How To Play Pai Gow Dominoes
- House Way Strategies
- Player Strategies
- Miscellaneous
On This Page
Introduction
All dominoes are shuffled and each player takes 4 tiles. Player must make 2 hands of 2 tiles each. The hand with lower value is called 'front hand' and hand with higher value is called 'rear hand'. Front hand can only be compared with front hand and rear hand with rear hand for comparison of two players.
- Pai gow poker (also called double-hand poker) is a version of pai gow that is played with playing cards, instead of traditional pai gow's Chinese dominoes.The game of pai gow poker was created in 1985 in the United States by Sam Torosian, owner of the Bell Card Club. 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.
- A game of Pai Gow begins with 32 wooden tiles randomly stacked into eight stacks of four tiles each. This is known as the woodpile, and to further achieve true randomization, a series of ritual shuffles are performed to rearrange the woodpile.
- Dominoes are stacked facedown in 2 piles, each pile containing 4 rows of 4 dominoes. Each player takes a turn throwing 3 dice, going counterclockwise around the table and ending with the player who becomes the first banker, to determine where the deal begins.
- Similar to other casino games, the players in Pai Gow Poker play against the house, not against each other. This game came to be when a Chinese game called Pai Gow in which dominoes were used, was mixed with poker cards. What came out as a result was a gambling game with a very reasonably low risk compared to other games.
Pai gow is the oldest of the casino games. It easily pre-dates roulette and baccarat. How such a complicated game ever got started, I have always wondered. Indeed, pai gow is a difficult game to learn. The concept is the same as pai gow poker, where both player and banker make high and low hands, and then compare against each other. What makes pai gow difficult is there is order of hands and tiles seems largely random, and is difficult to memorize.
What I love about pai gow is that for bankroll preservation, there is nothing that beats it. The pace is slow at about 30 hands per hour, and 41% of hands result in a push. If you are a pale-face, like me, you'll impress the dealer and some other players that you even understand it. However, some Asians immediately leave the table when I sit down, as if I'm unlucky. Don't be scared to try the game, even if you know nothing about the rules. You can always ask the dealer to set your hands according to the 'house way.' Better yet, keep reading to learn more about the game.
Rules
Following are the primary rules when it comes to pai gow. Each casino may have some its own fine points when it comes to player banking and prepaying the 5% commission.
- Pai gow is played with a set of 32 dominoes displayed below.
- Each player and dealer will be given four tiles.
- The player will separate his tiles into low and high hands. The player does not need to specify which is higher, as this will be obvious.
- Each pair of tiles will have a ranking order as follows:
- Pair: There are 16 pairs, as shown in the image above. The tiles are pictures in rank order, starting at the upper left, and reading like a page to the bottom right.
- Wong: This is a 2 or 12 tile with any 9 tile.
- Gong: This is a 2 or 12 tile with any 8 tile.
- 9 to 0 points (the more the better): For all other 2-tile hands, the total number of dots will be taken, and the terminal digit is used to determine the number of points (as in baccarat). For example, a 10 and 9 tile is worth 9 points; a 4 and 7 tile is worth 1 point.
- An exception to the above rule is that the two tiles in the highest ranking 'Gee Joon' pair are semi-wild and are worth either 3 or 6 points, whichever results in a higher total. For example, when combined with a 4-point tile, a Gee Joon tile counts as 3 points to make a 7-point hand, instead of counting as 6 points to make a 0-point hand.
- The player's high hand will be compared to the dealer's high hand, and the player's low hand compared to the dealer's low hand (as in pai gow poker).
- If both player and dealer have a Wong, Gong, or 1 to 9 points, the tie will be broken according to which hand has the higher-ranked high tile.
- If the high tile does not break the tie then the win will go to the banker.
- A 0-0 tie always goes to the banker.
- When using high tiles to break a tie, the rank order is the same as the pair order (see picture above), except the two tiles in the highest 'gee joon' pair are ranked lowest individually and will therefore never be a hand's high tile.
- If the player wins both hands he will win even money, less a 5% commission. If the player wins one and loses one then his wager will push. If the dealer wins both then the player will lose his wager.
- At most casinos, the turn to be banker rotates around the table. At some casinos, such as Foxwoods, the turn to be banker zig-zags between the player(s) and dealer, meaning that the dealer must bank at least every other hand.
- The player may invoke his turn to bank whenever it is his turn, although most players decline.
- The banker plays against every other player at the table and the dealer. The dealer will wager the same amount the player wagered the last time the dealer was the banker. More often than not, other players will sit out the hand when another player is banking, letting him or her take on the dealer alone.
Strategy
My assistant and I have spent lots of time studying and developing pai gow strategy. Here are the strategies we have come up with so far:- Wizard Basic Strategy (added Oct. 25, 2017)
A reader known as Charlie combined various parts of these strategies to create a nearly optimal strategy he could fit on a sheet of paper. He was nice enough to share it with us.
For a graphic version, click the image above for a larger version. I also have a PDF version (149K).
We also have the following strategy charts showing the correct play for every possible combination under three banking scenarios:
The next table shows the possible outcomes and house edge under various strategies, banking or not banking, and whether prepaying the commission. The table assumes the player is playing against the Foxwoods house way and a 5% commission. If the player prepays the commission, which is sometimes allowed, the house edge is reduced by 0.07%.
Pai Gow House Edge
Your Strategy | Banking? | Prob. Win | Prob. Loss | Prob. Push | House Edge |
---|---|---|---|---|---|
House Way | No | 29.21% | 30.18% | 40.61% | 2.44% |
House Way | Yes | 30.18% | 29.21% | 40.61% | 0.53% |
Wizard Basic Strategy | No | ? | ? | ? | 1.98% |
Wizard Basic Strategy | Yes | ? | ? | ? | 0.08% |
Wizard Way | No | 29.07% | 29.5% | 41.43% | 1.88% |
Wizard Way | Yes | 30.03% | 28.55% | 41.42% | 0.02% |
J.B. Simple | No | 29.29% | 29.72% | 41.00% | 1.90% |
J.B. Simple | Yes | 30.18% | 28.76% | 41.06% | 0.10% |
J.B. Advanced Strategy without exceptions | No | 29.37% | 29.74% | 40.89% | 1.84% |
J.B. Advanced Strategy without exceptions | Yes | 30.26% | 28.77% | 40.97% | 0.03% |
Optimal | No | 29.42% | 29.60% | 40.98% | 1.66% |
Optimal | Yes | 30.21% | 28.52% | 41.27% | -0.20% |
Inefficiencies in the standard casino house way cost the casino about 0.75% compared to optimal house strategy. If both player and dealer played optimal strategy, the house edge to the player when banking would be 0.54%, and when not banking 2.38%. For more on this topic see JB's optimal house strategy comparison table (24K). To see an enormous document on the actual optimal house strategies see JB's optimal house strategy charts (735K). I'm quite sure this is the first time it has ever been put in writing.
The perfect hand, seen at the Peppermill
in Reno. The odds are 1 in 35,960.
Prepaying the Commission
How To Play Pai Gow Dominoes
Some casinos let the player prepay the 5% commission. For example, betting $105 to win $100. This lowers the overall commission to 1/21, or 4.76%. The effect on the house edge is a reduction of 0.07%. This is an option the player should always invoke when available, yet many don't.
Betting 10% Extra as Banker
Some casinos let the player bet up to 10% more than he wagered against the dealer the last time the dealer was the banker. Assuming the player is banking every other hand, this lowers the combined house edge between banking and not banking by 0.07%.
Co-Banking
The player may make a back wager on the player acting as banker up to the amount he bet against the dealer the last time the dealer was banking. However, the player will forfeit his own turn to bank if he invokes this option. This rule will not have an effect on the overall house edge if the player is trying to maximize his action as banker (which he should), but can make the game more enjoyable if playing with friends. Rather than sitting out a hand where your friend is banking you can co-bank with him, so you're always in the game.
Calculator
My pai gow calculator will tell you the expected value and/or strategy for any hand, with lots of other features including the effect of tiles known to be held by other players or your opponent.
Power Ratings
The following table shows the power ratings for each hand. There are four columns of power ratings, according to whether the hand is high or low, and whether the player is acting as banker or not. The power ratings are on a 0 to 100 scale, which represents the probability an opponent playing the Foxwoods house way will beat that hand.
A practical application of this table is to add the two power ratings for the three ways to set a hand, and set it the way with the highest power rating sum.
Power Ratings in Pai Gow
Hand | Low Hand Not Banking | High Hand Not Banking | Low Hand Banking | High Hand Banking |
---|---|---|---|---|
Gee joon | 100 | 99 | 100 | 100 |
6/6 pair | 100 | 98 | 100 | 99 |
1/1 pair | 100 | 97 | 100 | 98 |
4/4 pair | 100 | 96 | 100 | 97 |
1/3 pair | 100 | 95 | 100 | 96 |
5/5 pair | 100 | 94 | 100 | 95 |
3/3 pair | 100 | 93 | 100 | 94 |
2/2 pair | 100 | 92 | 100 | 93 |
5/6 pair | 100 | 90 | 100 | 92 |
4/6 pair | 100 | 89 | 100 | 90 |
1/6 pair | 100 | 88 | 100 | 89 |
1/5 pair | 100 | 87 | 100 | 88 |
Mixed 9 pair | 100 | 86 | 100 | 87 |
Mixed 8 pair | 100 | 85 | 100 | 86 |
Mixed 7 pair | 100 | 84 | 100 | 85 |
Mixed 5 pair | 100 | 83 | 100 | 84 |
Wong with 6/6 | 100 | 80 | 100 | 83 |
Wong with 1/1 | 99 | 78 | 100 | 80 |
Gong with 6/6 | 99 | 73 | 99 | 78 |
Gong with 1/1 | 99 | 67 | 99 | 73 |
9 with 6/6 | 98 | 61 | 99 | 67 |
9 with 1/1 | 97 | 54 | 98 | 61 |
9 with 4/4 | 97 | 53 | 97 | 54 |
9 with 1/3 | 96 | 50 | 97 | 53 |
9 with 5/5 | 96 | 49 | 96 | 50 |
9 with 3/3 | 95 | 47 | 96 | 49 |
9 with 2/2 | 94 | 45 | 95 | 47 |
9 with 5/6 | 94 | 44 | 94 | 45 |
9 with 4/6 | 93 | 43 | 94 | 44 |
9 with 1/5 | 92 | 42 | 93 | 43 |
8 with 6/6 | 90 | 40 | 92 | 42 |
8 with 1/1 | 89 | 39 | 90 | 40 |
8 with 4/4 | 88 | 38 | 89 | 39 |
8 with 1/3 | 87 | 35 | 88 | 38 |
8 with 5/5 | 86 | 35 | 87 | 35 |
8 with 5/6 | 84 | 33 | 86 | 35 |
8 with 4/6 | 84 | 32 | 84 | 33 |
8 with 2/3 | 82 | 31 | 84 | 32 |
7 with 6/6 | 82 | 31 | 82 | 31 |
7 with 1/1 | 81 | 30 | 82 | 31 |
7 with 4/4 | 81 | 29 | 81 | 30 |
7 with 1/2 | 79 | 28 | 81 | 29 |
7 with 5/5 | 78 | 26 | 79 | 28 |
7 with 3/3 | 76 | 25 | 78 | 26 |
7 with 2/2 | 75 | 24 | 76 | 25 |
7 with 5/6 | 72 | 22 | 75 | 24 |
7 with 4/6 | 71 | 21 | 72 | 22 |
7 with 3/6 | 69 | 20 | 71 | 21 |
6 with 6/6 | 68 | 19 | 69 | 20 |
6 with 1/1 | 67 | 18 | 68 | 19 |
6 with 4/4 | 66 | 17 | 67 | 18 |
6 with 5/5 | 61 | 15 | 66 | 17 |
6 with 3/3 | 60 | 15 | 61 | 15 |
6 with 5/6 | 59 | 14 | 60 | 15 |
6 with 4/6 | 56 | 13 | 59 | 14 |
6 with 1/6 | 55 | 12 | 56 | 13 |
6 with 3/6 | 54 | 12 | 55 | 12 |
5 with 4/4 | 52 | 11 | 54 | 12 |
5 with 1/3 | 51 | 10 | 52 | 11 |
5 with 5/5 | 49 | 10 | 51 | 10 |
5 with 3/3 | 48 | 9 | 49 | 10 |
5 with 2/2 | 47 | 8 | 48 | 9 |
5 with 4/6 | 45 | 8 | 47 | 8 |
5 with 1/6 | 44 | 7 | 45 | 8 |
5 with 1/5 | 43 | 7 | 44 | 7 |
5 with 3/6 | 42 | 7 | 43 | 7 |
5 with 2/6 | 40 | 6 | 42 | 7 |
4 with 6/6 | 40 | 6 | 40 | 6 |
4 with 4/4 | 37 | 5 | 40 | 6 |
4 with 1/3 | 33 | 5 | 37 | 5 |
4 with 5/5 | 31 | 4 | 33 | 5 |
4 with 3/3 | 30 | 4 | 31 | 4 |
4 with 2/2 | 29 | 4 | 30 | 4 |
4 with 1/6 | 27 | 3 | 29 | 4 |
4 with 1/5 | 26 | 3 | 27 | 3 |
4 with 3/6 | 25 | 3 | 26 | 3 |
4 with 2/6 | 24 | 3 | 25 | 3 |
3 with 6/6 | 24 | 3 | 24 | 3 |
3 with 1/1 | 23 | 2 | 24 | 3 |
3 with 4/4 | 22 | 2 | 23 | 2 |
3 with 1/3 | 21 | 2 | 22 | 2 |
3 with 3/3 | 20 | 1 | 21 | 2 |
3 with 2/2 | 19 | 1 | 20 | 1 |
3 with 1/6 | 18 | 1 | 19 | 1 |
3 with 1/5 | 18 | 1 | 18 | 1 |
3 with 2/6 | 17 | 1 | 18 | 1 |
3 with 3/4 | 17 | 1 | 17 | 1 |
2 with 6/6 | 16 | 0 | 17 | 1 |
2 with 1/1 | 16 | 0 | 16 | 0 |
2 with 4/4 | 14 | 0 | 16 | 0 |
2 with 1/3 | 14 | 0 | 14 | 0 |
2 with 3/3 | 12 | 0 | 14 | 0 |
2 with 2/2 | 12 | 0 | 12 | 0 |
2 with 1/6 | 11 | 0 | 12 | 0 |
2 with 3/4 | 11 | 0 | 11 | 0 |
1 with 1/3 | 10 | 0 | 11 | 0 |
1 with 5/5 | 9 | 0 | 10 | 0 |
1 with 3/3 | 8 | 0 | 9 | 0 |
1 with 2/2 | 7 | 0 | 8 | 0 |
1 with 5/6 | 6 | 0 | 7 | 0 |
1 with 1/5 | 5 | 0 | 6 | 0 |
Zero | 0 | 0 | 5 | 0 |
The following graph shows how often the House Way will make each type of hand out of all 35960 combinations.
Suzie with a rare two pair.
The House Way
I'm proud to provide the following pai gow house ways. Most of them were rewritten into my own words. The one from the MGM is taken directly from their own rules and procedures on the game:
- MGM Grand (PDF -- 1,180 K)
- Marina Bay Sands (Singapore) (PDF -- 483K)
Where to Play
The following is a list of games I am aware of in the U.S.. I'm sure there are some I don't know about. Feel free to tell me if you are aware of others.
- Las Vegas: Aria, Bellagio, Caesars Palace, Encore, Harrah's, Lucky Dragon, MGM Grand, Mirage, Palace Station, Palazzo, Paris, Rio, Venetian, and Wynn. The Treasure Island and Mandalay Bay don't staff a table on a regular basis any longer, but may open one if a whale requests it.
- Atlantic City: Most, if not all, casinos.
- Connecticut: Mohegan Sun, Foxwoods.
- Indiana: Hammond Horseshoe, Southern Indiana Horseshoe.
- Lake Tahoe: Harrah's.
- Maryland: Horseshoe Baltimore. (unconfirmed)
- Pennsylvania: Sands Bethlehem, Mount Airy Casino in Mt Pocono (unconfirmed), Mohegan Sun at Pocono Downs near Scranton (unconfirmed), Sugar House Casino in Philadelphia (unconfirmed), Valley Forge Casino near King of Prussia, and Parx Casino near Bensalem (unconfirmed).
- Reno: Peppermill, Silver Legacy.
Play for Fun
Pai gow is a game that cries out for a way to practice before making a fool of yourself and blowing your money in a casino. For this reason please try my pai gow game.
Internal Links
- The Legend Behind Pai Gow — The story behind the game.
- Bonaza Pai Gow — Side bet seen at the Crown Casino in Melbourne.
- Pair Fortunes — Side bet seen at the Palace Station in Las Vegas.
- Pai Gow Game.
- Pai Gow Calculator.
External Links
- Pai Gow rules in Macau at WizardOfMacau.com.
- Where to play Pai Gow at Harrah's properties.
Acknowledgements
- Pai Gow Without Tears by Bill Zender. The author kindly gave me a copy of his booklet to help with my research on pai gow. If you are interested in the book it may be purchased from the Gambler's Book Club for $20.00.
- A Detailed Study of Pai Gow by Dr. John M.Gwynn, Jr. This study appears in the book Finding the Edge (Edited by Olaf Vancura, Judy A.Collins, and William R. Eadington).
- The many people who supplied me with house ways, which are not easy to get.
Written by:Michael Shackleford
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.
PAI GOW CUTS | ||
---|---|---|
TRADITIONAL NAME | OPTIONS | ENGLISH NAME |
Yat Dong Dong | (Right or Left) | One Stack |
Cup Say | (Right or Left, Top or Bottom) | Tiger |
Chee Yee | (Top or Bottom) | Chop the Ears |
Dai Pin | (Right or Left) | Big Slice |
Jung Quat | (Top or Bottom) | From the Heart |
Long Tau/Fong May | (Right or Left) | Dragon Head/Phoenix Tail |
Wui Fung Bank | Hong Kong Bank | |
Foot Say | Four Across | |
Sydney Harbour Bridge | Sydney Harbour Bridge | |
Ghan Dong Ping Say | (Right or Left) | Kangaroo Jump |
Pong Yun | (Right or Left) | Buddhas Signal |
Bo Bo Go Sing | (Right or Left) | Boy Walks Up Stairs |
Ghan Dong Cup Say | (Right or Left) | Striped Tiger |
Yat Kai Sum May | Chicken Three Ways | |
Arn Lok Peng Sar | (Right or Left) | Flying Dragon |
Sydney Tower | Sydney Tower | |
China Bank | China Bank | |
Chong Wan Sup Lok | Sixteen Across | |
Seung Gwai Pak Moon | Ghost Closing the Door | |
Gum Un Que | (Right or Left, Front to Back) | Double Bridge |
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:
- Look for pairs and look for unmatched pairs (i.e. same totals, but different arrangement of pips) which are harder to see.
- Play the [6-6] or [1-1] with any tile totaling 7, 8 or 9.
- Play the two smallest tiles that total to 7, 8 or 9.
- 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:
- [5-6] and [6-4] = one
[4-3] and [3-2] = two - [5-6] and [3-2] = six
[6-4] and [4-3] = seven - [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.
Pair | When to Split | |
---|---|---|
Banker | Player | |
Gee Joon (3/6) | Any 6 w/ 4, 5, 6 i.e., make a 9-7 or better | SAME |
Hev. and Earth (2 or 12) | God w/ 7, 8, 9 4 w/ 6, 7, 8, 9 (6 or 7) w/ 5, 6, 7, 8, 9 8 w/ 5, 8 MIXED 8 w/ 9 9 w/ 5, 11 | SAME |
This is almost splitting to make a 6-8 or better, but that's not quite perfect | ||
Man (8) | (2, 10, 12) w/ 10 or 11 2 w/ 12 9 w/ 11 | SAME |
Goose (4) | NEVER | NEVER |
Flower (10) | NEVER | NEVER |
Long (6) | (2, 12) w/ (2, 11, 12) | NEVER |
Board (4) | NEVER | NEVER |
Hatchet (11) | NEVER | NEVER |
P'ttn (10) | NEVER | NEVER |
Long Leg Seven | 2 and 12 (2, 12) w/ (10, 11) 10 and 11 | 2 and 12 (2, 12) w/ (10, 11) FLOWER 10 and 11 |
Big Head Six | 2 and 12 (2, 12) w/ (FLOWER 10, 11) | 2 and 12 |
Mixed Nine | 2 and 12 10 w/ 2, 12 Unpaired 10's | SAME |
Mixed Eight | 2 and 12 (2, 10, 12) w/ 10, 11 9 and 11 | SAME |
Mixed Seven | 2 and 12 (2, 10, 12) w/ 10, 11 | SAME |
Mixed Five | 2 and 12 | NEVER |
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:
- They split Heaven or Earth to make 6-8 or better;
- They split Sevens as (2, 12) w/ 2, 10, 11, 12;
- 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
- When you have two ranking pairs, play the two pairs as two hands.
- 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) - Split:
Gee Joon (Supreme) with High 6 and 6, 5, 4
9 and 8, 7, 6, 5, 4Teen (Twelve) or Day (Two) with 8 and 8, 7, 6, 5, 4
7 and 7, 6, 5, 4
Teen and DayChap Gow (Nines) with Teen/Day and 10
10 and 10
Teen and Day
Teen/Day and 11, 10Yun and Chap Paat (Eights) with 10 and 11, 10
10 and 10
11 and 9Ko Kiok Chaat and Chap Teen
and Day Chaat (Sevens)with Teen/Day and 11, 10 - 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.
- 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.
- 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.
- 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.
You can find other web sites with information on the game, set up by casinos or gambling equipment companies in Las Vegas. You can download a video game version of Pai Gow from ICA Inc. (Box #585; Franktown, CO 80116) from their web site. It will cost you about $10 to upgrade the shareware version to a full working copy or you can order it on a diskette for $14.99 plus $3.50 postage and handling.
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 ?
How To Play Pai Gow Dominoes Free
Zender, Bill; PAI GOW WITHOUT TEARS; 19??; ISBN ?