Pai Gow
牌九

• Introduction
• The Deal
• Ranking of Pairs
• Strategy
• Sources of Information

Introduction

Pai Gow is a gambling game played with Chinese dominoes. The set consists of all pairs of numbers from 1-1 to 6-6, with the following eleven tiles duplicated: 6-6, 6-5, 6-4, 6-1, 5-5, 5-1, 4-4, 3-3, 3-1, 2-2, 1-1. There are 32 tiles in all. Pai is the Cantonese word for a tile or card and Gow is the number nine.

Each player receives four tiles and forms them into two pairs, as does the banker. If both the player's pairs outrank the banker's pairs the player wins, if neither does the banker wins, and if just one does it is a draw.

Pai Gow should not be confused with Pai Gow Poker, which is a Californian game played with a deck of regular cards, also based on the idea of making two hands and having to win both of them.

The television show, KUNG FU: THE LEGEND CONTINUES, aired an episode entitled "Pai Gow" on 1993 March 1 in which Caine and Peter go undercover to investigate the murders of several participants in a high-stakes Pai Gow game (Written by: John Considine; Directed by: Zale Dalen.Guest Cast: Jennifer Sung: Betsy Soo; Mr. Wu: Fred Lee; Valdosta Sam: Robert Wisden; Mr. Sung: Kam Ray Chan; Quo Chen: Robert Chang; Dirk: Shawn Lawrence). The main character, Caine, had been a Pai Gow dealer at some time in his life and they did some close up shots with fancy shuffling and dealing.

Hardcore players do not even look at their tiles; they lift them up and feel the holes in face of the tiles, reading them like braille.

The description of Pai Gow on this page was compiled by Joe Celko. An earlier version of this text was published at the Game Cabinet.

The Deal

The woodpile is four tiles high and eight tiles long. The first player to recieve a hand is determined by throw three dice. The total of the dice is counted out starting with the bank in a counter clockwise direction.

Each player is dealt a stack of four tiles from the woodpile. The house starts the game as the bank, but then can pass the bank to other players, as in Baccarat. The option to take or refuse the bank moves counter clockwise around the table.

The dealing can be elaborate. These are the possible deals ("Pai Gow cuts") allowed by the Australian Casino commission.

The goal of the game is to divide the four tiles into two pairs or hands. If both your pairs outrank those held by the bank, then you win your bet. If both the bank's pairs outrank yours, then you lost your bet. If one of your pairs outranks those held by the bank and the other does not, then the hand is a draw and you get your money back.

Ranking of Pairs

How do you rank your hand? It is a bit complicated, so let's start with the easy stuff first. There are 992 possible hands per player if you do the math, but because of the duplicate tiles, and the fact that order does not matter, there are actually few possible hands. Numeric order has little to do with the ranking of hands; it is symbolism and not substance. The hands are scored as follows:

1) The highest possible pair is the Gee Joon ("supreme pair"), which is made up of the two tiles:

[4-2] and [2-1]

The [4-2] and [2-1] are the two "wild cards" in the woodpile, and can be used as either a 3 or a 6 when making pairs (i.e. they substitute for each other). This is not the same rule that Western card games use, where a wild card substitutes for any card.

2) Under the Gee Joon are the pairs (Bo), which can be made up of matched or unmatched tiles that have the same totals. In order of rank from high to low, they are:

Pair	Pair name
[6-6] and [6-6]	Heaven
[1-1] and [1-1]	Earth
[4-4] and [4-4]	Man
[3-1] and [3-1]	Goose
[5-5] and [5-5]	Plum Flower
[3-3] and [3-3]	Double Three
[2-2] and [2-2]	Board
[6-5] and [6-5]	Hatchet
[6-4] and [6-4]	Red Ten
[6-1] and [6-1]	Long Leg Seven
[5-1] and [5-1]	Big Head Six
[6-3] and [5-4]	Jaap Gow - mixed nine
[6-2] and [5-3]	Jaap Bart - mixed eight
[5-2] and [4-3]	Jaap Chut - mixed seven
[4-1] and [3-2]	Jaap Ng - mixed five

There is no numeric order to this ranking, so you just have to learn them.

3) The next level of hands beneath the Bo are called Wongs. They are a nine paired with a double six or double one. The double six combinations outrank the double one combinations.

[6-6] and [6-3]
[6-6] and [5-4]
[1-1] and [6-3]
[1-1] and [5-4]

4) The third level of hands are called Gongs. They are a eight paired with a double six or double one. The double six combinations outrank the double one combinations.

[6-6] and [6-2]
[6-6] and [5-3]
[6-6] and [4-4]
[1-1] and [6-2]
[1-1] and [5-3]
[1-1] and [4-4]

5) If you do not have any of these hands, then add up all the pips on the two tiles and take the total, modulus ten -- i.e. keep the last digit of the total as your score. This is the part that is like Baccarat.

6) After all of this, in the event of a tie, the ranking is settled based on individual tile values. From high to low the tiles are ranked and named:

Tile	Tile name
[6-6]	Teen
[1-1]	Day
[4-4]	Yun
[3-1]	Gor
[5-5]	Mooy
[3-3]	Chong
[2-2]	Bon
[6-5]	Foo
[6-4]	Ping
[6-1]	Tit
[5-1]	Look
[6-3] and [5-4]	Gow
[6-2] and [5-3]	Bot
[6-1] and [5-2]	Chut
[4-2]	Luk (part of Gee Joon)
[4-1]	Ng
[3-2]	Ng
[2-1]	Saam (part of Gee Joon)

The [4-2] and [2-1] tiles are scored by how they are played, but they are the lowest ranking single tiles.

Whoever has the bank keeps a marker called a "Chung" in front of his place on the table. The bets are settled against the banker one player at a time, with the money being racked into the center of the table. In the casino game, the house provides a dealer and the bank calls out which cut he wishes to use.

Strategy

About 80% of the time, you should play your hand by using the following strategy:

1. Look for pairs and look for unmatched pairs (i.e. same totals, but different arrangement of pips) which are harder to see.
2. Play the [6-6] or [1-1] with any tile totaling 7, 8 or 9.
3. Play the two smallest tiles that total to 7, 8 or 9.
4. Every hand can be played three different ways, so be careful. Getting a very good high hand can lead to a very weak low hand and result in a tie. However, a more balanced high and low hand can result in a win.

For example, assume are dealt [5-6], [3-2], [6-4], and [4-3]. This can be played as:

1. [5-6] and [6-4] = one
   [4-3] and [3-2] = two
2. [5-6] and [3-2] = six
   [6-4] and [4-3] = seven
3. [5-6] and [4-3] = eight
   [6-4] and [3-2] = five

Clearly, option (A) is the worst hand. But (B) is better balanced that (C) even though it has a weaker low hand.

An Optimal Strategy for Pai Gow was posted by Bernard James Luger III (email: bjliii@leland.Stanford.edu) on 1995 June 15, using the table below. The Pair column is the pair you hold in your hand. The Banker and Player columns tell you when to split that pair, using the other tiles in your hand as a guide. This table is exact for the no commission game, and is almost perfect for the commission game.

Casinos require there dealers to play their hands according to certain rules ("House way"), just as Black Jack or 21 dealers in Western casino games. Harrah's in Las Vegas uses the optimal strategy as given above, except:

1. They split Heaven or Earth to make 6-8 or better;
2. They split Sevens as (2, 12) w/ 2, 10, 11, 12;
3. They never split Long, Big Head Six, or the Mixed Five.

How much is Harrah's giving up? Not much; their 5% commission overwhelms the small differences caused by splitting incorrectly. But, as a player or banker, these rules will save you about 0.1% over the Harrah's strategy. Not much, but hey, it's money!

This is the "house way" as given by the Australian Casino

1. When you have two ranking pairs, play the two pairs as two hands.
2. Never split the following pairs:
   Ngor (High Four)
   Foo Tau (Eleven)
   Mooy (High Ten)
   Hoong Tau Sap (Low Ten)
   Cheong Sum (High Six)
   Lim Lum Lok (Low Six)
   Ban Tang (Low Four)
   Chap Ng (Mixed Fives)
3. Split:

   Gee Joon (Supreme)	with	High 6 and 6, 5, 4 9 and 8, 7, 6, 5, 4
   Teen (Twelve) or Day (Two)	with	8 and 8, 7, 6, 5, 4 7 and 7, 6, 5, 4 Teen and Day
   Chap Gow (Nines)	with	Teen/Day and 10 10 and 10 Teen and Day Teen/Day and 11, 10
   Yun and Chap Paat (Eights)	with	10 and 11, 10 10 and 10 11 and 9
   Ko Kiok Chaat and Chap Teen   and Day Chaat (Sevens)	with	Teen/Day and 11, 10

4. Wongs Gongs and High Nines
   • If no higher play is possible, always play Wong, Gong or High Nine. Even at the expense of the low hand.
   • Play High Nine instead of Gong or Wong and Gong instead of Wong when given a choice.
   • When given a choice of playing a Wong, Gong or High Nine with a Teen and Day, play the Teen on the high hand.
5. Exceptions to Wongs, Gongs and High Nines
   • Play Gong over High Nine when the fourth tile is four.
   • Play Wong over Gong or High Nine when the fourth tile is eleven.
6. General Play
   • Bring the low hand and the high hand as close together as possible unless they can be set to a higher value.
   • If the high hand is seven or less play the high tile on the low hand when given a choice.
   • If the high hand is eight or better play the high tile on the high hand when given a choice.
   • Where possible do not play the two highest tiles on the same hand.
7. Exceptions to General Play
   • High 10. Low 10, any 6 with 2 or 12. Play 0 and 8
   • High 10, Low 10, 11 any 7 or 8. Play 0 and 8 or 0 and 9
   • High 8, High 10, 11 any 7. Play 7 and 9
   • High 6, 5, Gee Joon any 2 or 12. Play 7 and 9
   • High 6, 5, Gee Joon any 7. Play 2 and 9
   • High 6, 5, Gee Joon any 8. Play 3 and 9
   • High 6, 5, Gee Joon any 10. Play 5 and 9
   • High 6, 5, Gee Joon and 11. Play 6 and 9
   • High 6, Low 6, 5 and Gee Joon. Play 1 and 9
   • High 6, 5, Gee Joon and nine. Play 4 and 9
   • High 4, Low 4, 5 any 6. Play 0 and 9
   • High 6, Low 6, 2 or 12 with any 4 or 5. Play 0 and 8 or 1 and 8
   • High 4, Low 4, 5, Gee Joon. Play 7 and 9 with the high 4 on the high hand
   • High 8, Low 8, High 6 with any 7. Play 4 and 5 with the high 8 on the high hand
   • High 8, Low 8, High 4 with any 7. Play 2 and 5 with the high 8 on the high hand
   • High 8, Low 8, High 4 with any 6. Play 2 and 4 with the High 8 on the high hand
   • High 10, Low 10, High 6 with any 7. Play 6 and 7 with the high 10 on the high hand
   • High 4, High 10, Low 4, Eleven. Play 4 and 5 with High 4 on the high hand
   • High 10, High 8, Low 8 and 9. Play 7 and 8 with the High 8 on the low hand.

   The exceptions listed above may also be known as using the format outlined below.

   • If after bringing both hands closer together you have 1 on the low hand and it is possible to make 8 or 9 on the high hand play the eight or nine.
   • If after bringing both hands closer together you have 2 on the low hand and it is possible to make 8 using a Teen or Day. Play the 8.
   • If after bringing both hands closer together you have two tiles in the first six rankings on the same hand and its possible to separate them without altering the point totals on the hands do so.
   • If after bringing both hands closer together you have an 8 with 5, Gee Joon on either hand and its possible to make a high 6 ranked nine or better do so.
   • High 8, High 10, 11 any 7, Play 7 and 9.

Sources of Information

From amazon.com you can obtain Pai Gow Tiles by Michael J. Musante, the classic book on Pai Gow rules and strategy.

Here are two sets of rules of Pai Gow:

• The rules of Pai Gow as approved by the NSW Government (archive copy) mention in point 8.2 a modifier between +4 and -4 that can be applied to dice roles.
• The rules from Marina Bay Sands in Singapore describe the 20 traditional cuts mentioned in the Deal section above complete with diagrams and variations. It seems that casinos change the names of some of the cuts to give them a local flavour. The document also describes the three types of 'laja' which can be used to further mix up the tiles prior to dealing.

There are some other reference books in English on the game, but they are difficult to find since they were usually small print runs.

Allen, George; HOW TO PLAY PAI GOW; 19??; ISBN ?

Gwynn, Jr., John M.; AN OPTIMAL STRATEGY FOR THE GAME OF PAI GOW; 1981; ISBN ?

Gwynn, Jr., John M.; PAI GOW REVISITED -- A SIGNIFICANT POSITIVE EXPECTATION; 1984; ISBN ?

Zender, Bill; PAI GOW WITHOUT TEARS; 19??; ISBN ?