Pay Gow Poker Strategy by Max Drayman

The odds
We could quote the straight probabilities of drawing different back and front hands, but that's not particularly meaningful. Since Pai Gow is a game of skill the odds are difficult to pin down. Suffice it to say that if you follow an optimal playing strategy you're going to win about 3-in-10 hands, lose about the same, and push about 4-in-10.

Assuming an optimum play strategy, the largest play advantage is to the dealer/banker because copies go to them. In fact, noted Pai Gow expert Stanford Wong has been quoted as saying that being dealer/banker as often as possible has the most significant impact on a winning strategy. The appeal of multi-player games is clear.

Strategy
Now the complexity of Pai Gow really shows. For the sake of discussion, lets call any pair of 2's through 6's a "low pair", 7's through J's a "medium pair", and Q's through A's a "high pair". To avoid confusion we'll call the two-card hand the "front" hand and the five-card the "back" hand.

No Pair:

• Back hand: the highest card; Front hand: the next two highest cards.

One pair:

• Back: the pair; Front: next two highest cards.

Two Pair:

• Pair of A's and any other Pair: Back: high pair; Front: other pair.
• Two High Pair: Back: best pair; Front: other pair.
• High Pair and Medium Pair: Back: high pair; Front: medium pair.
• High Pair and Low Pair with A or K: Back: both pair; Front: A or K.
• High Pair and Low pair without A or K: Back: highest pair; Front: low pair.
• Two Medium Pair with A or K: Back: both pair; Front: A or K.
• Two Medium Pair without A or K: Back: best pair; Front: other pair.
• Medium Pair and Low Pair with A or K: Back: both pair; Front: A or K.
• Medium Pair and Low Pair without A or K: Back: medium pair; Front: low pair.
• Two Low Pair with A or K: Back: both pair; Front: A or K.
• Two Low Pair without A or K: Back: best pair; Front other pair.

Three Pair:

• Back: second and third highest pair; Front: highest pair.

Three of a Kind:

• Three A's: Back: pair of A's; Front: A and next highest card.
• All others: Back: three of a kind; Front: two highest remaining cards.

  Three of a Kind twice:

• Back: lower three of a kind; Front: highest pair.

  Full House:

• With second Three of a kind: play the highest pair to Front hand.
• With second Pair: Back: full house with low pair; Front: highest pair.
• Pair is 2's with A or K: Back: full house; Front: A or K.
• All others: Back: three of a kind; Front: the pair.

  Straights, Flushes, Straight Flushes and Royal Flush:

• With no pair: Back: lowest full hand; Front: two highest cards.
• With one or two Pair: Back: lowest full hand; Front: two highest cards, pair or otherwise.
• With Three of a Kind: Back: full hand; Front: pair.
• With Full House: Back: three of a kind; Front: pair.
• With Three of a Kind twice: Back: lower three; Front: highest two.

  Four of a Kind:

• With Three of a Kind: Back: four of a kind; Front: pair from the tree of a kind.
• With a Pair: Back: four of a kind; Front: pair.
• Four A's: Back: pair of A's; Front: pair of A's.
• J's through K's with an A: Back: four of a kind; Front: the A.
• J's through K's without an A: Back: one pair from the four; Front: the other pair.
• 7's through 10's with A or K: Back: four of a kind; Front: A or K.
• 7's through 10's without A or K: Back: one pair from the four; front: the other pair.
• 2's through 6's: Back: four of a kind; front: highest remaining two.