Pai gow poker, or double-hand poker, is an Americanized version of Pai Gow, in that Pai Gow Poker is played with playing cards using poker hand rankings while Pai Gow is played with Chinese dominoes.
The game is played with a standard 52-card deck, plus a single joker. It is played on a table set for six players plus the dealer.
Each player is playing against the banker, who may be the casino dealer or one of the other players at the table.
Object of the Game
The object of the game is to create two poker hands out of the seven cards in your hand: A five-card poker hand and a two-card poker hand. The five-card hand must rank higher than your two-card hand. The two-card hand is often called the hand “in front” or “on top”, and the five-card hand is called the hand “behind” or “bottom”, as they are placed that way in front of the player when he is done setting them.
The Deal
The cards are shuffled, and then dealt to the table in seven face-down piles of seven cards, with four cards unused, regardless of the number of people playing.
Betting positions are assigned a number from 1 to 7, starting with whichever player is acting as banker that hand, and counting counter-clockwise around the table. A random number from 1 to 7 is determined (either electronically or manually with dice), and the deal begins with that assigned position and proceeds counter-clockwise.
One common way of using dice to determine the dealer starting number is to roll three six-sided dice, then count betting spots clockwise from the first until the number on the dice is reached.
If a player is not sitting on a particular spot, the hand is still assigned but then placed in the discards with the four unused cards.
Hand Rankings
The only two-card hands are one pair and high cards; no straights, flushes, and so on. The joker plays as a bug: that is, in the five-card hand it can be used to complete a straight or flush, if possible; otherwise it is an ace. In the two-card hand, it always plays as an ace. Five-card hands use standard poker hand rankings, with one exception: in most Nevada casinos, the hand A-2-3-4-5 ranks above a king-high straight, but below the ace-high straight A-K-Q-J-10. In California & Michigan, this rule doesn’t apply. The A-2-3-4-5 is the lowest possible straight.
Determining a Win
If each of your now-separated hands beats the banker’s corresponding hand, then you win your bet. If only one of your hands beats the banker, then you push. If both of your hands lose to the banker, then you lose.
On each individual hand, ties go to the banker (for example, if your five-card hand loses to the banker and your two-card hand ties him, you lose). This gives the banker a small advantage. If you foul your hand, meaning that your low hand outranks your high hand or that there are an incorrect number of cards in each hand, there will be a penalty, either re-arrangement of the hand according to house rules or forfeiture of the hand.
In casino-banked games, the banker is generally required to set their hand in a pre-specified manner called “house way”, so the dealer does not have to implement any strategy in order to beat the players. When a player is banking, he is free to set the hand however he chooses. However, the player has the option of “co-banking” with the house, and if this option is chosen, the player’s hand must also be set the house way.
California casinos typically charge a flat fee per hand, such as 50 cents or one dollar, to play, win or lose. Other casinos take out of winnings a 5% commission. While this seems high, it should be noted that a hand of Pai Gow poker takes a long time to play compared to, say, blackjack, and there are many pushes, so the house doesn’t collect that 5% as often as it would collect the house percentage on other games.
The fundamental theorem of poker is a principle first articulated by David Sklansky that he believes expresses the essential nature of poker as a game of decision-making in the face of incomplete information.
Every time you play a hand differently from the way you would have played it if you could see all your opponents’ cards, they gain; and every time you play your hand the same way you would have played it if you could see all their cards, they lose. Conversely, every time opponents play their hands differently from the way they would have if they could see all your cards, you gain; and every time they play their hands the same way they would have played if they could see all your cards, you lose.
The Fundamental Theorem is stated in common language, but its formulation is based on mathematical reasoning. Each decision that is made in poker can be analyzed in terms of the concept of expected value. The expected value expresses the average payoff of a decision if the decision is made a large number of times. The correct decision to make in a given situation is the decision that has the largest expected value. (Although sometimes it is correct not to choose this decision for the larger goal of long-term deception.) If you could see all your opponents’ cards, you would always be able to calculate the correct decision with mathematical certainty. (This is certainly true heads-up, but is not always true in multi-way pots.) The less you deviate from these correct decisions, the better your expected long-term results. This is the mathematical expression of the Fundamental Theorem.
Blind man’s bluff is a version of poker which is unconventional in that each person sees the cards of all players except his own.
The standard version (also called Indian poker) is simply high card. Each player is dealt one card which he places on his forehead facing outwards, and a round of betting occurs, as players attempt to guess if they have the highest card based on what they see around them.
Other versions (forehead stud) are variations on stud poker, in which one or more of the hole cards is hidden from its owner, but shown to all other players, as above.
During its coverage of the 2004 World Series of Poker, ESPN showed a Blind Man’s Bluff version of Texas hold’em.
Because Manila has five betting rounds, it does not play well at no limit or pot limit. This can be easily modified by eliminating the betting round between the second and third community cards. So, each player is dealt two private cards and a single community card is dealt to the board, followed by the first betting round. Then two community cards are dealt, followed by a second betting round. Then a fourth community card and third betting round, a fifth and final community card and fourth betting round, followed by a showdown as above.
The three-card variant can be played this way as well (as with Manila, the player must use exactly two of his three hole cards with three of the board cards to make a hand).
Razz is seven-card stud played with ace-to-five low hand values. It is usually played with a bring-in, paid by the player with the highest-ranking upcard on the initial deal (aces are always low cards in Razz, even for the purpose of assigning the bring-in). On the second and subsequent rounds, the player with the lowest exposed hand starts the betting.
London lowball is seven-card stud played with ace-to-six low hand values. It is usually played at pot limit or no limit, and is otherwise identical to Razz.
Here’s a sample Razz deal (suits are omitted here because they are never of consequence in Razz; in London lowball, a flush cannot play as a low hand but otherwise they don’t generally matter either). Alice deals each player two downcards and then one upcard: Bob’s upcard is a J, Carol is dealt a 3, David an A, and Alice a 4. Bob’s J is the high card (David’s A is low), so he pays a $1 bring-in. Carol, David, and Alice all call. Now Bob is dealt a 9, Carol another 3, David a 4, and Alice a 2. The best low hand showing is now David’s 4-A, just beating Alice’s 4-2. David bets $1, Alice calls. Bob folds his J-9, and Carol calls (her pair of 3s is the worst hand showing, but there are still many cards to come). Alice now deals Carol an A, David a K, and herself an 8. The low hand showing is now Alice’s 8-4-2, so she bets $2. Carol raises $2, and David folds. Alice calls, ending the round. Carol is now dealt a 6, and Alice another 8. Now the lowest hand showing is Carol’s 3-3-6-A, a pair of 3s being lower than Alice’s pair of 8s. She bets $2 and Alice calls. A final downcard is dealt, Carol again best $2, and Alice calls. Alice reveals that her downcards are 7-J-A, making her lowest five-card hand an 8-7-4-2-A. Carol reveals her downcards to be a 4-6-7, making her lowest five-card hand a 7-6-4-3-A, which wins the pot.
Five-card draw, with no joker, and deuce-to-seven low hand values is called “Kansas City” or “Low Poker” or even “Billy Baxter” draw in honor of the player who dominated the world championship in the event for many years. The 7-high rule and the no check-and-raise rule do not apply. In the eastern United States, the United Kingdom, and elsewhere, ace-to-six low hand values are common.
California high/low split
Played as above, with a single joker, used as a bug. High hand and low hand (using the ace-to-five low values) split the pot. An 8-high or better low is required to win low. If no hand qualifies low, high hand takes the whole pot. Played cards speak, that is, players do not declare whether they intend to win the high or low half of the pot (or both); they simply show their cards and the best hands win. Because ace-to-five low values are used, a hand such as a low straight or flush can win both high and low, called “scooping” or “hogging” the pot.
High/low with declare
This is common in home games but is rarely found in casinos today. Played as are other versions of five-card draw, but after the second betting round and before the showdown, there is a simultaneous declaration phase. Each player takes two chips from his stack and takes them under the table, bringing up a closed fist that contains either no chips (indicating that the player intends to win the low half of the pot), one chip (indicating that the player intends to win the high half), or two chips (indicating that he intends to scoop). When everyone has brought up the closed fist, the players all open their hands simultaneously to reveal their choices. If any player shows two chips, and his hand is the best low and the best high, he scoops the pot. Otherwise, half of the pot goes to the player with the highest hand who declared high, and the other half to the player with the lowest hand of those who declared low. There is no qualifying hand to win either high or low, and if no one declares in one direction, the full pot is awarded in the other (for example, if all players declare low, the low hand wins the whole pot rather than half). A player who declares for a scoop must win both ends outright, with no ties. For example, if a player declares scoop, has the lowest hand clearly but ties for high, he wins nothing. The other player with the same high hand wins the high half of the pot and the next-lowest hand wins low (assuming he declared low–if no other player declared low, the high hand who declared high wins the whole pot).
This game can be played with deuce-to-seven low or ace-to-six low hand values, but in that case it is nearly impossible to scoop (though you can still win the whole pot if everyone declares the same direction).
Double-draw and Triple-draw
Any game above can be played with two or three draw phases and therefore three or four betting rounds. Double-draw California lowball is a particularly good game. Triple draw lowball, either ace-to-five or deuce-to-seven, has gained some popularity among serious players. The 2004 World Series of Poker included a deuce-to-seven triple-draw lowball event.
Four-before
Another variation that can be applied to any game above, but that is especially suited to lowball. On the initial deal, only four cards are dealt to each player. A betting round follows, then each player draws one more card than he discards, completing his hand to five cards. Then the final betting round and showdown. Note that it is impossible to be dealt a “pat” hand, that is, a hand (such as a straight or flush) that is complete before the draw.
Also sometimes known as Padooki, Badougi is a four card ace-to-five low lowball variant where traditional poker hand rankings are changed. A Badougi is a four card hand where all the cards are of different ranks and suits. Any cards which match another card in rank or suit does not play and the first criteria for evaluating hands is the number of cards which are playing. The following is the ranking of several example of hands from best to worst:
Ace of spades, 2 of clubs, 3 of hearts, 4 of diamonds: 4 card 4 high best possible Badougi
4 of spades, 6 of hearts, 8 of diamonds, J of clubs: 4 card J high Badougi
Ten of clubs, J of hearts, Q of Diamonds, K of hearts: 4 card worst possible Badougi
Ace of hearts, Ace of diamonds, 4 of clubs, 5 of spades: 3 card hand, 5 high
Ace of clubs, Ace of spades, 4 of spades, 6 of spades: 2 card hand, 4 high
The primary deck of fifty-two playing cards in use today, called Anglo-American playing cards, includes thirteen ranks of each of the four English suits, spades (♠), hearts (♥), diamonds (♦) and clubs (♣), with reversible Rouennais court cards. Each suit includes an ace, depicting a single symbol of its suit; a king, queen, and jack, each depicted with a symbol of its suit; and ranks two through ten, with each card depicting that many symbols (pips) of its suit. Two (sometimes one or four) Jokers, often distinguishable with one being more colorful than the other, are included in commercial decks but many games require one or both to be removed before play. Modern playing cards carry index labels on opposite corners (rarely, all four corners) to facilitate identifying the cards when they overlap.
The fanciful design and manufacturer’s logo commonly displayed on the Ace of Spades began under the reign of James I of England, who passed a law requiring an insignia on that card as proof of payment of a tax on local manufacture of cards. Until August 4, 1960, decks of playing cards printed and sold in the United Kingdom were liable for taxable duty and the Ace of Spades carried an indication of the name of the printer and the fact that taxation had been paid on the cards. The packs were also sealed with a government duty wrapper.
Though specific design elements of the court cards are rarely used in game play, a few are notable. The jack of spades and jack of hearts are drawn in profile, while the rest of the courts are shown in full face (the exception being the King of Diamonds), leading to the former being called the “one-eyed” jacks. When deciding which cards are to be made wild in some games, the phrase, “acey, deucey, one-eyed jack,” is sometimes used, which means that aces, twos, and the one-eyed jacks are all wild. Another such variation, “deuces, aces, one-eyed faces,” is used to indicate aces, twos, the jack of hearts, the jack of spades, and the king of hearts are wild. The king of hearts is shown with a sword behind his head, leading to the nickname “suicide king”. The King of Diamonds is armed with an ax while the other three kings are armed with swords. The king of Diamonds is sometimes referred to as “the man with the ax” because of this. The Ace of Spades, unique in its large, ornate spade, is sometimes said to be the death card, and in some games is used as a trump card. The Queen of Spades appears to hold a scepter and is sometimes known as “the bedpost queen.”
There are theories about who the court cards represent. For example, the Queen of Hearts is believed by some to be a representation of Elizabeth of York – the Queen consort of King Henry VII of England. However the Kings, Queens and Jacks of standard Anglo/American cards do not represent anyone. They stem from designs produced in Rouen before 1516 and by 1540-67 these Rouen designs show well-executed pictures in the court cards with the typical court costumes of the time. In these early cards the Jack of Spades, Jack of Hearts and the King of Diamonds are shown from the rear, with their heads turned back over the shoulder so that they are seen in profile. However the Rouen cards were so badly copied in England that the current designs are gross distortions of the originals.
Other oddities such as the lack of a moustache on the King of Hearts also have little significance. The King Of Hearts did originally have a moustache but it was lost by poor copying of the original design. Similarly the objects carried by the court cards have no significance. They merely differentiate one court card from another and have also become distorted over time.
The most common sizes for playing cards are poker size (2½in × 3½in, approx. 63mm × 88mm) and bridge size (2¼in × 3½in, approx. 56mm × 87mm), the latter being more suitable for games such as bridge in which a large number of cards must be held concealed in a player’s hand. Interestingly, in most casino poker games, the bridge sized card is used. Other sizes are also available, such as a smaller size (usually 1¾in × 2⅝in, approx. 44mm × 66mm) for solitaire and larger ones for card tricks.
Some decks include additional design elements. Casino blackjack decks may include markings intended for a machine to check the ranks of cards, or shifts in rank location to allow a manual check via inlaid mirror. Many casino decks and solitaire decks have four indices instead of the usual two. Many decks have large indices, largely for use in stud poker games, where being able to read cards from a distance is a benefit and hand sizes are small. Some decks use four colors for the suits in order to make it easier to tell them apart: the most common set of colors is black (spades ♠), red (hearts ♥), blue (diamonds ♦) and green (clubs ♣).
When giving the full written name of a specific card, the rank is given first followed by the suit, e.g., “Ace of Spades”. Shorthand notation may list the rank first “A♠” (as is typical when discussing poker) or list the suit first (as is typical in listing several cards in bridge) “♠AKQ”. Tens may be either abbreviated to T or written as 10.
Most fixed limit games are played with a four bet maximum. This means that in a given betting round, there can be no more than three raises, meaning that on the betting round, only four bets of the given limit have been made.
Consider this example in a $20/$40 game, during a $20 round with three players that proceeds as follows:
Player A bets $20.
Player B puts in another bet, raises another $20, making it $40 to play.
Player C puts in a third bet, raising another $20 on that, thus making it $60 to play.
Player A puts in the fourth bet (she is usually said to cap the betting).
Once Player A has made her final bet, Players B and C may only call another three and two bets (respectively); they may not raise again because the betting is capped.
A common exception in this rule practiced in some card rooms is to allow unlimited raising when a pot is played heads up (when only two players remain). Usually, this has occurred because all other players have folded, and only two remain. Many card rooms will permit these two players to re-raise each other until one player is all in.
Some variations do exist for this exception. For example, some card rooms require that the pot became heads up before the third bet has entered the pot on that betting round. It is widely believed that this variation exists to prevent two colluding players from raising a third player out of the pot.
This exception to the four bet maximum has been observed in nearly all card rooms in the USA. It has never been observed in Internet card rooms.
In some card rooms, there is a five bet maximum instead of four.
In poker, a dominating hand is one with an overwhelming statistical advantage over another specific hand. For example, in Seven-card stud, while a Starting hand of K♠ K♥ Q♦ has the lead over A♦ K♦ 10♥, the latter has many outs (ways to improve) to beat the former (catching an ace, the straight, the flush, etc.), making it a roughly even contest. However, the first hand dominates in a contest with a hand like Q♥ Q♠ J♣, because this hand has no ways to improve that the first one doesn’t also have (two pair, trips, straight), and the first hand has some of the second hand’s outs as well (unseen cards include two kings, but only one queen), giving it a significant advantage.
This concept is most important in no limit play, where it is possible to bet all your money early in the hand. One must judge not only whether your opponent’s hand might be better than yours, but whether or not it might dominate yours to such a degree that long-run fluctuations of luck will amplify the consequences of a mistaken play rather than mitigating them.
One of the things that makes no limit Texas hold ‘em strategically rich and interesting is the unusual relationship of advantage and dominance among various Starting hands. For example, the hand A♣ K♦ is a slight favorite over J♠ 10♠; this hand is a slight favorite over 4♠ 4♣; and in a non-transitive relationship, the fours are a small favorite over A♣ K♦. None of these hands dominates any other, but A♣ K♦does domimate A♥ Q♦, 4♠ 4♣is dominated by 7♠ 7♥, and J♠ 10♠ is dominated by Q♣ 10♣.
