Royal Flush
Ace high Straight Flush.
The product 52×51×50×49×48 must be divided by 5! Because the order in which the five cards are added to the hand is of no importance, e.g., 7♣8♣9♣10♣J♣ is the same hand as 9♣7♣10♣J♣8♣. Thus there are C(52, 5) = 2598960 different hands. The poker sample space consists of 2598960 equally probable elementary events. So A♥ 10♥ 8♥ 3♥ 2♥ always beats K♥ Q♥ J♥ 9♥ 7♥. If neither player has the Ace of the flush suit, the King is next highest and so on. If the Ace is on the board, the player with the next highest card wins. For more common Texas Hold'em Winning Hand scenarios explained, see our How to Determine the Winning Poker Hand article. In other words, a Pair of Kings beats a Pair of Tens, and a Straight 7-8-9-10-J beats a Straight 3-4-5-6-7. The lowest possible hand is no hand at all - no pairs, no Straight, nothing. This kind of hand is known by the highest card it contains, so K-7-5-3-2 of different suits would be 'King High.'
Ace of Spades King of Spades Queen of Spades Jack of Spades 10 of Spades in a single suit. Also frequently referred to as 'Broadway'.
Straight Flush
Five consecutive cards of the same suit.
Five sequential cards in the same suit. The highest type of Straight Flush is a Royal Flush, and the lowest is an A-2-3-4-5 hand (if Aces are low or high/low). This type of hand is referred to as a 'Steel Wheel'. Other Straight Flushes with special names include:
- King of Clubs Queen of Clubs Jack of Clubs 10 of Clubs 9 of Clubs - Off Broadway (because it's shifted down one rank from a Royal Flush, or 'Broadway').
Four of a Kind
LEVEL: SMALL BLIND: BIG BLIND: BB ANTE: 1: 100: 200: 200: 2: 200: 300: 300: 3: 200: 400: 400: 4: 300: 500: 500: Break 10 min: 5: 200: 300: 600: 6: 200: 400: 800: 7. Poker dice is known from the latter half of the 19th century. Several variants exist—for example, Spanish poker dice with differing rules and eight-sided dice marked with ace, king, queen, jack, 10, 9, 8, and 7. Poker dice may also be played with ordinary six-sided dice; the sides then count 1 (aces)-6-5-4-3-2 in descending order.
One of each suit in a single rank.
Also known as Quads. Many of the Four of a Kind hands have their own nicknames:
- King of Clubs King of Diamonds King of Hearts King of Spades - Four Horsemen (of the Apocalypse)
- Queen of Clubs Queen of Diamonds Queen of Hearts Queen of Spades - Village People (four Queens)
- 10 of Clubs 10 of Diamonds 10 of Hearts 10 of Spades - Larry, after Larry Fortensky (four-ten-sky), Elizabeth Taylor's eighth husband
- 4 of Clubs 4 of Diamonds 4 of Hearts 4 of Spades - Yacht Club (because the 4 resembles a sail)
- 3 of Clubs 3 of Diamonds 3 of Hearts 3 of Spades - Forest (four 'trees')
- 2 of Clubs 2 of Diamonds 2 of Hearts 2 of Spades - Mighty Ducks (because the 2 resembles a duck)
Full House
Three of a Kind and One Pair.
A Full House is called as 'X over Y' where X is the Three of a Kind and Y is the Pair (e.g., in a A-A-A-Q-Q hand, you would call it as 'Full House, Aces over Queens').
A Full House is sometimes called a boat or a full boat. When called a Boat/Full Boat, the hand is announced as 'X full of Y' (e.g., the same A-A-A-Q-Q hand would be called a 'Full Boat, Aces full of Queens'). Some Full House hands have special nicknames:
- Ace of Clubs Ace of Diamonds 2 of Clubs 2 of Diamonds 2 of Hearts - Marksman (bows and arrows)
- 7 of Clubs 7 of Diamonds 7 of Clubs 4 of Diamonds 4 of Hearts - Sailing rednecks
- 3 of Clubs 3 of Diamonds 3 of Clubs 2 of Diamonds 2 of Hearts - Nits and Lice, Mites and Lice
Flush
Five cards of the same suit.
Any five cards, all of which are in the same suit. A Flush all in hearts is referred to as 'Valentine's' while a flush all in clubs is known as a 'Golf Bag'.
Straight
Five consecutive cards.
Five cards in sequential order (but not all in the same suit, or it would be a Straight Flush). Also known as a Run (in many melding/counting games, such as gin and its variants, cribbage, and canasta, a Straight is referred to as a Run, and the name has carried over into poker).
- 6 of Clubs 5 of Diamonds 4 of Hearts 3 of Spades 2 of Clubs - Rabbit (the lowest Straight Flush if Aces are high)
- 5 of Clubs 4 of Diamonds 3 of Hearts 2 of Spades Ace of Clubs - Wheel, Bicycle, Bike, Spike, First Street, Little Wheel (the lowest run if Aces are low or high/low)
Three of a Kind
Three cards of the same rank. Also known as Trips, a Set, or Triplets. Three-card combinations that have special names include:
- Ace of Clubs Ace of Diamonds Ace of Hearts - Beatles reunion
- King of Clubs King of Diamonds King of Hearts - Three Wise Men, Christmas Special (both references to 'Three Kings'), Alabama Night Riders, Ku Klux Klan (KKK is an abbreviation for the Ku Klux Klan, and 'Alabama Night Riders' is a colloquial term used to refer to this group, which has a history of carrying out their acts at night in rural ateas)
- Queen of Clubs Queen of Diamonds Queen of Hearts - Six Tits
- Jack of Clubs Jack of Diamonds Jack of Hearts - Hart, Schaffner, and Marx (Three Jacks)
- 10 of Clubs 10 of Diamonds 10 of Hearts - Dallas to Fort Worth (the I-10 connects these two Texas Cities), San Jose to Gilroy, Gilroy, Thirty Miles of bad road (the distance between San Jose and Gilroy, California, used to be 30 miles, although the two cities are now adjoining)
- 7 of Clubs 7 of Diamonds 7 of Hearts - 21, Slot Machine, Jackpot (all named after results in other casino games like Blackjack and Slots)
- 6 of Clubs 6 of Diamonds 6 of Hearts - The Devil, The Beast, Lucifer, Devil's Area Code
- 5 of Clubs 5 of Diamonds 5 of Hearts - Washington Monument, Pork Chop Sandwiches
- 4 of Clubs 4 of Diamonds 4 of Hearts - Grand Jury
- 2 of Clubs 2 of Diamonds 2 of Hearts - Huey, Dewey, and Louie (three ducks)
Two Pairs
Two pairs, each with two cards of the same rank. Notable named two pair combinations include:
- Ace of Clubs Ace of Diamonds 8 of Clubs 8 of Diamonds - Dead Man's Hand (Arrows and Nooses)
- King of Clubs King of Diamonds Queen of Clubs Queen of Diamonds - Mommas and Poppas
- King of Clubs King of Diamonds 9 of Clubs 9 of Diamonds - Pair of Dogs (because it's K9K9-- two canines)
- Queen of Clubs Queen of Diamonds 3 of Clubs 3 of Diamonds - San Francisco Waiters (Queens with Trays/Treys)
- Jack of Clubs Jack of Diamonds 5 of Clubs 5 of Diamonds - Jackson Five (Jacks and Fives), Motown, Rock and Roll
- Jack of Clubs Jack of Diamonds 3 of Clubs 3 of Diamonds - Hookers with Crabs (because the Jacks hook and the 3 is like a sideways crab)
- 9 of Clubs 9 of Diamonds 8 of Clubs 8 of Diamonds - Oldsmobile
- 9 of Clubs 9 of Diamonds 6 of Clubs 6 of Diamonds - Dinner for Four
- 3 of Clubs 3 of Diamonds 2 of Clubs 2 of Diamonds - Socks and Shoes, Mites and Lice, Mits and Mites, Nits and Lice
One Pair
Two cards of the same rank. The poker hand that contains a single pair that is the most worth noting is the Princess Leia (an A-A-2-3), so called because the room in which Leia was imprisoned in Star Wars was room A-A-2-3. The best known names given to (pocket) pairs include:
- Ace of Clubs Ace of Diamonds - Pocket Rockets, Bullets, American Airlines
- King of Clubs King of Diamonds - Cowboys, King Kong
- Queen of Clubs Queen of Diamonds - Bitches, Double date, Canadian Aces, Siegfried and Roy
- Jack of Clubs Jack of Diamonds - Fish Hooks
- 9 of Clubs 9 of Diamonds - German Virgin (no, we don't know why.)
- 8 of Clubs 8 of Diamonds - Snowmen
- 7 of Clubs 7 of Diamonds - Sunset Strip, Hockey Sticks
- 6 of Clubs 6 of Diamonds - Route 66
- 5 of Clubs 5 of Diamonds - Speed limit
- 4 of Clubs 4 of Diamonds - Magnum, Sail Boat
- 3 of Clubs 3 of Diamonds - Crabs
- 2 of Clubs 2 of Diamonds - Ducks
Poker 7 8 9 10 J Balvin
High Card
While the high card is the lowest possible hand in poker (every poker hand automatically has a 'high card' in it-- the card with the greatest value), it comes into play in some poker variants more than others. Poker rookies often underestimate the value of the high card.
Texas Hold'em, for instance, is frequently referred to as a game of high cards because a player with higher cards always has an advantage. If player 1 holds K-Q and player 2 holds J-10, there are three possible outcomes:
- The flop makes player 1's hand, and player 1 wins.
- The flop makes player 2's hand, and player 2 wins.
- The flop doesn't make either player's hand, and player 1 wins again.
The player with high cards has a statistical advantage and will win 63% of the time.
Well known nicknames given to pocket hands are:
- Ace of Clubs King of Diamonds - Big Slick, Anna Kournikova (looks great, never wins!)
- Ace of Clubs Queen of Diamonds - Big Chick
- Ace of Clubs Jack of Diamonds - Black Jack, Jack-Ass
- King of Clubs Queen of Diamonds - Royalty, Marriage
- King of Clubs Jack of Diamonds - Kojak
- Jack of Clubs 5 of Diamonds - Jackson Five
- Queen of Clubs 3 of Diamonds - Gay Waiter
- 9 of Clubs 5 of Diamonds - Dolly Parton
- Ace of Clubs 8 of Diamonds - Dead Man's Hand (player Wild Bill Hickok was shot in 1876 after winning with it!)
- King of Clubs 9 of Diamonds - Canine
- Jack of Clubs 4 of Diamonds - Flat Tire
Sanderson M. Smith
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In many forms of poker, one is dealt 5 cards from astandard deck of 52 cards. The number of different 5 -card pokerhands is
A wonderful exercise involves having students verify probabilitiesthat appear in books relating to gambling. For instance, inProbabilities in Everyday Life, by John D. McGervey, one findsmany interesting tables containing probabilities for poker and othergames of chance.
This article and the tables below assume the reader is familiarwith the names for various poker hands. In the NUMBER OF WAYS columnof TABLE 2 are the numbers as they appear on page 132 in McGervey'sbook. I have done computations to verify McGervey's figures. Thiscould be an excellent exercise for students who are studyingprobability.
7 8 9 Barenaked Ladies
There are 13 denominations (A,K,Q,J,10,9,8,7,6,5,4,3,2) in thedeck. One can think of J as 11, Q as 12, and K as 13. Since an acecan be 'high' or 'low', it can be thought of as 14 or 1. With this inmind, there are 10 five-card sequences of consecutive dominations.These are displayed in TABLE 1.
TABLE 1The following table displays computations to verify McGervey'snumbers. There are, of course , many other possible poker handcombinations. Those in the table are specifically listed inMcGervey's book. The computations I have indicated in the table doyield values that are in agreement with those that appear in thebook.
N = NUMBER OF WAYS listed by McGervey | |||
Straight flush | There are four suits (spades, hearts, diamond, clubs). Using TABLE 1,4(10) = 40. | ||
Four of a kind | (13C1)(48C1) = 624. Choose 1 of 13 denominations to get four cards and combine with 1 card from the remaining 48. | ||
Full house | (13C1)(4C3)(12C1)(4C2) = 3,744. Choose 1 denominaiton, pick 3 of 4 from it, choose a second denomination, pick 2 of 4 from it. | ||
Flush | (4C1)(13C5) = 5,148. Choose 1 suit, then choose 5 of the 13 cards in the suit. This figure includes all flushes. McGervey's figure does not include straight flushes (listed above). Note that 5,148 - 40 = 5,108. | ||
Straight | (4C1)5(10) = 45(10) = 10,240 Using TABLE 1, there are 10 possible sequences. Each denomination card can be 1 of 4 in the denomination. This figure includes all straights. McGervey's figure does not include straight flushes (listed above). Note that 10,240 - 40 = 10,200. | ||
Three of a kind | (13C1)(4C3)(48C2) = 58,656. Choose 1 of 13 denominations, pick 3 of the four cards from it, then combine with 2 of the remaining 48 cards. This figure includes all full houses. McGervey's figure does not include full houses (listed above). Note that 54,912 - 3,744 = 54,912. | ||
Exactly one pair, with the pair being aces. | (4C2)(48C1)(44C1)(40C1)/3! = 84,480. Choose 2 of the four aces, pick 1 card from remaining 48 (and remove from consider other cards in that denomination), choose 1 card from remaining 44 (and remove other cards from that denomination), then chose 1 card from the remaining 40. The division by 3! = 6 is necessary to remove duplication in the choice of the last 3 cards. For instance, the process would allow for KQJ, but also KJQ, QKJ, QJK, JQK, and JKQ. These are the same sets of three cards, just chosen in a different order. | ||
Two pairs, with the pairs being 3's and 2's. | McGervey's figure excludes a full house with 3's and 2's. (4C2)(4C1)(44C1) = 1,584. Choose 2 of the 4 threes, 2 of the 4 twos, and one card from the 44 cards that are not 2's or 3's. |
'I must complain the cards are ill shuffled 'til Ihave a good hand.'
-Swift, Thoughts on Various Subjects
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