# All Poker Hands

This post works with 5-card Poker hands drawn from a standard deck of 52 cards. The discussion is mostly mathematical, using the Poker hands to illustrate counting techniques and calculation of probabilities

Working with poker hands is an excellent way to illustrate the counting techniques covered previously in this blog — multiplication principle, permutation and combination (also covered here). There are 2,598,960 many possible 5-card Poker hands. Thus the probability of obtaining any one specific hand is 1 in 2,598,960 (roughly 1 in 2.6 million). The probability of obtaining a given type of hands (e.g. three of a kind) is the number of possible hands for that type over 2,598,960. Thus this is primarily a counting exercise.

Know your poker hand order Royal flush. A royal flush is an ace high straight flush. For example, A-K-Q-J-10 all of diamonds. A straight flush is a five-card straight, all in the same suit. For example, 7–6–5–4–3 all of spades. Four of a kind, or quads, are four. It high to low poker hands does not matter if you lost a load of cash your time or income then this could be able to high to low poker hands accommodate you with a abundant bigger befalling of demography home the jackpot is shared cards that are ranked as 2. Email Extractor 14 (EE14 or EX14) is a. TOP 10 MOST AMAZING POKER HANDS EVER!Help us to 200K Subscribers — you are reading this, comment what poker video you want to see next.

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*Preliminary Calculation*

Usually the order in which the cards are dealt is not important (except in the case of stud poker). Thus the following three examples point to the same poker hand. The only difference is the order in which the cards are dealt.

*These are the same hand. Order is not important.*

The number of possible 5-card poker hands would then be the same as the number of 5-element subsets of 52 objects. The following is the total number of 5-card poker hands drawn from a standard deck of 52 cards.

The notation is called the binomial coefficient and is pronounced “n choose r”, which is identical to the number of -element subsets of a set with objects. Other notations for are , and . Many calculators have a function for . Of course the calculation can also be done by definition by first calculating factorials.

Thus the probability of obtaining a specific hand (say, 2, 6, 10, K, A, all diamond) would be 1 in 2,598,960. If 5 cards are randomly drawn, what is the probability of getting a 5-card hand consisting of all diamond cards? It is

This is definitely a very rare event (less than 0.05% chance of happening). The numerator 1,287 is the number of hands consisting of all diamond cards, which is obtained by the following calculation.

The reasoning for the above calculation is that to draw a 5-card hand consisting of all diamond, we are drawing 5 cards from the 13 diamond cards and drawing zero cards from the other 39 cards. Since (there is only one way to draw nothing), is the number of hands with all diamonds.

If 5 cards are randomly drawn, what is the probability of getting a 5-card hand consisting of cards in one suit? The probability of getting all 5 cards in another suit (say heart) would also be 1287/2598960. So we have the following derivation.

Thus getting a hand with all cards in one suit is 4 times more likely than getting one with all diamond, but is still a rare event (with about a 0.2% chance of happening). Some of the higher ranked poker hands are in one suit but with additional strict requirements. They will be further discussed below.

Another example. What is the probability of obtaining a hand that has 3 diamonds and 2 hearts? The answer is 22308/2598960 = 0.008583433. The number of “3 diamond, 2 heart” hands is calculated as follows:

One theme that emerges is that the multiplication principle is behind the numerator of a poker hand probability. For example, we can think of the process to get a 5-card hand with 3 diamonds and 2 hearts in three steps. The first is to draw 3 cards from the 13 diamond cards, the second is to draw 2 cards from the 13 heart cards, and the third is to draw zero from the remaining 26 cards. The third step can be omitted since the number of ways of choosing zero is 1. In any case, the number of possible ways to carry out that 2-step (or 3-step) process is to multiply all the possibilities together.

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*The Poker Hands*

Here’s a ranking chart of the Poker hands.

The chart lists the rankings with an example for each ranking. The examples are a good reminder of the definitions. The highest ranking of them all is the royal flush, which consists of 5 consecutive cards in one suit with the highest card being Ace. There is only one such hand in each suit. Thus the chance for getting a royal flush is 4 in 2,598,960.

Royal flush is a specific example of a straight flush, which consists of 5 consecutive cards in one suit. There are 10 such hands in one suit. So there are 40 hands for straight flush in total. A flush is a hand with 5 cards in the same suit but not in consecutive order (or not in sequence). Thus the requirement for flush is considerably more relaxed than a straight flush. A straight is like a straight flush in that the 5 cards are in sequence but the 5 cards in a straight are not of the same suit. For a more in depth discussion on Poker hands, see the Wikipedia entry on Poker hands.

The counting for some of these hands is done in the next section. The definition of the hands can be inferred from the above chart. For the sake of completeness, the following table lists out the definition.

*Definitions of Poker Hands*

**Poker HandDefinition**1Royal FlushA, K, Q, J, 10, all in the same suit2Straight FlushFive consecutive cards,all in the same suit3Four of a KindFour cards of the same rank,one card of another rank4Full HouseThree of a kind with a pair5FlushFive cards of the same suit,not in consecutive order6StraightFive consecutive cards,not of the same suit7Three of a KindThree cards of the same rank,2 cards of two other ranks8Two PairTwo cards of the same rank,two cards of another rank,one card of a third rank9One PairThree cards of the same rank,3 cards of three other ranks10High CardIf no one has any of the above hands,the player with the highest card wins

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*Counting Poker Hands*

*Straight Flush*

Counting from A-K-Q-J-10, K-Q-J-10–9, Q-J-10–9–8, …, 6–5–4–3–2 to 5–4–3–2-A, there are 10 hands that are in sequence in a given suit. So there are 40 straight flush hands all together.

*Four of a Kind*

There is only one way to have a four of a kind for a given rank. The fifth card can be any one of the remaining 48 cards. Thus there are 48 possibilities of a four of a kind in one rank. Thus there are 13 x 48 = 624 many four of a kind in total.

*Full House*

Let’s fix two ranks, say 2 and 8. How many ways can we have three of 2 and two of 8? We are choosing 3 cards out of the four 2’s and choosing 2 cards out of the four 8’s. That would be = 4 x 6 = 24. But the two ranks can be other ranks too. How many ways can we pick two ranks out of 13? That would be 13 x 12 = 156. So the total number of possibilities for Full House is

Note that the multiplication principle is at work here. When we pick two ranks, the number of ways is 13 x 12 = 156. Why did we not use = 78?

*Flush*

There are = 1,287 possible hands with all cards in the same suit. Recall that there are only 10 straight flush on a given suit. Thus of all the 5-card hands with all cards in a given suit, there are 1,287–10 = 1,277 hands that are not straight flush. Thus the total number of flush hands is 4 x 1277 = 5,108.

*Straight*

There are 10 five-consecutive sequences in 13 cards (as shown in the explanation for straight flush in this section). In each such sequence, there are 4 choices for each card (one for each suit). Thus the number of 5-card hands with 5 cards in sequence is . Then we need to subtract the number of straight flushes (40) from this number. Thus the number of straight is 10240–10 = 10,200.

*Three of a Kind*

There are 13 ranks (from A, K, …, to 2). We choose one of them to have 3 cards in that rank and two other ranks to have one card in each of those ranks. The following derivation reflects all the choosing in this process.

*Two Pair and One Pair*

These two are left as exercises.

*High Card*

The count is the complement that makes up 2,598,960.

## All Poker Hands In Texas Roadhouse

The following table gives the counts of all the poker hands. The probability is the fraction of the 2,598,960 hands that meet the requirement of the type of hands in question. Note that royal flush is not listed. This is because it is included in the count for straight flush. Royal flush is omitted so that he counts add up to 2,598,960.

*Probabilities of Poker Hands*

**Poker HandCountProbability**2Straight Flush400.00001543Four of a Kind6240.00024014Full House3,7440.00144065Flush5,1080.00196546Straight10,2000.00392467Three of a Kind54,9120.02112858Two Pair123,5520.04753909One Pair1,098,2400.422569010High Card1,302,5400.5011774Total2,598,9601.0000000

## All 169 Poker Hands Ranked

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2017 — Dan Ma

## All Poker Hands Ranking

**HOME | PREFLOP STRATEGIES | CONTACT**

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On this site you can find all possible combinations of preflop hands that can occur in Texas Hold’em Poker. As a bonus you will also learn the nicknames of the different hands.

The hands are ranked from #1 to #169, where #1 is the best. This ranking is applicable when the poker table is full ring (9–10 people). The ranking is based on computer calculation results with all the players staying to the river card. It is not applicable to any real play.

If the hand is named XXs then it means the hand is suited, if XXo then the hand is off suit.

**#1**AA

Pocket Rockets

American Airlines

The Hand

Bullets

Rocky Mountains

**#2**

KK

Cowboys

Kamikaze

King Kong

Cold Turkey

Kangaroos

**#3**QQ

Hilton Sisters

Ladies

West Hollywood

The Bitches

The Witches

Double Date

4 Tits

Flower Girls

**#4**AKs

Big Slick in a suit

Anna Kournikova

Santa Barbara

Mike Haven

**#5**JJ

Jokers

Brothers

Hooks

Jackson Hole

SHIP

Gays Online

**News »**

**January 10, 200**7

A lot more nicknames added

November 29

More nicknames added

November 29

**November 25**

More nicknames added

**November 11, 2006**

Site complete with all possible hands.

**November 7, 2006**

Site was online for the first time.

**#6**AQs

Big Chick

Little Slick

Anthony & Cleopatra

**#7**KQs

Mamas and Papas

Newlyweds

Marriage

Royal Couple

Parents

**#8**AJs

Ajax

Black Jack

Jack Ass

J-birds

**#9**KJs

Kojak

King John

Hary Potter

Bachelor’s Hand

Tucson Monster

**#10**TT

TinTin

Tension

Twenty Miles

**#11**AKo

Big Slick

Anna Kournikova

**#12**ATs

Johnny Moss

Bookends

**#13**QJs

Oedipus

Maverick

**#14**KTs

Katie

Big Al

**#15**QTs

Quint

Varkony

Gratitude

Greyhound

**#16**JTs

Morgan

**#17**99

Wayne Gretzky

German Virgin

Popeye’s

Phil Hellmuth

**#18**AQo

Big Chick

Little slick

**#19**A9s

Rounders Hand

Driving the Truck

**#20**KQo

Mixed Marriage

Othello

**#21**88

Snowmen

Little Oldsmobile

Two Fat Ladies

Catnuts

**#22**K9s

Canine

Pair of Dogs

Turner & Hooch

Pedigree

Fido

Sawmill

**#23**T9s

Count Down

**#24**A8s

Dead Mans Hand

**#25**Q9s

Quinine

**#26**J9s

Jeanine

**#27**AJo

Ace Jack-off

**#28**A5s

High Five

**#29**77

Buggy Tops

Saturn

Sunset Strip

Hockey Sticks

Mullets

Walking Sticks

**#30**A7s

Red Baron

**#31**KJo

Kojak

King John

Jack-King-off

Harry Potter

**#32**A4s

Sharp Tops

Amen

Tranny’s

**#33**A3s

Ash Tray

Baskin Robbins

**#34**A6s

Mile High

**#35**QJo

Maverick

Fred & Ethel

**#36**66

Route 66

Kicks

**#37**K8s

The Feast

Kokomo

**#38**T8s

Tetris

Tenaciously

**#39**A2s

Hunting Season

Arizona

Acey-Deucy

**#40**98s

Oldsmobile

**#41**J8s

Jeffrey Dalmer

**#42**ATo

Bookends

**#43**Q8s

Kuwait

**#44**K7s

King Salmon

Kevin

**#45**KTo

Katie

Woodcutter

**#46**55

Presto

Double Nickels

Speed Limit

Sammy

**#47**JTo

Morgan

**#48**87s

RPM

Tahoe

**#49**QTo

Quint

Greyhound

**#50**44

Robert Varkonyi

Quint

Magnum

Colt 44

Sail Boats

Diana Dors

**#51**33

Crabs

City Parks

**#52**

22

Quackers

Pocket Swans

Ducks

Barely Legal

The Strippers

**#53**K6s

The Concubine

**#54**97s

Grapefruit

**#55**K5s

King of Nickels

**#56**76s

America

Union Oil

**#57**T7s

The Bowling Hand

Split

**#58**K4s

Fork

**#59**K3s

King Crab

Sizzler

Commander Crab

**#60**K2s

White Men Can’t Jump

**#61**Q7s

Computer Hand

**#62**86s

Eubie

Maxwell Smart

**#63**65s

Ken Warren

**#64**J7s

Dice Hand

**#65**54s

Colt

**#66**Q6s

**#67**75s

Heinz 57 Sauce

**#68**96s

Overtime

Soixante Neuf

**#69**Q5s

Granny Mae (if spades)

**#70**64s

Revolution

The Rabbit

**#71**Q4s

**#72**Q3s

Bitch with Crabs

Gay Waiter

**#73**T9o

Countdown

**#74**T6s

Driver’s License

**#75**Q2s

Windsor Waiter

**#76**A9o

Jesus

Chris Ferguson

**#77**53s

**#78**85s

Finky Dink

**#79**J6s

Jack Sikma

**#80**J9o

Emergency

9–11

**#81**K9o

Sawmill

**#82**J5s

Jackson Five

Motown

**#83**Q9o

Quinine

**#84**43s

Waltz Time

**#85**74s

Barn Owl

**#86**J4s

Done Hand

Jermaine

Flat Tire

**#87**J3s

J-Lo

Bird Table

**#88**95s

Dolly Parton

Hard Working

**#89**J2s

The Jew

**#90**63s

JFK

Three Dozen

**#91**A8o

Dead Man’s Hand

**#92**52s

Two Bits

Quarter

**#93**T5s

Dimestore

Woolworth

Five and Dime

**#94**84s

Big Brother

George Orwell

**#95**T4s

Roger That

Over and Out

Convoy

The Good Buddy

**#96**T3s

**#97**42s

The Answer

Lumberjack

**#98**T2s

Texas Dolly

Terminator II

**#99**98o

Oldsmobile

**#100**T8o

Tetris

**#101**A5o

High Five

**#102**A7o

Red Baron

**#103**73s

Dutch Waiter

Swedish Busboy

**#104**A4o

Crashing Airlines

**#105**32s

Hooter Hand

Jordan

**#106**94s

San Fransisco

**#107**93s

Jack Benny

**#108**J8o

Jeffery Dalmer

**#109**A3o

Baskin Robbins

Ash Tray

**#110**62s

**#111**92s

Twiggy

**#112**K8o

The Feast

Dr Spoon

Kokomo

**#113**A6o

Mile High

**#114**87o

Tahoe

**#115**Q8o

Kuwait

**#116**83s

Raquel Welch

**#117**A2o

Arizona

Big Balls

Hunting Season

**#118**82s

Fat Lady and a Duck

**#119**97o

Grapefruit

**#120**72s

Beer Hand

**#121**76o

Union Oil

**#122**K7o

King Salmon

**#123**65o

Ken Warren

**#124**T7o

Split

**#125**K6o

The Concubine

**#126**86o

Maxwell Smart

**#127**54o

Colt 45

Jesse James

Jane Russell

**#128**K5o

Rotten Cowboy

**#129**J7o

Dice

**#130**75o

Filipino Slick

Heinz

**#131**Q7o

Computer Hand

**#132**K4o

Fork

**#133**K3o

Commander Crab

King Crab

**#134**96o

Percy

**#135**K2o

Big Fritz

**#136**64o

The Question

**#137**Q6o

**#138**53o

Bully Johnson

**#139**85o

The Scag

**#140**T6o

Sweet Sixteen

**#141**Q5o

**#142**43o

Waltz Time

**#143**Q4o

**#144**Q3o

Gay Waiter

**#145**74o

Cambodian Slick

**#146**Q2o

The Vesty

**#147**J6o

Jack Sikma

**#148**63o

JFK

Blocky

**#149**J5o

Jackson Five

**#150**95o

Dolly Parton

**#151**52o

Quarter

**#152**J4o

Kid Grenade

**#153**J3o

Fortran

**#154**42o

The Answer

**#155**J2o

Bennifer

**#156**84o

Big Brother

**#157**T5o

Nickels and Dimes

**#158**T4o

CB Hand

Roger That

**#159**32o

Big Gulp

Hooter Hand

Mississippi Slick

Can of Corn

**#160**T3o

**#161**73o

Rusty Trombone

**#162**T2o

Texas Dolly

**#163**62o

Bed & Breakfast

**#164**94o

Joe Montana Banana

**#165**93o

Jack Benny

**#166**92o

Montana Banana

Twiggy

**#167**83o

Suzanna Banana

Sven

Raquel Welch

**#168**82o

Sixty Nine

**#169**72o

Death

The Big Man Hand

The Hammer

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