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Dealer Open Pai Gow
Introduction
Dealer Open Pai Gow is pai gow poker variant played with a fully-exposed dealer hand. It has much in common with Face Up Pai Gow Poker, however there is a different mechanism to achieve a house advantage.
Rules
Following are the full rules. If you already understand convention pai go poker, you may skip over this part and go right my section following titled "Differences between Dealer Open Pai Gow and conventional Pai Gow Poker.
- A single 53-card deck is used, consisting of the usual 52 cards, plus one joker.
- The joker is semi-wild. It may be used as an ace, or to complete a straight, flush, straight flush or royal flush.
- 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.
- Play starts with the player making a bet. The player may also make an optional Push Ace High side bet at this time.
- The dealer will deal the player and dealer seven cards.
- There is no player banking.
- 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.
- If the dealer has at least two jacks, then the dealer shall automatically win.
- 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.
- 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.
- 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.
- 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.
- The optional Jacks Beat side bet wins if the dealer automatically wins with two or more jacks. The multiple it wins depends on the players hand. More details on that below.
- The Chan Chu is another optional side bet that pays based on the value of the player's hand. More details below.
Differences between Dealer Open Pai Gow and conventional Pai Gow Poker
- Dealer cards dealt face up.
- No 5% commission.
- If the dealer has at least two jacks, then the dealer automatically wins.
- No player banking
Differences between Dealer Open Pai Gow and Face Up Pai Gow Poker
The two games achieve a house edge in different ways, as follows. Otherwise the base game is the same.
- In Dealer Open Pai Gow, two or more dealer jacks are an automatic player loss.
- In Face Up Pai Gow Poker, a dealer ace-high pai gow hand is an automatic push.
Analysis
AGS, the distributors of Dealer Open Pai Gow, kindly shared their math report by GLI with me for this page. For the base game, all it says is the house edge is 1.82%. It doesn't break it down into detail, but the the section on the Jacks Beat bet indicates the dealer will get an automatic winning hand of two jacks or more with probability 7.98%.
By way of comparison, it is 1.81% in Face Up Pai Gow Poker.
Chan Chu
The Chan Chu follows the same winning hand order as the Fortune bet in conventional pai gow poker and Face Up Pai Gow Poker. However, the pay table is different. The following analysis is based on the pay table as found at Binion's In Las Vegas on December 16, 2022. The lower right corner shows a house edge of 8.00%, before considering the envy bonus.
Chan Chu
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Natural seven-card straight flush | 5,000 | 32 | 0.00000021 | 0.001038 |
| Royal Flush + R/M | 1,000 | 72 | 0.00000047 | 0.000467 |
| Wild seven-card straight flush | 750 | 196 | 0.00000127 | 0.000954 |
| Five Aces | 250 | 1,128 | 0.00000732 | 0.001829 |
| Royal Flush | 100 | 26,020 | 0.00016880 | 0.016880 |
| Straight flush | 50 | 184,644 | 0.00119787 | 0.059894 |
| Four of a Kind | 20 | 307,472 | 0.00199472 | 0.039894 |
| Full house | 5 | 4,188,528 | 0.02717299 | 0.135865 |
| Flush | 4 | 6,172,088 | 0.04004129 | 0.160165 |
| Three of a kind | 3 | 7,672,500 | 0.04977518 | 0.149326 |
| Straight | 2 | 11,034,204 | 0.07158417 | 0.143168 |
| Three pair | 0 | 2,862,000 | 0.01856717 | 0.000000 |
| All other | -1 | 121,694,196 | 0.78948855 | -0.789489 |
| Total | 154,143,080 | 1.00000000 | -0.080008 |
The player qualifies for the following envy bonuses if he bets at least $5 on the Chan Chu. The lower right cell shows that every additional player has a value of 2.7¢.
Chan Chu Envy Bonus
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Natural seven-card straight flush | 1,000 | 32 | 0.00000021 | 0.000208 |
| Royal Flush + R/M | 250 | 72 | 0.00000047 | 0.000117 |
| Wild seven-card straight flush | 100 | 196 | 0.00000127 | 0.000127 |
| Five Aces | 50 | 1,128 | 0.00000732 | 0.000366 |
| Royal Flush | 25 | 26,020 | 0.00016880 | 0.004220 |
| Straight flush | 10 | 184,644 | 0.00119787 | 0.011979 |
| Four of a Kind | 5 | 307,472 | 0.00199472 | 0.009974 |
| Total | 0 | 0.00337066 | 0.026990 |
The next table shows the overall house edge, including the value of the envy bonuses, according to the number of other players along the left column and bet amount on the Chan Chu along the top row.
Chan Chu House Edge
| Other Players |
$5 Bet | $10 Bet | $25 Bet |
|---|---|---|---|
| 6 | 4.76% | 6.38% | 7.35% |
| 5 | 5.30% | 6.65% | 7.46% |
| 4 | 5.84% | 6.92% | 7.57% |
| 3 | 6.38% | 7.19% | 7.68% |
| 2 | 6.92% | 7.46% | 7.78% |
| 1 | 7.46% | 7.73% | 7.89% |
| 0 | 8.00% | 8.00% | 8.00% |
Jacks Beat
The following table shows the possible outcomes of the Jacks Beat bet, according to the table found at Binion's in Las Vegas in December 2022. The bet wins if the dealer gets at least two jacks. The lower right cell shows a house edge of 8.84%.
Jack Beat
| Event | Pays | Probability | Return |
|---|---|---|---|
| Five Aces | 1,000 | 0.00000070 | 0.000700 |
| Royal Flush | 500 | 0.00001006 | 0.005030 |
| Straight flush | 250 | 0.00010112 | 0.025280 |
| Four of a Kind | 100 | 0.00017322 | 0.017322 |
| Full house | 50 | 0.00226068 | 0.113034 |
| Flush | 25 | 0.00321074 | 0.080269 |
| Three of a kind | 20 | 0.00579853 | 0.115971 |
| Straight | 15 | 0.00397154 | 0.059573 |
| Three pair | 10 | 0.01859837 | 0.185984 |
| Two pair | 5 | 0.03310110 | 0.165506 |
| Pair | 5 | 0.01261686 | 0.063084 |
| Dealer qualified | -1 | 0.92015708 | -0.920157 |
| Total | 1.00000000 | -0.088405 |
House Way
The following is the house way used by GLI in determining the 1.82% house edge. This appears to me to be a very solid house way. Many casinos use ones that are more complicated, but the one below I believe to be just as effective but with greater simplicity.
The "front" refers to the two-card hand and the "back" refers to the five-card hand. The dealer will set their hands according to the highest 5-card hand that can be formed:
- Five Aces: Set two Kings in front if possible, otherwise set two Aces in front. - Royal Flush: See the ‘Complete Hand’ rule.
- Four of a Kind: Set according to the rank of the Four of a Kind:
- Aces: If the hand contains a pair of Sevens or better, set the pair in front. Otherwise set two Aces in front.
- Jacks to Kings: If the hand contains a pair of Tens or better, set the pair in front. Otherwise, set two of the Four of a Kind in front.
- Sevens to Tens: If the hand contains a pair, set the pair in front. If the hand contains a singleton Ace, set the two highest singletons in front. Otherwise, set two of the Four of a Kind in front.
- Two to Sixes: If the hand contains a pair, set the pair in front. Otherwise, set the two highest singletons in front.
- Full House: If the hand contains two Three of a Kinds, set the highest possible pair in front and Three of a Kind in back. If the hand contains a Three of a Kind and two Pairs, set the highest possible pair in front with Full House or Two Pair in back. If the hand contains a pair of Twos and a singleton King or better, set the two highest singletons in front. Otherwise, set the pair in front with Three of a Kind in back.
- Flush: See the ‘Complete Hand’ rule.
- Straight: See the ‘Complete Hand’ rule.
- Three of a Kind: If three Aces, set one Ace and the highest singleton in front. Otherwise, set the two highest singletons in front.
- Two Pair: If the hand contains three Pair, set the highest pair in front. Otherwise, if both pair are Sevens or better and the hand does not contain a singleton Ace, set the low pair in front. If the hand contains Jacks or better over Sixes or better, and a singleton Ace, set the low pair in front. If the high pair is Aces, set the low pair in front. Otherwise, set the two highest singletons in front.
- Pair: Set the two highest singletons in front.
- High Card: Set the second and third highest singletons in front.
- Complete Hand (Straight, Flush, Straight Flush, or Royal Flush): If the hand contains a Four of a Kind, follow the Four of a Kind rule. If the hand contains a Full House, follow the Full House rule. If the hand contains Two Pair, Jacks or better over Sixes or better, or if it contains Two Pair with one or more Aces, follow the Two Pair rule. Otherwise, find the best front hand settings that allow you to set a royal flush, a straight flush, or a straight or flush in back. If there are multiple ways to do it, set according to the first eligible rule:
- Set the highest front hand possible, King-high or better, that allows a Straight or Flush of any kind in back.
- Set the highest front hand possible that allows a Royal Flush in back.
- Set the highest front hand possible, Jack-high or better, that allows a Straight or Flush of any kind in back.
- Set the highest front hand possible that allows a Straight Flush in back.
- Set the highest front hand possible that allows a Straight or Flush in back.
Acknowledgements
I would like to thank AGS, the distributors of the game, for sharing their math report with me on the game.