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EZ Pai Gow Poker (with Fully Wild Joker)
Introduction
EZ Pai Gow Poker is a commission-free pai gow poker variant. Instead of the usual 5% commission, if the dealer has exactly a queen high "pai gow" hand, then the hand will automatically resolve in a push. In addition, there are four side bets the player may wager on. The game launched in June 2009 at the Pechanga and Barona casinos in the San Diego area. There is also a partially-wild joker version.
Rules
The rules are the same as conventional pai gow poker, except:
- There is no commission.
- If the dealer has a queen-high hand, meaning the poker-value of the best five-card hand is exactly a queen high, the hand will automatically result in a push.
- Some casinos allow player banking. If the player invokes this option, then the rules will revert to those for normal pai gow poker.
- This page reflects the version of EZ Pai Gow Poker, played in California, where the joker is fully wild.
- There are four side bets available, descibed separtely below.
Dynasty Bonus
Similar to the Fortune Bonus in conventional pai gow, the Dynasty Bonus pays if the player's best five-card hand is at least a three of a kind. It does not matter how the player sets his hand. If another player gets a straight flush or higher, the player will win an "envy bonus." If the player only wins an Envy Bonus, he will still win the bonus but lose his Dynasty Bonus wager. Following is the complete pay table.
Dynasty Bonus Pay Table — 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 pays if the player's best five-card hand is an ace high or less. Following is the complete pay table.
Protection Pay Table — 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 wagers pay if the chosen color is in the majority of the player's cards. In other words, the player needs at least four cards of the chosen side to win. The joker counts as neither 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 pays if the dealer has exactly a queen-high pai gow hand. Winning bets pay 45 to 1.
Strategy
I can't offer any better strategy than the house way itself, which can be found on my page for the Barona pai gow poker house way.
Analysis
This section will present the analysis of the main EZ Pai Gow Poker bet analysis, and that of all four side bets.
EZ Pai Gow Poker Analysis
The following table shows the house edge when the player is not banking, assuming both the player and dealer or banker follow the same house way strategy. The lower right cell shows 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 following table shows the probability and contribution to the return for the Dynasty Bonus, before considering the Envy Bonus. The lower right cell shows a house edge of 6.94%.
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 following table shows the probability and contribution to the return for the Dynasty Bonus Envy Bonus, for each additional player, based on a $5 wager. The bottom right cell shows that each additional player lowers 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 following table shows the overall return on the Dynasty Bonus, according to the total number of players, including the player making the wager. It shows the house edge 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
The following table shows the probability and return for each event of the Protection bet. The lower right cell shows 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 following table shows the probability and return for each event of the Red and Black bets. The lower right cell shows 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 shows the probability and return for each event of the Queen's Dragon bet. The lower right cell shows a 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 would like to thank game inventor Dan Lubin and mathematician Charles Mousseau of Future Sight Gaming for providing me the mathematical analysis report of this game, which this page is based on.