Pai Gow Tiles

Last update: July 6, 2010

Introduction

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

Pai gow is played with a set of 32 dominos displayed below.

The object of the game is the same as in pai gow poker, to beat the banker. Unlike most casino games, in pai gow the player can have a turn to be the banker in which case the goal is to beat everybody else. The dealer also acts as a player in pai gow, acting as banker in turn. When the dealer is not banking he will bet an amount equal to the bet the banker made the last time he played against the house bank. The dealer always plays his hand according to predetermined rules, known as the house way. If a player wishes to bank, but is uncomfortable with the financial risk of covering all other bets on the table, then he may request to co-bank with the house. If this option is selected his hand must be set according to the house way. The opportunity to bank is usually offered in turn to each player and dealer in a counter-clockwise direction. At some casinos, such as at Foxwoods, the turn to bank zig-zags beteen the dealer and players, with the dealer banking every other hand.

The game is played with a set of 32 dominos, three dice, and a dice shaker. Play begins with all players making a wager. As the players decide how much to bet, the dealer mixes up the dominos and puts them in 8 neat stacks of 4. Then the dice are rolled to determine who gets the first stack, and then proceeds counter-clockwise. After the dice are exposed, the player may not change his bet. Each player is given one stack of 4 dominos, which they are to arrange into two groups of two.

Each pair of dominos has a ranking. The player must decide how to arrange his dominos into the strongest possible pairs. Sometimes the choice is obvious but often a decision must be made whether to have a strong hand and a weak hand or two more balanced hands. At most there will be three possible and viable ways to play the hand. After a decision is reached the player should lay the dominos face down with the higher pair laying horizontally and the lower pair vertically. Only after all players have set their hands can the banker examine and set his dominos.

After all dominos have been arranged the banker and player will turn over their hands. Each player will in turn compare his hands to those of the banker. If the player wins both hands his bet pays even money less a 5% commission. If the player loses both he loses his entire wager. If the hands split, one win and one loss, then the bet is a push. After all bets have been settled the banker pays a 5% commission on the net win, if there was one.

Usually the dealer will let the player prepay the 5% commission. For example if you bet $100 you may put out an additional $5 as the commission, should you lose. Mathematically speaking, this is equivalent to paying a commission of 1/21 of your total bet, rather than 1/20. This lowers the house edge by about 0.07%, and is definitely advised.

Ranking

How the hands are ranked is complicated and there is no easy way to memorize the order. The image above shows the tiles in rank order. The highest pair in the upper right is known has "gee joon." Note that one tile has 3 dots, and the other has 6. Individually these two tiles are semi-wild, and both may count as 3 or 6. The next highest pair is the 12 or "heaven" pair. Then keep going like you are reading a book, with the lowest "mixed 5" pair the bottom right.

After the pairs, next in rank are special combinations known as Wongs. These combinations inlude either the 2 or 12 point domino and any 9 point domino.

Following the Wongs are other special combinations known as Gongs. These combinations inlude either the 2 or 12 point domino and any 8 point domino.

Finally, if a pair, Wong, or Gong can not be formed then the hand is ranked according to the terminal digit of the total pip value of dots on the dominos. For example a hand consisting of a 12 and 7 dominos would have a total of 19 spots for the highest possible value of 9.

In the event the player and banker have the same point total, or there is a wong/wong or gong/gong tie, then the highest ranking domino in each will will be used to break the tie, the high domino wins. The order of the tiles is the same as the order of the pairs, with the exception that the "gee joon" tiles are not highest, but lowest. There is another exception that a 0-0 tie always goes to the banker.

In the event that the high dominos are equal then the tie shall go to the banker. Note that the second highest dominos are not used to break the tie.

Calculator

My pai gow calculator will tell you the expected value for all three ways to play any hand. Click on the image below.

Strategy

My assistant and I have spent lots of time developing pai gow strategy. Here are the strategies we have come up with so far:

Wizard Way
J.B. Easy Strategy
J.B. Intermediate Strategy
J.B. Advanced Strategy

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 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%	1.90%
J.B. Simple	Yes	30.18%	28.76%	41.06%	0.10%
J.B. Intermediate Strategy	No	29.38%	29.72%	40.89%	1.81%
J.B. Intermediate Strategy	Yes	30.26%	28.73%	41.01%	-0.02%
J.B. Advanced Strategy without exceptions	No	29.20%	29.68%	41.12%	1.93%
J.B. Advanced Strategy without exceptions	Yes	30.12%	28.66%	41.22%	0.04%
J.B. Advanced Strategy with exceptions	No	29.33%	29.64%	41.03%	1.78%
J.B. Advanced Strategy with exceptions	Yes	30.24%	28.65%	41.11%	-0.08%
Optimal	No	29.27%	29.48%	41.26%	1.67%
Optimal	Yes	30.17%	28.46%	41.37%	-0.2%

Inefficiencies in the standard casino house way cost the casino about 0.75%, compared to optimal 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 J.B.’s optimal strategy table (24K). To see an enormous document on the actual optimal strategy, I’m quite the first time it has ever been put in writing, see J.B.’s optimal strategy (735K).

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

I also offer the unrounded power ratings, on a 0 to 35960 scale.

The following graph shows how often the House Way will make each type of hand out of all 35960 combinations.

The House Way

I'm proud to have written up two house ways. It is not easy getting house way rules, and putting the into HTML is tedious and time consuming. The house ways I have are for Foxwoods and the Taj Majal.

Where to Play

In Las Vegas pai gow tiles can be played at Bellagio, Caesars Palace, Encore, Harrah's, Mandalay Bay, MGM Grand, Mirage, Palace Station, Palazzo, Paris, Rio, Treasure Island, Venetian, and Wynn. It can be found at most casinos in Atlantic City and there are lots of tables at Foxwoods. When last I checked, in Lake Tahoe, Harrah's had a table.

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 Java game.

My other Pai Gow info

Pai gow main page
Pai gow game
J.B. level 1 strategy
J.B. beginner strategy
J.B. Intermediate Strategy
J.B. advanced strategy
Wizard Way strategy
Pai gow calculator
Foxwoods house way
Taj Majal house way
Casino Canberra house way
Hammond IN Horseshoe house way (PDF 6K)
Generic house way (PDF 82K), by William E. Brennan

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.

The Wizard's other sites: Wizard of Vegas, Wizard of Macau, Math Problems The Wizard recommends: The Bear Growls, Casinomeister, Online Casino Suite