Face Up Pai Gow Poker

Introduction

As the title says, Face Up Pai Gow Poker is pai gow poker played with a fully-exposed dealer hand. "What's the catch?," you might ask. If the best five-card hand the dealer can make is ace-high, then the hand is an automatic push. Naturally, there is a side bet to cover that contingency.

Rules

Following are the full rules. If you want to know only how Face Up Pai Gow poker differs from conventional pai gow poker, then you can skip over the rules.

1. A single 53-card deck is used, consisting of the usual 52 cards, plus one joker.
2. The joker is semi-wild. It may be used as an ace, or to complete a straight, flush, straight flush or royal flush."
3. Standard poker ranking rules are followed with one strange exception — the A2345 straight (known as "the wheel") is considered the second highest straight. Some casinos have dropped this ridiculous rule, but most still cling to it.
4. Play starts with the player making a bet. The player may also make an optional Push Ace High side bet at this time.
5. The dealer will deal the player and dealer seven cards.
6. There is no player banking.
7. The dealer cards will be exposed face up. The dealer will then set his cards into a 5-card High Hand and a 2-card Low Hand, according to specified rules known as the "house way." The poker value of the High Hand must be greater than the Low Hand.
8. If the best five-card hand the dealer can make is an ace high, then the outcome is an automatic push, regardless of the player cards. This is known as an "ace-high pai gow."
9. Otherwise, the player will separate his seven cards into a five-card high hand and two-card low hand. As with the dealer hand, the high hand must be of higher poker value than the low hand.
10. The five-card hand is ranked according to conventional poker rules. The only poker hand in the two-card hand is a pair or no pair, after which the individual cards determine the value based on the value of the highest ranking card first.
11. After the player has set his hand, then player and dealer high hands will be compared, and their two low hands. In each case, the hand with the higher poker value wins. If the hands are of equal rank, for example both two-card hands are ace/king, then the dealer wins the tie.
12. If the player wins both comparisons, then the player will win even money on his bet. There is no commission. If the player wins one and loses one, then the bet shall push. If the player loses or ties both, then the player shall lose his wager.
13. The Push Ace High bet has the following pay table:
    • Both player and dealer have ace-high pai gow: Pays 40 to 1
    • Dealer has ace-high pai gow with joker: Pays 15 to 1
    • Dealer has ace-high pai gow without joker: Pays 5 to 1
    • Neither player nor dealer has ace-high pai gow: Loss

 

Differences between Face Up Pai Gow Poker and conventional Pai Gow Poker

 

• Dealer cards dealt face up.
• No 5% commission.
• Dealer ace-high pai gow is an automatic push.
• No player banking

Analysis

The following table shows the probability and contribution to the return for all outcomes of the primary game. The lower right cell shows a house edge of 1.81%.

 

 

It should be noted that the website for this game, which I won't link to because I get very strong warnings that the site is infected with viruses, says the house edge is 1.60%. I imagine the exact house edge will vary depending on the house way used by the dealer. Personally, I use the one for the Trump Plaza.

In case you were wondering, if there were no ace-high pai gow rule, then the player would have a 3.98% advantage.

Push Ace High

There are two known pay table for the Push Ace High bet, as follows.

The following table shows the probability and contribution to the return for all outcomes of the Push Ace High side bet with a 5-15-40 pay table. The lower right cell shows a house edge of 9.29%.

 

 

The following table shows the probability and contribution to the return for all outcomes of the Push Ace High side bet with a 5-12-40 pay table. The lower right cell shows a house edge of 10.52%.

 

 

Methodology

The analysis above is the result of a simulation of over 900 million pairs of random hands. A Fisher-Yates shuffle was done between rounds, which used a Mersenne Twister random number generator.

Progressive Jackpot

Caesars properties in Las Vegas offer a $5 progressive jackpot side bet. The following is the pay table. Wins are on a "for one" basis.

• Seven-card straight flush — Mega jackpot
• Five aces — Major jackpot
• Royal flush — Minor jackpot
• Straight flush — $500
• Four of a kind — $375
• Full house — $20

The following table shows my analysis. The lower right cell shows the expected return on the fixed wins is $1.89, or 37.81% of money bet.

As mentioned above, the expected return on the fixed wins is 37.81%. To calculate the return for any given set of jackpots, add the following:

• 2.96% for every $100,000 in the Mega jackpot.
• 1.46% for every $10,000 in the Magor jackpot.
• 3.39% for every $1,000 in the Minor jackpot.

As an example, the image above was taken on December 17, 2022, when the Mega jackpot was unusually large. Using my formula would yield an expected return of 37.81% + 2.96%*($5,626,390.50/$100,000) + 1.46%*($25,955.61/$10,000) + 3.39%*($3,257.75/$1,000) = 219.08%. That is an 119.08% player advantage, or expected net win per bet of $5*119.08% = $5.95.

External Links

• FACE UP PAI GOW POKER @ NYNY — Discussion in my forum at Wizard of Vegas.
• FACE UP PAI GOW POKER PROGRESSIVE JACKPOT — Discussion about the progressive side bet, when the Mega jackpot was over $3.8 million.

Written by: Michael Shackleford