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EZ Pai Gow Poker (featuring a Fully Wild Joker)
Introduction
EZ Pai Gow Poker operates without any commission charges Pai Gow Poker in this variation. Instead of the typical 5% fee, if the dealer gets a hand where the highest card is a queen, the round ends in a tie or push. Furthermore, players have the option to place four additional side bets. This game debuted in June 2009 at Pechanga and Barona casinos located in the San Diego region. Partially-Wild Joker Version .
Rules
The gameplay adheres to the standard pai gow poker rules, with a few exceptions:
- There is no commission.
- If the dealer's best hand is a queen high, meaning their best five-card combination is exactly a queen high, the outcome will automatically be a push.
- Some establishments permit players to act as the banker. If a player opts for this, the game rules will change back to those of regular pai gow poker.
- This page details the specific version of EZ Pai Gow Poker played in California, where the joker is deemed completely wild.
- There are four available side bets, which are elaborated on separately below.
Dynasty Bonus
Similar to the Fortune Bonus In traditional pai gow poker, the Dynasty Bonus activates if the player's best five cards form at least a three of a kind. It does not depend on how the player arranges their hand. If another player achieves a straight flush or better, the player can win what is called an 'envy bonus.' If only an Envy Bonus is won, the player will receive that bonus but forfeit their Dynasty Bonus wager. Below is the complete pay table.
Dynasty Bonus Pay Table — Featuring Fully Wild Joker
| Event | Pays | Envy Bonus |
|---|---|---|
| Five of a Kind | 100 | $125 |
| Royal Flush | 25 | $50 |
| Straight Flush | 15 | $10 |
| Four of a Kind | 10 | $0 |
| Full House | 5 | $0 |
| Flush | 4 | $0 |
| Straight | 2 | $0 |
| Three of a Kind | 1 | $0 |
| All other | -1 | $0 |
Protection
Similar to Pai Gow Insurance The Protection bet rewards players if their best five-card hand consists of an ace high or lower. Below is the complete pay table.
Protection Pay Table — Featuring Fully Wild Joker
| Event | Pays |
|---|---|
| 9 High Pai Gow | 100 |
| T High Pai Gow | 25 |
| J High Pai Gow | 10 |
| Q High Pai Gow | 6 |
| K High Pai Gow | 5 |
| A High Pai Gow | 4 |
| Non-Pai Gow | -1 |
Red/Black
The Red/Black bets pay out when the majority of the player's cards match the chosen color. Specifically, the player needs to have at least four cards of their selected color to win, and the joker does not count for either color.
Red/Black Pay Table
| Winning Cards | Pays |
|---|---|
| 7 | 5 |
| 4 to 6 | 1 |
| 0 to 3 | -1 |
Queen's Dragon
The Queen's Dragon bet pays off if the dealer has a hand consisting of exactly a queen-high pai gow hand, with winning wagers paying out at 45 to 1.
Strategy
I have no better strategy to offer than the house way itself, which can be found on my dedicated page for that subject. Barona pai gow poker house way .
Analysis
This section will delve into the analysis of the primary EZ Pai Gow Poker bet and the four side bets.
EZ Pai Gow Poker Analysis
The table below illustrates the house edge when the player is not taking on the role of the banker, assuming both the player and dealer use the same house strategy. The bottom right cell indicates a house edge of 2.54%.
EZ Pai Gow Poker Return Table — Fully Wild Joker
| Event | Pays | Probability | Return |
|---|---|---|---|
| Win | 1 | 0.288288 | 0.288288 |
| Push | 0 | 0.398045 | 0 |
| Lose | -1 | 0.313667 | -0.313667 |
| Total | 1 | -0.025380 |
Dynasty Bonus Analysis
The table that follows presents the probabilities and contributions to the return for the Dynasty Bonus, excluding the Envy Bonus considerations. It reveals a house edge of 6.94% in the bottom right cell.
Dynasty Bonus Return Table before Envy Bonus — Fully Wild Joker
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Five of a Kind | 100 | 14664 | 0.000095 | 0.009513 |
| Royal Flush | 25 | 26132 | 0.00017 | 0.004238 |
| Straight Flush | 15 | 184832 | 0.001199 | 0.017986 |
| Four of a Kind | 10 | 1121024 | 0.007273 | 0.072726 |
| Full House | 5 | 5997144 | 0.038906 | 0.194532 |
| Flush | 4 | 6027224 | 0.039101 | 0.156406 |
| Straight | 2 | 11083940 | 0.071907 | 0.143814 |
| Three of a Kind | 1 | 13315300 | 0.086383 | 0.086383 |
| All other | -1 | 116372820 | 0.754966 | -0.754966 |
| Total | 154143080 | 1 | -0.069368 |
The subsequent table displays the probabilities and contributions to the return from the Dynasty Bonus and Envy Bonus for each additional player, based on a wager of $5. The bottom right cell shows that adding more players decreases the house edge by 0.65%.
Dynasty Bonus Envy Bonus Return Table — Fully Wild Joker
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Five of a Kind | 25 | 14664 | 0.000095 | 0.002378 |
| Royal Flush | 10 | 26132 | 0.00017 | 0.001695 |
| Straight Flush | 2 | 184832 | 0.001199 | 0.002398 |
| All other | 0 | 153917452 | 0.998536 | 0 |
| Total | 154143080 | 1 | 0.006472 | |
The table that follows showcases the overall returns from the Dynasty Bonus correlated with the total number of participants, including the betting player. The house edge shown ranges from 3.70% to 6.94%.
Overall Dynasty Bonus Return — Fully Wild Joker
| Total Players | Return |
|---|---|
| 6 | -0.037009 |
| 5 | -0.043481 |
| 4 | -0.049953 |
| 3 | -0.056424 |
| 2 | -0.062896 |
| 1 | -0.069368 |
Protection Analysis
This table outlines the probability and return for each instance of the Protection bet. The bottom right cell indicates a house edge of 7.69%.
Protection Return Table
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| 9 High Pai Gow | 100 | 31080 | 0.000202 | 0.020163 |
| T High Pai Gow | 25 | 248640 | 0.001613 | 0.040326 |
| J High Pai Gow | 10 | 963480 | 0.006251 | 0.062506 |
| Q High Pai Gow | 6 | 2719500 | 0.017643 | 0.105856 |
| K High Pai Gow | 5 | 6386940 | 0.041435 | 0.207176 |
| A High Pai Gow | 4 | 12944820 | 0.083979 | 0.335917 |
| Non-Pai Gow | -1 | 130848620 | 0.848878 | -0.848878 |
| Total | 154143080 | 1 | -0.076934 |
Red/Black Analysis
The subsequent table illustrates the probability and return for each event related to the Red and Black bets. The lower right cell denotes a house edge of 2.68%.
Red/Black Return Table
| Winning Cards | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| 7 | 5 | 657800 | 0.004267 | 0.021337 |
| 4 to 6 | 1 | 73033740 | 0.473805 | 0.473805 |
| 0 to 3 | -1 | 80451540 | 0.521928 | -0.521928 |
| Total | 154143080 | 1 | -0.026786 |
Queen's Dragon Analysis
The following table reveals the probabilities and returns for every event concerning the Queen's Dragon bet. The lower right cell shows a substantial house edge of 18.84%.
Queen's Dragon Return Table
| Winning Cards | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Win | 45 | 2719500 | 0.017643 | 0.793921 |
| Lose | -1 | 151423580 | 0.982357 | -0.982357 |
| Total | 154143080 | 1 | -0.188436 |
Acknowledgement
I want to extend my gratitude to game creator Dan Lubin and mathematician Charles Mousseau from Future Sight Gaming for providing me with the mathematical analysis report that this page is based on.