We’ve covered basic and advanced Pai Gow Poker strategy elsewhere on this site. We provided a detailed blueprint for splitting your cards based upon their individual values and combined hand rankings. If you follow basic strategy, you’ll do well.If you apply a few of our advanced tweaks, you’ll maximize your winnings and minimize your losses.
It’s important to underscore that the strategy we’ve given you – both basic and advanced – is based completely on Pai Gow Poker odds.
On this page, we’ll give you a crash course on Pai Gow Poker odds and hand probabilities. We’ll explain the basics before digging more deeply into the details. We’ll also describe the odds you’re facing as you square off against the dealer. You won’t need to remember anything that you’re about to learn in order to enjoy the game and play like a professional. However, a basic understanding of Pai Gow Poker odds provides useful insight into the probability of beating the dealer.
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Basic Pai Gow Poker Odds
The game of Pai Gow is played with 53 cards – a standard 52-card deck and a joker. There are 154,143,080 possible hand combinations that can emerge from those 53 cards. You’ll remember that Pai Gow Poker is based on traditional hand rankings. Those include pairs, straights, 3s of a kind, flushes, full houses, 4s of a kind, and straight and royal flushes. Because the joker functions as an Ace (if it cannot be used to complete a straight or flush), it is also possible to make a hand with 5 Aces.
First, here are the number of combinations for making each hand:
- Single Pair: 64,221,960
- Two Pairs: 35,553,816
- Straight: 11,236,028
- 3 of a Kind: 7,470,676
- Flush: 6,172,088
- Full House: 4,188,528
- 4 of a Kind: 307,472
- Straight Flush or Royal Flush: 210,964
- 5 Aces: 1,128
Now, here are the probabilities for making each hand:
- Single Pair: 0.416639
- Two Pairs: 0.230655
- Straight: 0.072894
- 3 of a Kind: 0.048466
- Flush: 0.040041
- Full House: 0.027173
- 4 of a Kind: 0.001995
- Straight Flush or Royal Flush: 0.001369
- 5 Aces: 0.000007
Let’s convert those probabilities into Pai Gow Poker odds (binary format):
- Single Pair: 1 in 1.40
- Two Pairs: 1 in 3.34
- Straight: 1 in 12.72
- 3 of a Kind: 1 in 19.63
- Flush: 1 in 23.97
- Full House: 1 in 35.80
- 4 of a Kind: 1 in 500.25
- Straight Flush or Royal Flush: 1 in 729.46
- 5 Aces: 1 in 142,856
Those are the basic odds in pai gow poker. They only take into account the odds and probabilities of making ranked hands from your initial seven cards. They ignore the manner in which you split your cards.
Advanced Pai Gow Poker Odds: Digging More Deeply
Understanding your odds of making specific ranked hands is useful, but mostly in the context of your chances of beating the dealer’s two hands. In other words, suppose that you receive three Kings within your 7-card hand. If you split them and place two Kings in your 2-card hand, there’s a high likelihood that you’ll beat the dealer’s 2-card hand. The probability of the dealer’s 2-card hand containing two Kings is approximately 0.0103.
On the other hand, if you keep the three Kings intact within your 5-card hand, your odds of winning that hand are much lower. There are far more combinations the dealer can make that will outrank your three Kings.
Admittedly, considering Pai Gow Poker odds in this context is an academic exercise. But, it’s still worth noting.
Pai Gow Poker Odds: Player Versus Dealer
The house edge is 2.66%. That number is based on the probability of three different outcomes: winning both hands, tying, or losing both hands. To clarify, by “tie,” we’re referring to a push; you win one hand and lose one hand. We’re not referring to an event in which one of your hands is identical to the dealer’s, a circumstance in which the dealer would win.
There is a 28.61% probability that you’ll win both hands. There’s a 29.91% chance you’ll lose both hands. And there’s a 41.48% chance that you’ll tie, or push. Those numbers may not seem to support the 2.66% edge. The missing factor is the 5% commission the house takes when you win both hands.
Where To Test Pai Gow Poker Odds
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