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PaiGow Poker
Strategy  House Edge  The Houseway  Probabilities  Appendices
Provided by The Wizard of Odds

PaiGow Poker

Pai gow poker is a variation of the Chinese domino game gai gow. Pai gow poker is played with a 53 card deck, including a joker. The game is one on one, the player(s) against the banker, each competing to make the best possible hands. Due to a rather slow pace and a lot of ties pai gow poker is less intense than most casino games and a modest buy in can usually last a long time. This page will discuss the rules and strategy for pai gow as found in casinos as opposed to card clubs. Pai gow in legal in the card clubs of southern California but the rules are somewhat different, often in the direction of being to the player's advantage.

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. The players then each arrange their seven cards into a five-card hand and a two-card hand. The five-card hand is ranked as in poker, with the exception that an A-2-3-4-5 straight is the second highest straight. The two-card hand will either be a pair or two individual cards. The highest two-card hand is a pair of aces and the lowest is a 2-3.

After all the players have arranged their hands the banker arranges theirs 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. Likewise the player's two-card hand is compared to the dealer's two-card hand. The highest hand wins. 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. At some places if there is an empty seat the dealer will also deal a "dragon" hand. Another player may assume the dragon hand if they wish, essentially playing two positions rather than one. The player may 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 usually rotates from person to person, including the house, but sometimes will zig-zag between the players and the dealer. 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 casinos will allow the player to 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 their hand according to the house way if co-banking.

Strategy

The most important factor in improving your odds in pai gow 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. In my pai gow poker appendix I have a 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.

In addition my pai gow poker appendix 2 I 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.

Possible Outcomes in Pai Gow Poker
Outcome Probability
Player wins both 28.55%
Tie 41.47%
Banker wins both 29.98%

Based on this table the following table shows the house edge for playing as the banker, player, and combined. This table assumes a one on one game.

House Edge in Pai Gow Poker
Status House
Edge
Player 2.85%
Banker 0.08%
Combined 1.46%

The probability that the front hands will copy is 2.55%. The probability that the back hands will copy is 0.32%.

If the player were to use the Optimal single house way against the Trump Plaze 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:

The Wizard of Odds would like to thank the above casinos for allowing me to see their house way. At least a dozen other casinos refused to reveal their house way. I would especially like to thank the Flamingo Hilton who were very friendly and accomodating about my request.

Pai Gow 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.

Probabilities in Pai Gow Poker
Hand Combinations Probability
Five aces11280.00000732
Straight/royal flush2109640.00136862
Four of a kind3074720.00199472
Full house41885280.02717299
Flush61720880.04004129
Straight 112360280.07289350
Three of a kind74706760.04846585
Two pair355538160.23065464
Pair642219600.41663862
Nothing247804200.16076246
Total1541430801

Appendices

Appendix 1: Shows the probability the dealer will form any given hand or less. Useful for making accurate strategy decisions.

Appendix 2: My advice on when to split a two pair.

Appendix 3: Analysis of the Fortune Pai Gow Poker side bet.

Appendix 4: Analysis of No Push Pai Gow Poker.

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