10call).

Theusefulnessofcardoddsandpotoddsbecomesveryapparent

whenyoustartcomparing the two.Asweknownow, ina flush

draw,yourcardodds formakingyour flushare1.9 to1or35%.

Letssayyoureinahandwithanutflushdrawandits$5toyou

on theflop tocall.Doyoucall?Youranswershouldbe:Whatare

mypotodds?

Ifthereis$15inthepotplusa$5betfromanopponent,thenyou

aregetting20:5or4:1potodds25%.Thismeansthatinorderto

breakeven,youmustwin1outofevery5 times.However,with

yourflushdraw,youroddsofwinningare1outofevery3times!

You shouldquickly realize thatnotonlyareyoubreakingeven,

butyouremakinganiceprofitonthistoo.Letscalculatetheprofit

margin

on

this

by

theoretically

playing

this

hand

100

times

from

theflop,whenisthencheckedtotheriver.

TotalCosttoPlay=100hands*$5tocall= $500

PotValue=$15+$5bet+$5call=$25

OddstoWin=1.9:1or35%(Fromtheflop)

TotalHandsWon=100*OddstoWin(35%)=35wins


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= $500+(35*$30)

= $500+$1,050

=$550Profit

Asyoucansee,youhaveagreatreason toplay this flushdraw,

becauseyoullbemakingmoneyinthelongrunaccordingtoyour

cardoddsandpotodds.Themostfundamentalpointtotakefromthisis:

IfyourPotOdds>CardOdds,thenyouaremakingaprofit.

So,eventhoughyoumaybefacedwithagutshotstraightdrawat

times,whichisaterribledrawat5to1handodds,itcanbeworth

it to call if you are getting pot odds greater than 5 to 1.Othertimes, ifyouhaveanexcellentdrawsuchas the flushdraw,but

someonehasjustraiseda largeamountsoyourpotoddsare1:1

for instance, then you obviously should not continue trying to

draw to a flush, asyouwill losemoney in the long run. In this

situation, a fold or semibluff is your only solution, unless you

knowtherewillbecallersbehindyouthatimproveyourpotodds

to

better

than

break

even.

Yourability tomemorizeor calculateyour cardoddsand figure

out your pot odds will lead you to make many of the right

decisionsinthefuture.Justbesuretorememberthatfundamental

principle of playing drawing hands when your pot odds are

greaterthanyourcardodds.

Anothergoodrule tofollow a lotofplayerswant tosomehow

factor in money they wagered on previous rounds With the last


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ofthat$200pot.Letssay$50.Doesthatmeanyoushouldplayor

foldbecauseofthatmoneyyoualreadyhaveinthere?$50/$200?

Thatsabigno.

Thats not your money anymore! Its in a pool ofmoney tobe

given to thewinner. You have no stake in that pot. The only

stakeyoumighthaveistotallymentalandhasnobearingonhard

statistics.

Thenextstepistousebetoddsandimpliedodds.Thatstougher,

becauseitinvolvespredictingreactionsofotherplayers.Withbet

odds, you try to factor in howmany people are going to call a

raise.With impliedodds,youre thinkingabout reactions for the

restofthegame.Oneexampleonimpliedodds...

Sayitsanother$5/$10Holdemgameandyouhaveafourflushontheflop.

Yourneighbourbets,andeveryoneelsefolds.Thepotis$50atthis

point.Firstyoufigureoutyourchanceofhittingyourflushonthe

turn,anditcomesouttoabout19%(about1in5).Youhavetocall

this$5betvs.a$50pot,sothatsa10xpayout.1/5ishigherthan

1/10,

so

bet

odds

are

okay,

but

you

must

consider

that

this

guy

s

goingtobetintoyouontheturnandriveralso.Thatsthe$5plus

twomore$10bets.

Sonowyourfacing$25moretilltheendofthehand.Soyouhave

toconsideryourchancesofhittingthatflushontheturnorriver,

whichmakesitabout35%(betterthan1in3now),butyouhaveto

invest $25 for a finishing pot of $100. $100/$25 is 1 in 4. Thats

prettyclose.


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Ifyoudontmake itonthe turn, itllchangeyouroutsandodds!

Youllhavea19.6%chanceofhittingtheflush(littleworsethan1

in5),buta$20investmentforafinishingpotof$100!$100/$20is1

in 5. So the chances could take anasty turn if youdidnthit it!

Whatsmakes itmorecomplicated is that ifyoudidhit iton the

turn,youcouldraisehimback,andgetanextra$20ormaybeeven

$40inthepot.

Onceyouvemasteredsimpleoutsandpotodds,betandimplied

odds arejust a longer extensionof theseequations. Ifyou thinkabout these thingswhile you play, theywill eventuallybecome

secondnaturetoyou.

MoreOddsExamples:Apocketpair

YoustartwithapairofJacks in thepocket.Not tooshabby.The

flophowever,doesntcontainanotherJack.

YOURPOCKET

THEFLOP


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Lesson 1: Whats my chance of getting a Jack on the turn?

Youneedtojustfigureoutthenumberofoutsanddivideitbythe

numberof cards in thedeck.Thereare2moreJacks.Theres 47

morecardssinceyouveseenfivealready.Theanswer is2/47,or

.0426,closeto4.3%.

Lesson 2: No luck on the turn, how about the river card?

Still2Jacks left,butone lesscard in thedeckbringingthegrand

total to46.Whats2/46?Thats .0434,which isalsoclose to4.3%.

Yourchancesdidntchangemuch.

Lesson3: ForgetjustgettingjustoneJack!Iwantthemboth!What

aremychances?

Sincewere trying tofigureout thechancesofgettingoneon the

turnAND the river,andnotgettingoneonEITHER the turnor

river, we dont have to reverse our thinking.Just multiply theprobabilityofeacheventhappening.Chancesofgetting thatfirst

Jack on the turnwas .0426, remember? The chance of getting a

secondJackon the riverwouldbe 1/46,because therellonlybe

oneJackleftinthedeck.Thatsabout.0217,or2.2%.

Togettheanswer,multiplythem..0426X.0217isabout.0009!

Thatsaroundonetenthofapercent. Iwouldntbankonthat

one.

Lesson4:Hey,whatweremychancesofgettingapairofJacks

anyway?

To figure that out, think of it as getting dealt one card, then

another.Whatareyourchancesof thesecondcardmatching the

fi t ? Th ill b 3 d l ft lik th h Th


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itllbeJacks?Well,thereare13differentcards.So,.059/13isabout

.0045,alittlelessthanhalfapercent.

Lesson 5:Whatweremy chances of getting aJack on the flop?

Nowyoudohaveto thinkinreverse asinthepreviousexample.

Figureout thechancesofNOTgettingaJackoneachsuccessive

cardflip.Firstcardyouhavea48/50chance(48nonJackcardsleft,

50cardsleftinthedeck),secondcardis47/49,thirdcardis46/48.

Thosecomeoutto.96,.959,and.958.Multiplythemandget.882,

oran88.2%chanceofNOTgettinganyJacksontheflop.Invertit

to figure outwhat your chances really are and you get .118 or

11.8%.ThiswillbeyourchancetogetoneortwoJacks.

Example#2 Thestraightdraw

THEPOCKET

You startwithaJackofSpades and aTenofSpades.Youget a

rainbowflopwithaQueenofSpades,aThreeofDiamonds,anda

NineofClubs.Youvegotastraightdraw.

THEFLOP


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Lesson 1: What aremy chances of hitting it on the next card?

Sameasbefore,butwithdifferentouts.AKingoranEightwill

completeyourhand.There ispresumably fourofeach left in the

deck.Youvegot8outs.Thechanceofgettingoneofthemonthe

turn is 8 over 47,because theres 47 cards left in thedeck.That

comesouttoabout.170,oraround17%.

Lesson 2: Ididntget iton the turn!Whataremy chancesnow?

Therearestill8cardsleftinthedeckthatllhelpyou,but46cards

leftinthedeck.Thats8over46.Itchangesto.174.Itsimprovedto

awhopping17.4%!

Lesson3:Ishouldofthoughtaboutmytotalchancesfirst,Imsuch

anidiot.WhataremychancesofgettingthatcardontheturnOR

theriver?

Onceagainwellhave tocalculate thechancesofaKingorEight

NOTappearing,sowecandoitlikethelastproblem(inthiscase,

{39/47}X{38/46}).Or,sincewevealreadyfiguredoutourchances

in the previous two lessons,we canjust invert theprobabilities

andmultiplythem.Youhada.170chanceontheturn,anda.174

ontheriver.Byinverting,Imeansubtractingthemfromone.Now

weve

got

.830

and

.826!

Multiply

and

get

.686!

That

sour

chance

of

NOT hitting our card at all. So invert it again and get .314, or

31.4%.

Example#3 Toptwopair

THEPOCKET


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THEFLOP

YougetdealtaKingofDiamondsandaNineofHearts.Theflopis

looking pretty good for youwith a King of Spades, aNine of

Clubs,andaFourofClubs.Toptwopair!

Lesson 1: What are my chances of getting a full house on the

turn?

To get a full house, you need anotherKing orNine topopup.

Thereistwoofeachleftinthedeck.Soyouvegot4outs.Afterthe

floptheresalways47cardsunaccountedfor.4/47isaround.085or

an8.5%chanceofyougettingtheFullHouse.

Lesson 2: What are my chances of getting a full house on the

river?

Ifitdidnthappenontheturn,yourchancesusuallydontchangeall toomuch,but lets check.Youve stillgot 4outsandnow46


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unseencards left.4/46 isabout .087oraroundan8.7%chanceof

hittingitontheriver.A.2%difference.

Lesson3:Howaboutthechancesofgettingtheboatontheturn

ORtheriver?

Like theprevious examples, to figureyour chanceof something

happeningonmultipleevents,youneedtocalculatethechanceof

itNOThappening first.On the turn itwonthappen43/47times.

Ontheriveritwonthappen42/46times.43/47is.915,and42/46is

.913. Multiply them and get .835, or 83.5% chance of it not

happening.Invertthatandyougeta16.5%ofgettingatleastafull

housebytheshowdown.

Lesson4:Whatdoyoumeanby atleast aFullHouse?

Sincewe figured the chances toNOTgetdealt a fullhouse, thechancesarebuiltiniftheturnandriveraretwoKings,twoNines,

oraKingandaNine.IfyouaredealttwocardsbothofeitherKing

orNine,itllbefourofakindandnotaKingandNine33%ofthe

time.Thinkof itasbeingdealtonecardthentheother.Whatare

thechancesof the firstcardmatching thesecond?Whether itsa

KingorNine, therewillbeonlyoneunaccountedfor,but twoof

theother.

That

s1/3,

or

33%.

Lesson5:Thenwhataremychancesofgettingfourofakind?

Thisone requires a littlemore thought. Itdoesntmatterwhich

cardwerehopingfor.Weneedtofirstgetafullhouseontheturn.

According to lesson#1, thechanceof thathappening is .085.The

chanceofgettingthesamecardwegotontheturnis1/46.Theres

onlyoneout,andtheusual46unseencards.1/46isaround.022,or

2 2% Multiply the t o probabilities ( 022 X 085) and get 002 or


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onefifthofapercent. ItwillbeKingshalfof the timeandNines

theotherhalf

Is thismaking any sense? If you reallywant tobe amaster of

calculatingodds,youneedtoseethesecalculationsinaction,over

and over. Like anything else, practice makes perfect. In online

games especially with very few if any tells (shown cards),

statistical knowledge becomes the main factor when choosing

whethertobet,call,orfold.

Ifyoudohaveahandthatyouknowcantloseyouhavethenut.

Betlikecrazy.

While there isa lotmore toTexasHoldempoker than this this

should open your eyes tomore things about thegame ofpoker

thanjustthecardsandtheirstatistics.

Yes YouDOneedtoknowyourgeneralchancesofpullingwhat

typesofhands but ifyou learn to studyyouropponents, they

will tellyou theirhandsandyoullbeable tobeat themwithout

evenknowingyours.

RETURNONINVESTMENT(ROI)

When the stakes required to play a game of Texas Holdem

increase, there is not a proportional increase in the average

winnings ormoney flowbecausemostplayers, especially at the

startofplay,playtighterathigherstakes.

Hereshowthatworks.

Higherstakescauseplayerstobemorecautious.Potsdonotgrow

ti t l th t k d bli d i Y t


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Max Bet Pot Size

$ 2 Max 28 - 37$ 4 Max 25 - 35$ 6 Max 20 - 22$ 10 Max 10 - 28$ 20 Max 6 - 7$ 50 Max 12$ 60 Max 7.6$ 100 Max 6.11$ 200 Max 5.5

Most major online casinos release data on hands played (for a

price)ona regularbasis.A recentstudy (June2004) fromoneof

thelargestonlinecasinos,basedonseveralmillionactualhandsof

Pokerplayed,revealedthatthereturnoninvestmentvariesquitea

bitbasedonthemaximumbet.

Inthe

$2

games,

the

value

of

the

winning

pot

varied

from

28

to

37

timestheBigBlind(BB)themostyouwouldhavetoinvesttosee

theflop(shortofraises).Theaveragepotswereinthe$60range.

With the right cards, you could expect a return of 3000% on a

winninghand.

Asyoucanseeinthechartabove,thisratiofallsastheBlindsgo

up. In the $200 game, with pots averaging $6001200, the ratio

averages5.5:1.Sure,greateroverallwinnings butmuchgreater

riskbasedontheinvestmentyouhavetomaketoseetheflop.

Also notice the volatility or variance of this ratio.On the high

stakes tables, play is very tight and often passive, so the ratio

remainsverynarrowpotsarepredictably56timestheBigBlind.

At thesmallerstakestables,there isconsiderablymorevolatility,

indicativeofa lotof looserplayersandmoreaggressiveplayingstyles.


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The$1/$2tablesaretheloosestwithpotsrangingfrom2837times

theBigBlind.

AreLowStakeTablesFaster?

Notnecessarily.TexasHoldem is thekingof fastplay. Several

$1000pluspotswereplayed in less thanaminuteandrangedas

longas6minutesthesamerangeforthesmallstaketables.Over

all,theaveragelengthofanonlinePokergametodayisjustover

oneminuteor5060handsperhour.

Inhigherstakesgames,onethingisquiteclear.Thereareahigher

percentageoftighterandaggressiveplayersatthesetablesthanat

thesmallstakegames.Thatmeanstherearemoresharksatthebig

tablesandamuchbetterchance thatyouwillbeoneof the fish.

The smart thing to do here is to say away from these kinds of

tables.

Given the fact that the returnon investment is lowerat thehigh

stake games, that the average level of play is much more

aggressiveand thatamuch largerstake isrequired,there isvery

littleopportunitytobeaconsistentwinnerontableswith$50and

upblinds.

Alloftherecentresearchpointsto$5/$10Limittables

asidealcombinationofriskandreward.

InsiderTip

FACT!Whentheaverageloosegamblerloses,heorshekeepson

playinginanattempttorecovertheloss.Thisisirrationaland

unplannedplayandcanbeveryexpensive.


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Ontheotherhand,whenmostinnategamblerswin,theyforgetall

about their lossesandconclude incorrectly that theyhave finally

learnedhow towin orthat their luckhasfinallychanged.They

express what is an irrational optimism at this point a totally

unfoundedandundeservedoptimismthatkeepstheminthegame

untiltheyrevertbacktoalosingstreak.

Sharksexploitthisirrationalplayingstyleingamblerstogenerate

acontinuousincome.

OUTSODDSCHART

OutsHolding

HandDrawing To 2 to come 1 to come

21 98 % 83%

20 98 % 77%

15openstraightflush draw

straight, flush,straight flush

85% 48%

14 96% 44%

13 92% 39%

12gutshotstraightflush draw

straight, flush,straight flush

82% 35%

11 71% 31%

10 54% 28%

9 four flush flush 54% 24%


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draw

7 39% 18%

6 32% 15%

5 26% 12$

4gutshotstraight

straight 20% 9%

3 14% 7%

2 pocket pair 3 of a kind 9% 4%

1 3 of a kind 4 of a kind 4% 2%

POCKETCARDODDS

HoleCardsDealt Dealt Percent Expected Percent

SuitedStarters 680,351 23.56% 679,596 23.53%

ConnectedStarters 454,220 15.73% 453,064 15.69%

SuitedConnected

Starters114,304 3.96% 113,266 3.92%

PairedStarters

AADealt 13,010 0.45%

KKDealt 13,182 0.46%

QQDealt 13,122 0.45%

JJDealt 13,069 0.45%

TTDealt 12,886 0.45%

99Dealt 13,092 0.45%

88Dealt 13,046 0.45%

77 D lt 13 111 0 45%


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66Dealt 13,130 0.45%

55Dealt 13,173 0.46%

44Dealt 13,015 0.45%

33Dealt 13,075 0.45%

22Dealt 13,076 0.45%

AllPairedStarters 169,987 5.89% 169,899 5.88%

AKSuitedStarters 8,717 0.30% 8,713 0.30%

AKOffsuitStarters 26,051 0.90% 26,138 0.90%

AllAKStarters 34,768 1.20% 34,851 1.21%

THERULEOFFOURTWO

Theruleoffourtwoisaneasierwaytofiguretheoddsforany

situationwhereyouknowyourouts.Itisnotcompletelyaccurate

but itwillgiveyouaquick ballpark figureofyourchances for

makingahand.

Hereishowitworks.

With twocards tocomeaftertheflopyoumultiplyyournumber

ofoutsbyfour.Withonecardtocomeaftertheturn,youmultiply

yournumberofoutsbytwo.

Thiswillgiveyouaquickfiguretoworkwith.

If you have a fourcard flush after the flop youhavenine outs.

Withtwocardstocome,youmultiplytheninebyfourandyouget

36percentchanceofmakingtheflush.


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The chart shows the true odds at 35 percent.With one card to

come you multiply nineby two and get 18 percent. The chart

showsthatthetruefigureis19.6.Itisnotcompletelyaccuratebut

itisprettyclose,anditisaneasycalculationtodoinyourhead

Howtocalculatehandodds(thelongerway):

Onceyou knowhow to correctly count thenumber ofoutsyou

haveonahand,youcanusethattocalculatewhatpercentofthe

time you will hit your hand by the river. Probability can be

calculated easily for a single event, like the flippingof the river

cardfromtheturn.Thiswouldsimplybe:TotalOuts/Remaining

Cards.Fortwocardshowever,likefromthefloptotheriver,itsa

bitmorecomplicated.Thisiscalculatedbyfiguringtheprobability

ofyourcardsnothittingtwiceinarow.Thiscanbecalculatedas

shownbelow:

FloptoRiver%=1 [((47 Outs)/47)*((46 Outs)/46)]

TurntoRiver%=(47 Outs)/46

Thenumber47representstheremainingcardsleftinthedeckafter

theflop(52totalcards,minus2inourhandand3ontheflop=47

remaining cards).Even though theremightnot technicallybe47

cardsremaining,

we

do

calculations

assuming

we

are

the

only

players in the game. To illustrate,here is a two overcarddraw,

whichhas3outs foreachovercard,givinga totalof6outs fora

toppairdraw:

TwoOvercardDraw=1 [(47 6)/47*(46 6)/46]

=1 [(41/47)*(40/46)]

=1 [0.87*0.87]

=1 0.76

= 0 24


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However, most of the time we want to see this in hand odds,

whichwillbeexplainedafteryoureadaboutpotodds.Tochange

apercenttoodds,theformulais:

Odds=(1/Percentage) 1

Thus,tochangethe24%drawintoanoddwecanuse,wedothe

following:

Odds=(1/24%TwoOvercardDraw) 1=(1/0.24) 1

=4.17 1

=3.17orapprox3.2

ANALYZINGPROBABILITIESINDEPTH

Youmaywanttoskipthissectionandgobacktoitlater.Someofthisisprettydeep.Butimportant!

Gettingahandleon theprobabilityofbeingdealtvariouspoker

handsisoneofthemostimportantandvaluableskillsaplayercan

have. We present a number of different ways to do these

calculations,fromaroughguesstimatesystemcalledthe24Rule

totheactualcombinationmath.

Thefirstoddscalculationthatmustbemadeistodeterminethe

totalnumberofpossiblepokerhandsinadeck.

Asweveshown,apokerhandconsistsof5cardsdrawn froma

deck of 52 cards. Therefore, the number of combinations is

COMBIN(52,5)=2,598,960.

If you use Microsoft Excel, you can duplicate these calculations


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combinationsforagivennumberof items. TofindtheCOMBIN

factorinExcelgotoINSERT...FUNCTION ...MATH&TRIG.

Foreachoftheabove NumberofCombinations wedivideby

thisnumbertogettheprobabilityofbeingdealtanyparticular

hand.

For the calculations,wewill first split out the No Pair hands

which includeRoyal Straight Flushes, Straight Flushes, Flushes,

Straights,and Nothings.Then,wewill lookatallcombinationsthathaveatleast1pair.

The cards in a hand without any pairs will have 5 different

denominations selected randomly from the 13 available (2, 3,

4...Ace).Also,eachof the5denominationswillselect1suitfrom

the four available suits.Thus the totalnumberofnopairhands

willequal:

COMBIN(13, 5) * (COMBIN(4, 1))^5 = 1287 * 1024 = 1,317,888.

AStraightFlushismadeupof5consecutivecardsinthesamesuit

andmayhaveahighcardof5,6,7,8,9,10,Jack,Queen,King,or

Aceforatotalof10differentranks.Eachofthesemaybeinanyof

4

suits.

Thus

there

are

40

possible

Straight

Flushes.

An

Ace

high

Straight Flush is aRoyal Flush. Since there are only 4 different

suits there are only 4possibleRoyal StraightFlushes.Whenwe

subtractthe4RoyalStraightFlushesfromthetotalof40Straight

Flusheswe are leftwith 36 other Straight Flushes that areKing

highorless.

AFlush consists of any 5of the 13 cards from aparticular suit.

There are 4 possible suits. The number of possible Flushes is:

COMBIN(13 5) * 4 = 5 148 However this includes the 40 possible


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Straight Flushes.Whenwe subtract these out,we are leftwith:

5,148 40=5,108possibleordinaryflushes.

Astraightconsistsof5cardswithconsecutivedenominationsand

mayhaveahighcardof5,6,7,8,9,10,Jack,Queen,King,orAce

foratotalof10differentranks.Eachofthese5cardsmaybeinany

of the4 suits.Thus thereare10 *4^5= 10,240differentpossible

straights. However, this total includes the 40 possible Straight

Flushes.Thuswesubtract40,whichleavesuswith10,200possible

ordinarystraights.

Finally,wecometothe nothing handswhicharebasicallyallthe

left over garbage. This is simply the total number of No Pair

handsminusall thegoodstuff.Thisgivesus:1,317,888 4 36

5,108 10,200=1,302,540 nothing hands.

Howabouttheoddsofgetting1pairorbetter?

A handwithjust 1 pair has 4 different denominations selected

randomly from the 13 available denominations. 3 of these

denominationswill select 1 card randomly from the 4 available

suits.The4thdenominationwillselect2cardsfromtheavailable4

suits. Finally, the pair can be any one of the four available

denominations. Thus the calculation is: COMBIN(13, 4) *

(COMBIN(4,

1))^3

*

COMBIN(

4,

2)

*

4

=1,098,240

possible

hands

thathavejustonepair.

Insider Secrets to Playing Texas Hold'Em Online Poker by Theo Cage Poker eBook

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Transcript of Insider Secrets to Playing Texas Hold'Em Online Poker by Theo Cage Poker eBook