Pai Gow Poker

Last update: May 5, 2008

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The Rules

Play begins by making a wager. Next everyone receives seven cards. A roll of the dice or a randomly generated number determines which player gets the first set of cards. Each player then each arranges his seven cards into a five-card hand and a two-card hand. The five-card hand is ranked as in poker. Most, but not all, casinos treat A2345 (the "wheel") as the second highest straight. The two-card hand is scored by pairs beating two singletons, then by the individual ranks. The highest two-card hand is a pair of aces, and the lowest is 3-2.

After each player has arranged his hand, the banker arranges his according to a set of fixed rules known as the "house way." Then the player's five-card hand is compared to the dealer's five-card hand, the higher hand wins. Likewise, the player's two-card hand is compared to the dealer's two-card hand. In the event of an exact match between hands, called a copy, the tie goes to the banker. If the player beats the dealer with both hands the player wins even money, less a 5% commission. If the player wins one and loses one the bet is a push. If the player loses both the player loses the entire wager.

When setting the hands, the two-card hand may not be higher then the five-card hand. If it is, then both hands are deemed "foul" and both lose. The joker can only be used to complete a straight, flush, or straight flush, otherwise it is treated as an ace. When used in a flush, the joker takes the rank of the highest unused card.

At some casinos, if there is an empty seat, the dealer will also deal a "dragon" hand. Another player may assume the dragon hand if he wishes, essentially playing two positions rather than one. The player will have to use the house way in setting the dragon hand.

In pai gow poker any player may elect to be the banker in turn. If a player banks the 5% commission is charged on the net win. When a player is the banker the dealer will still play, betting an amount equal to the last bet the player made when the dealer was banking. It is strongly to the advantage of the player to be the banker as much as possible because the dealer wins on copies and the 5% commission is charged after losses are set against winnings.

The opportunity to bank should rotate around the table, skipping players who decline to bank. Some, less reputable, casinos will zig-zag the turn to bank between the players and the dealer. I have even seen it happen at the now defunct Nevada Landing that not only the the turn to bank zig-zag, but if a player was not present or declined to bank, the turn to bank reverted to the dealer. So any given player could only bank once every 14 hands, regardless of the number of other players.

If the player wants to bank they must have enough money on the table to pay off all winning bets of the other players and dealer. The player must also have played a previous hand against the house banker to bank. Some books say that they player may co-bank with the house. If this option is elected the casino will assume half the financial responsibility of the outcome. The player must set his hand by the house way, if co-banking. Once I asked to co-bank at the Venetian. The dealer didn't know what I was talking about, so called over the floorman. The floorman said in his many years in the casino business he had never seen anyone invoke his rule. He temporarily declined to let me do it because he couldn't find the proper laminated marker for it. Then I could see him making lots of calls and consulting the computer. After about 15 minutes he came back and said the Venetian no longer allowed co-banking.

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 a 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.

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 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 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:

• Trump Plaza (Atlantic City)
• Claridge (Atlantic City)
• Flamingo Hilton (Las Vegas)
• Golden Nugget (Las Vegas)
• Texas Station (Las Vegas)
• Four Queens (Las Vegas)
• Bally's (Atlantic City)
• Canterbury Park (Minnesota)
• British Columbia (Canada)
• Great Britain (See page 80, 1124K)

Pai Gow Poker Probabilities

The following table shows the probability of forming any specified poker hand. These probabilites consider all seven cards and without regard to how the player may play the hand.

Note: The number of ways for a royal flush is 26,132; 21620 wild and 4512 natural.

Links

German translation of this page.