Pai Gow Tiles

Last update: Apr. 22, 2008

Introduction

There can be little debate that the rules to Pai Gow are the most difficult to learn of all the American casino games. However, if you already understand pai gow poker , then it will be easier to understand Pai Gow, which Pai Gow Poker originated from. Briefly, both player and banker get four tiles each and set them into two hands, one high and one low. The high hands are comared to each other, as are the low hands, to determine the winner. Where the rules get complicated is in rating the tiles and the hands.

Personally, I like pai gow and have been playing it often. It is a very slow paced game and results in frequent pushes, resulting in a good game for bankroll preservation. Usually you can bank every other hand, resulting in a fairly low overall house edge. When I'm expected to put in a lot of play for a tournament or special event, I often start with blackjack for the low house edge. However, if I get beaten up in blackjack, I switch to slow down and cut my losses. Here are the rules in their entirity.

Rules

Pai gow is played with a set of 32 dominos displayed below. Notice that some dominos appear once and some twice.

There is no significance to the color of the dots.

The Rules

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 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 offered in turn to each player and dealer in a counter-clockwise direction.

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 may 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 the complicated and there is no easy way to memorize the order. The highest hands are the matched pairs as follows. The highest pair, known as the supreme pair consists of the two wild dominos. Each of these wild dominos, known as "gee" may count as either 3 or 6 points if used individually. The Chinese name for the supreme pair is "Gee Joon" which is also the name of a restaurant in Binion's Horseshoe in downtown Las Vegas.

Following in rank are certain non-matching 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. The highest among these hands are the 6+6 and 1+1 dominos combined with a 7, known as a "high nine" because of their composition with one of the two highest individual dominos. In the event the player and banker have the same point total then the highest ranking domino in each will will be used to break the tie, the high domino wins. 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. There is an exception, in the event of a 0-0 copy then the tie will go to the banker. The following list shows every domino in order of their rank.

Note that while the two wild dominos together are the highest ranking pair (the supreme pair) individually they are the lowest in rank.

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

On July 4, 2007, I proudly released by "Wizard Way" for Pai Gow. As the table below shows it cuts 0.56% off the house edge, compared to the house way, when banking and assuming a 5% commission.

The next table shows the possible outcomes and house edge under various strategies, banking or not banking, and whether prepaying the commission.

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.

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 moved my Foxwoods house way to a separate page.

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. The code is a little buggy, so please forgive me if it sets the hands incorrectly sometimes.

Links

This page at pokerstrategy.usshows the house way for lots of hands.

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 Foxwoods dealer, who shall remain anonymous, who provided me with the Foxwoods house way.