Pai Gow Poker
Last Update: Nov. 11, 2013
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IntroductionPai Gow Poker is a variation of the Chinese domino game pai gow. The game is known for a slow rate of play and lots of pushes, resulting in low risk game. While a game of skill, most hands are obvious how to play, and it is not difficult to learn proper strategy for the rest of them. Every player plays against the same dealer hand, which causes the table to often win and lose together, resulting in a fun and social game.
Pai Gow Poker was invented in 1985 by Sam Torosian, owner of the Bell card club in southern California. However, his is a name few people recognize. While other have made millions inventing casino games, Sam received some bad legal advice that card games were not patentable, and never filed one for his game. When his game was a success at his own casino there was nothing to prevent competing casinos from offering the game as well, and they didn't have to pay Sam a dime.
Source: Casino Boss Can't Cash In on Game He Developed — Los Angeles Times, Nov. 3, 2002.
The most important factor in improving your odds in Pai Gow Poker is the ratio of how much is bet when you are the banker to as a player. The greater the ratio the better your odds are. The second most important factor is how well you arrange your cards. The house way (explained below) is a very safe strategy that is difficult to improve upon. Here is my table that shows the probability of any given 5 or 2 card hand beating the house way. Theoretically you could use these charts to play any hand, maximizing your odds of winning, but in real life nobody would have enough time to look up the numbers and add them up.
I also present my own strategy for splitting two pair that will shave 0.04% off the house edge compared to the house way rule for splitting a two pair.
The house advantage in Pai Gow Poker depends on partially on your skill setting hands but more on how much of the action you bank. An entire book could be written on this topic. For the sake of simplicity I shall only address the head to head game against the dealer. I shall assume that both the player and dealer are following the Trump Plaza house way.
Based on this table the following table shows the house edge for playing as the banker, player, and combined in a one-on-one game. The table assumes the player pre-pays the commission.
The probability that the front hands will copy is 2.55%. The probability that the back hands will copy is 0.10%.
If the player were to use the optimal single house way against the Trump Plaza house way then the house edge as the banker would be -0.19% and as the player would be 2.60%, for an average of 1.20%.
The next table shows the house edge as banker according to the number of other players (including the dealer), assuming everyone is using the same house way and betting the same amount. A negative house advantage denotes a player advantage.
Commission Free Pai Gow Poker
Often in Washington State the casino will not charge the 5% commission on banker wins. They make a profit on the banker's advantage and side bets only. With no commission, the banker has a 1.30% advantage, and all others playing against the banker a 1.30% disadvantage.
The House Way
The house way is how the dealer arranges their own hand. It can vary from place to place the differences are marginal and happen infrequently. The house way is available for the following casinos:
Pai Gow Poker Probabilities
The following table shows the probability of forming any specified poker hand. These probabilities consider all seven cards and without regard to how the player may play the hand.
Note: The number of combinations for a Royal Flush is 26,132; 21,620 wild and 4,512 natural.
German translation of this page.