Pai Gow Poker

Last Update: Feb. 28, 2013

Introduction

Pai 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.

History

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 Rules

1. A single 53-card deck is used, consisting of the usual 52 cards, plus one joker.
2. The joker is semi-wild. It may be used as an ace, or to complete a straight, flush, or straight flush, or royal flush. After the player makes a bet, the dealer will deal the player and himself seven cards each.
3. The player will separate his seven cards into a five-card high hand, and two-card low hand. The high hand must be of higher poker value than the low hand.
4. The five-card hand is ranked according to conventional poker rules. The only poker hand in the two-card hand is a pair or no pair, after which the individual cards determine the value.
5. After the player has set his hand, the dealer will turn over his cards and divide his hand in the same manner, according to specified rules known as the "house way."
6. The two high hands will be compared, and the two low hands, the hand with the higher poker value winnings. If the event of a tie, for example both two-card hands are ace/king, then the tie has go to the "banker."
7. If the player wins both comparisons, then the player will win even money on his bet, less a 5% commission. If the player wins one and loses one, then the bet shall push. If the player loses or ties both, then the player shall lose his wager.
8. Unlike most casino games, the player may bet against the dealer, and other players in pai gow poker. This is known as "banking."
9. The turn to act as banker is supposed to rotate around the table, but at some casinos it zig-zags between the dealer and each player in turn.
10. The player may always decline to bank (which usually happens), in which case the option will revert to the next player, or dealer.

Strategy

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.

House Edge

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.

Possible Outcomes in Pai Gow Poker
Outcome	Probability
Player wins both	28.61%
Tie	41.48%
Banker wins both	29.91%

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.

House Edge in One-on-One Pai Gow Poker
Status	House Edge
Player	2.73%
Banker	0.20%
Combined	1.46%

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.

House Edge as Banker by Number of other Players
Other Players	House Edge
1	+0.20%
2	-0.02%
3	-0.10%
4	-0.15%
5	-0.19%
6	-0.21%

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:

• Bally's (Atlantic City)
• Barona (San Diego)
• British Columbia (Canada)
• Canterbury Park (Minnesota)
• Claridge (Atlantic City)
• Flamingo Hilton (Las Vegas)
• Four Queens (Las Vegas)
• Golden Nugget (Las Vegas)
• Great Britain (1124K PDF; see page 80)
• Santa Ana Star (New Mexico)
• Texas Station (Las Vegas)
• Trump Plaza (Atlantic City)

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.

Probabilities in Pai Gow Poker
Hand	Combinations	Probability
Five Aces	1,128	0.00000732
Straight/Royal Flush	210,964	0.00136862
Four of a Kind	307,472	0.00199472
Full House	4,188,528	0.02717299
Flush	6,172,088	0.04004129
Straight	11,236,028	0.07289350
Three of a Kind	7,470,676	0.04846585
Two Pair	35,553,816	0.23065464
One Pair	64,221,960	0.41663862
All Other	24,780,420	0.16076246
Total	154,143,080	1

Note: The number of combinations for a Royal Flush is 26,132; 21,620 wild and 4,512 natural.

Internal Links

• Ask the Wizard questions about Pai Gow Poker.
• EZ Pai Gow Poker.
• Dealer Probabilities: Shows the probability the dealer will form any given hand or less. Useful for making accurate strategy decisions.
• When to split Two Pair: My advice on when to split two pair.
• Side Bets: Analysis of various side bets such as Fortune, Jackpot, and Emperor's Challenge.
• No Push Pai Gow Poker: My analysis of this Pai Gow Poker variant.
• Pai Gow Mania: My analysis.
• Play Pai Gow Poker. Play my Pai Gow Poker game.

External Links

German translation of this page.