pai gow poker odds

Pai Gow poker (or Double-hand poker) is an Americanized version of Pai Gow, in that it is played with playing cards using poker hand rankings, while Pai Gow is played with Chinese dominoes. The games of Pai Gow poker and Super Pan-9 were co-created by Sam Torosian and Fred Wolf.
The game is played with a standard 52-card deck plus a single joker. It is played on a table set for six players plus the dealer.
Each player is playing against the banker, who may be the casino dealer or one of the other players at the table.
The object of the game is for a player to create two poker hands out of the seven cards in his hand: a five-card poker hand and a two-card poker hand. The five-card hand must rank higher than the two-card hand. The two-card hand is often called the hand "in front" or "on top", and the five-card hand is called the hand "behind" or "bottom", as they are placed that way in front of the player when he is done setting them.
The cards are shuffled, and then dealt to the table in seven face-down piles of seven cards. Four cards are unused regardless of the number of people playing.
Betting positions are assigned a number from 1 to 7, starting with whichever player is acting as banker that hand, and counting counter-clockwise around the table. A number from 1 to 7 is randomly chosen (either electronically or manually with dice), then the deal begins with the corresponding position and proceeds counter-clockwise. One common way of using dice to determine the dealer starting number is to roll three six-sided dice, and then count betting spots clockwise from the first position until the number on the dice is reached.
If a player is not sitting on a particular spot, the hand is still assigned, but then placed on the discard pile with the four unused cards.
The only two-card hands are one pair and high cards.
Five-card hands use standard poker hand rankings with one exception: in most Nevada casinos, the hand A-2-3-4-5 ranks above a king-high straight, but below the ace-high straight A-K-Q-J-10. At most casinos in California and Michigan this rule doesn't apply; the A-2-3-4-5 is the lowest possible straight.
The joker plays as a bug, that is, in the five-card hand it can be used to complete a straight or flush if possible; otherwise it is an ace. In the two-card hand it always plays as an ace, except in several southern Californian casinos where the joker is completely wild.
If each of the player's now-separated hands beat the banker's corresponding hand then he wins the bet. If only one of his hands beats the banker then he pushes. If both of his hands lose to the banker then he loses.
On each hand, ties go to the banker (for example, if a player's five-card hand loses to the banker and his two-card hand ties to him then he loses); this gives the banker a small advantage. If the player fouls his hand, meaning that his low hand outranks his high hand, or that there are an incorrect number of cards in each hand, there will be a penalty: either re-arrangement of the hand according to house rules or forfeiture of the hand.
In casino-banked games, the banker is generally required to set their hand in a pre-specified manner, called the "house way", so that the dealer does not have to implement any strategy in order to beat the players. When a player is banking, he is free to set the hand however he chooses; however, players have the option of "co-banking" with the house, and if this option is chosen then the player's hand must also be set in the house way.
Californian casinos typically charge a flat fee per hand (such as 5 cents or one dollar) to play, win or lose. Other casinos take, out of the winnings, a 5% commission (usually known as the rake). While this may seem high, a hand of Pai Gow poker takes a long time to play compared to a game like blackjack, and there are many pushes; therefore the house doesn't collect that 5% as often as it would collect the house percentage on other games.
Generally speaking, players should try to set the highest two-card hand that they can legally set: the best two-card hand that still leaves a higher five-card hand behind. More specifically, players should expect an average hand to be something like a medium-to-high pair behind in the five-card hand and an ace-high in front. Detailed computer analysis has been done to determine the ideal strategy, but this requires memorizing large tables; a close approximation can be done with only a few rules of thumb: when playing in a casino and in doubt, a player can always ask that his hand be set house way. Most house strategies are quite reasonable and can be quite close to optimal strategy.
If a player has no pairs, straights or flushes, he can set the second- and third-highest cards in his two-card hand. For example, with K-Q-J-9-7-4-3 he can play Q-J and K-9-7-4-3. There are a few minor exceptions to this, for example, with A-Q-10-9-5-4-2 it is slightly better to play Q-9 and A-10-5-4-2, but these situations are rare and do not affect a player's win rate much. If a player has nothing but a single pair, he can set it in his five-card hand and put the two highest remaining cards in his two-card hand. For example, with A-Q-Q-9-6-5-3 he can play A-9 and Q-Q-6-5-3. There are no exceptions to this rule. This and the above rule will cover approximately 90% of played hands. Two pair is the most common case where strategy isn't obvious. A player can either play high pair behind and small pair in front, or else two pair behind and high cards in front. The smaller the high pair and higher the remaining cards, the more inclined he should be to play two pair behind. If his side cards are small or his larger pair is large, he should split the pairs. He should always split the pairs if his high pair is of aces, and should almost always split if his high pair is of kings or queens: they are high enough by themselves. With cards like J-J-4-4-A-Q-5 he can consider playing A-Q and J-J-4-4-5- since A-Q in front is not much worse than 4-4; however, two pair behind is much better than a single pair of jacks. A player with jacks and tens might be more inclined to split, because tens in front is much better than A-Q. With pairs as small as 7s and 8s, a player might consider playing two pair behind if he can play a king-high or better in front. With 2s and 3s he may even play as little as a queen-high in front. If he has no side cards higher than a jack, he should always split pairs, even 2s and 3s (most house ways split if there's a pair of 6s or higher, and split small pairs if there's no ace for the low hand). Three pair is a very good hand. A player should always play the highest pair in front with no exceptions. For example, with K-K-7-7-4-4-A he should play K-K and 7-7-4-4-A. If a player has three of a kind and nothing else, he should play three of a kind behind and the remaining high cards in front unless they are aces. He should always split three aces, playing a pair of aces behind and ace-high in front. Occasionally, he can even split three kings if his remaining side cards are not queen-high; for example, with K-K-K-J-9-7-6 it is slightly better to play K-J and K-K-9-7-6 than to play J-9 and K-K-K-7-6. Most house ways only split three aces. If a player can play a straight or a flush or both, he should play whichever straight-or-better five-card hand makes the best two-card hand. For example, with K♠-9♠-8♣-7♠-6♣-5♠-4♠ playing the flush would put 8-6 in front, playing the 9-high straight would put K-4 up front, but the correct play is K-9 and 8-7-6-5-4. Occasionally the player will have a straight or flush with two pair; in that case, he should play as if it were two pair and ignore the straight or flush. This rule applies even if a player can play a straight flush; if a straight or flush makes a better hand in front, play it that way. With a full house, a player should generally play the three of a kind behind and the pair in front. The exception is if the pair is very small and the side cards are very high; for example, with 5-5-5-3-3-A-Q it might be better to play A-Q with the full house behind. However, these cases are rare, and a player will never be making a big mistake if he never play a full house behind. House ways will always split the full house. With two three of a kinds, a player should play the higher as a pair in front and the smaller three of a kind behind. For example, with Q-Q-Q-7-7-7-A he should play Q-Q and 7-7-7-A-Q — no exceptions. With four of a kind, a player should play as if it were two pair, but should be slightly less inclined to split. For example, with 10-10-10-10-J-5-4 he should play 10-10 and 10-10-J-5-4, and with 3-3-3-3-K-Q-7, K-Q and 3-3-3-3-7. Most house ways always split the four of a kind. With three pair and a straight or flush (only possible with the joker), a player should play his hand as three pair (with aces in front). The cases below rarely happen, but deserve mention:
With four of a kind and a pair, a player should play the pair in front unless it is very small, and the four of a kind is very large. For example, with 9-9-9-9-7-7-K he should play 7-7 and 9-9-9-9-K, but with K-K-K-K-3-3-9 he might play K-K and K-K-3-3-9. With a full house and a pair, a player should play the higher pair in front and a full house in back. With four of a kind and three of a kind, a player should split the four to play a pair in front and full house behind, unless the three of a kind has a higher rank than the four of a kind; in that case he should play the four of a kind, with a pair from the three of a kind in front. With all four aces and the joker, a player should play a pair of aces in front and three aces (or a full house) behind, unless the back pair is of kings.