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EZ Pai Gow Poker (with Partially 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 5-card hand, then the hand will automatically resolve in a push. In addition, there are four side bets the player may wager on. There is also a fully-wild joker version is available to play in California.
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.
- Most casinos do not allow player banking. If they do, then the rules revert to normal pai gow poker for that hand.
- There are various side bets available, described separtely below.
Strategy
My strategy advice is that same as that for conventional pai gow poker. If you don't have time to study it, then if in doubt, ask the dealer to set your hand by the house way.
Analysis
The following table shows the probability and return from each outcome. The lower right cell shows a house edge of 2.47%.
EZ Pai Gow Poker Return Table — Partially Wild Joker
| Event | Pays | Probability | Return |
|---|---|---|---|
| Win | 1 | 0.274597 | 0.274597 |
| Push | 0 | 0.426112 | 0 |
| Lose | -1 | 0.299291 | -0.299291 |
| Total | 1 | -0.024694 |
Side Bets
There are lots of side bets that are available for casino management to tack onto EZ Pai Gow Poker. Here are some that I know of. You won't see all of these at any one table, probably just two or three of them.
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 four of a kind or higher, the player will win an "Envy Bonus." The following table shows what each hand pays for both the player's hand and the Envy Bonus. The cell bottom row in the second to last column shows a house edge of 8.16%, before considering the Envy Bonus. The cell in the bottom row and last column shows that each additional player lower the house edge by 0.90%, because of the Envy Bonus.
Version 1
In this version the player has to bet only $1 to qualify for the Envy Bonus.
Dynasty Bonus Return Table — Version 1
| Event | Dynasty Pays | Envy Bonus | Combinations | Probability | Dynasty Return | Envy Bonus |
|---|---|---|---|---|---|---|
| A-5 Straight Flush + Natural AQ Suited | 2000 | $100 | 12 | 0.000000 | 0.000156 | 0.000008 |
| Natural 7-card Straight Flush | 2000 | $80 | 32 | 0.000000 | 0.000415 | 0.000017 |
| Wild 7-card Straight Flush | 1000 | $40 | 196 | 0.000001 | 0.001272 | 0.000051 |
| Royal Flush + Natural AQ Suited | 1000 | $60 | 72 | 0.000000 | 0.000467 | 0.000028 |
| Five Aces | 500 | $20 | 1128 | 0.000007 | 0.003659 | 0.000146 |
| Royal Flush | 120 | $10 | 26020 | 0.000169 | 0.020257 | 0.001688 |
| A-5 Straight Flush | 120 | $15 | 4308 | 0.000028 | 0.003354 | 0.000419 |
| Straight Flush | 50 | $4 | 180324 | 0.001170 | 0.058492 | 0.004679 |
| Four of a Kind | 25 | $1 | 307472 | 0.001995 | 0.049868 | 0.001995 |
| Full House | 5 | $0 | 4188528 | 0.027173 | 0.135865 | 0.000000 |
| Flush | 4 | $0 | 6172088 | 0.040041 | 0.160165 | 0.000000 |
| Three of a Kind | 3 | $0 | 7672500 | 0.049775 | 0.149326 | 0.000000 |
| Straight | 2 | $0 | 11034204 | 0.071584 | 0.143168 | 0.000000 |
| Losing combinations | -1 | $0 | 124556196 | 0.808056 | -0.808056 | 0.000000 |
| Total | 154143080 | 1.000000 | -0.081593 | 0.009031 |
The next table shows the overall house edge according to the number of players, including yourself, and various bet amounts. Note that the high edge is lowest at a bet of $1. This is because the win for the Envy Bonus is the same, regardless how much the player bets.
Dynasty Bonus House Edge — Version 1
| Players | $1 bet | $2 bet | $3 bet | $5 bet | $10 bet |
|---|---|---|---|---|---|
| 6 | 3.64% | 5.90% | 6.65% | 7.26% | 7.71% |
| 5 | 4.55% | 6.35% | 6.96% | 7.44% | 7.80% |
| 4 | 5.45% | 6.80% | 7.26% | 7.62% | 7.89% |
| 3 | 6.35% | 7.26% | 7.56% | 7.80% | 7.98% |
| 2 | 7.26% | 7.71% | 7.86% | 7.98% | 8.07% |
| 1 | 8.16% | 8.16% | 8.16% | 8.16% | 8.16% |
Version 2
In this version the player has to bet $5 to qualify for the Envy Bonus, which are usually five times as large as the Envy Bonuses in version 1.
Dynasty Bonus Return Table — Version 2
| Event | Dynasty Pays | Envy Bonus | Combinations | Probability | Dynasty Return | Envy Bonus |
|---|---|---|---|---|---|---|
| A-5 Straight Flush + Natural AQ Suited | 2000 | $500 | 12 | 0.000000 | 0.000156 | 0.000008 |
| Natural 7-card Straight Flush | 2000 | $400 | 32 | 0.000000 | 0.000415 | 0.000017 |
| Royal Flush + Natural AQ Suited | 1000 | $300 | 72 | 0.000000 | 0.000467 | 0.000028 |
| Wild 7-card Straight Flush | 1000 | $200 | 196 | 0.000001 | 0.001272 | 0.000051 |
| Five Aces | 500 | $100 | 1128 | 0.000007 | 0.003659 | 0.000146 |
| Royal Flush | 120 | $75 | 26020 | 0.000169 | 0.020257 | 0.002532 |
| A-5 Straight Flush | 120 | $50 | 4308 | 0.000028 | 0.003354 | 0.000279 |
| Straight Flush | 50 | $20 | 180324 | 0.001170 | 0.058492 | 0.004679 |
| Four of a Kind | 25 | $5 | 307472 | 0.001995 | 0.049868 | 0.001995 |
| Full House | 5 | $0 | 4188528 | 0.027173 | 0.135865 | 0.000000 |
| Flush | 4 | $0 | 6172088 | 0.040041 | 0.160165 | 0.000000 |
| Three of a Kind | 3 | $0 | 7672500 | 0.049775 | 0.149326 | 0.000000 |
| Straight | 2 | $0 | 11034204 | 0.071584 | 0.143168 | 0.000000 |
| Losing combinations | -1 | $0 | 124556196 | 0.808056 | -0.808056 | 0.000000 |
| Total | 154143080 | 1.000000 | -0.081593 | 0.009735 |
The next table shows the overall house edge according to the number of players, including yourself, and various bet amounts. Note that the high edge is lowest at a bet of $1. This is because the win for the Envy Bonus is the same, regardless how much the player bets.
Dynasty Bonus House Edge — Version 2
| Players | $5 bet | $10 bet | $15 bet | $20 bet | $25 bet |
|---|---|---|---|---|---|
| 6 | 3.64% | 5.90% | 6.65% | 7.03% | 7.26% |
| 5 | 4.55% | 6.35% | 6.96% | 7.26% | 7.44% |
| 4 | 5.45% | 6.80% | 7.26% | 7.48% | 7.62% |
| 3 | 6.35% | 7.26% | 7.56% | 7.71% | 7.80% |
| 2 | 7.26% | 7.71% | 7.86% | 7.93% | 7.98% |
| 1 | 8.16% | 8.16% | 8.16% | 8.16% | 8.16% |
Bonus Bet
This is very similar to the Dynasty Bonus, and is paired with games offering the G3 electronic side bet wagering. As far as I can tell at the Rampart casino, it is just titled the "Bonus Bet."
Bonus Bet Return Table
| Event | Dynasty Pays | Envy Bonus | Combinations | Probability | Dynasty Return | Envy Bonus |
|---|---|---|---|---|---|---|
| Natural 7-card Straight Flush | 8000 | $5000 | 32 | 0.000000 | 0.001661 | 0.000208 |
| Royal Flush + Natural AQ Suited | 2000 | $1000 | 72 | 0.000000 | 0.000934 | 0.000093 |
| Wild 7-card Straight Flush | 1000 | $500 | 196 | 0.000001 | 0.001272 | 0.000127 |
| Five Aces | 400 | $250 | 1128 | 0.000007 | 0.002927 | 0.000366 |
| Royal Flush | 150 | $50 | 26020 | 0.000169 | 0.025321 | 0.001688 |
| Straight Flush | 50 | $20 | 184644 | 0.001198 | 0.059894 | 0.004791 |
| Four of a Kind | 25 | $5 | 307472 | 0.001995 | 0.049868 | 0.001995 |
| Full House | 5 | $0 | 4188528 | 0.027173 | 0.135865 | 0.000000 |
| Flush | 4 | $0 | 6172088 | 0.040041 | 0.160165 | 0.000000 |
| Three of a Kind | 3 | $0 | 7672500 | 0.049775 | 0.149326 | 0.000000 |
| Straight | 2 | $0 | 11034204 | 0.071584 | 0.143168 | 0.000000 |
| Losing combinations | -1 | $0 | 124556196 | 0.808056 | -0.808056 | 0.000000 |
| Total: | 154143080 | 1.000000 | -0.077656 | 0.009268 |
The next table shows the overall house edge according to the number of players, including yourself, and various bet amounts. Note that the high edge is lowest at a bet of $1. This is because the win for the Envy Bonus is the same, regardless how much the player bets.
Bonus Bet House Edge
| Players | $1-$4 bet | $5 bet | $10 bet | $15 bet | $25 bet |
|---|---|---|---|---|---|
| 6 | 7.77% | 3.13% | 5.45% | 6.22% | 6.84% |
| 5 | 7.77% | 4.06% | 5.91% | 6.53% | 7.02% |
| 4 | 7.77% | 4.99% | 6.38% | 6.84% | 7.21% |
| 3 | 7.77% | 5.91% | 6.84% | 7.15% | 7.39% |
| 2 | 7.77% | 6.84% | 7.30% | 7.46% | 7.58% |
| 1 | 7.77% | 7.77% | 7.77% | 7.77% | 7.77% |
Protection
Similar to Pai Gow Insurance, the Protection bet pays if the player?s best five-card hand is an ace high or less. The following table shows what each event pays, the probability, and contribution to the return. The lower right cell shows a house edge of 7.01%.
Protection Return Table
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| A-5 Straight flush | 120 | 4320 | 0.000028 | 0.003363 |
| 9 High Pai Gow | 100 | 31080 | 0.000202 | 0.020163 |
| T High Pai Gow | 25 | 248640 | 0.001613 | 0.040326 |
| J High Pai Gow | 15 | 963480 | 0.006251 | 0.093758 |
| Q High Pai Gow | 7 | 2719500 | 0.017643 | 0.123499 |
| K High Pai Gow | 5 | 6386940 | 0.041435 | 0.207176 |
| A High Pai Gow | 3 | 14430780 | 0.093619 | 0.280858 |
| Non-Pai Gow | -1 | 129358340 | 0.83921 | -0.83921 |
| Total: | 154143080 | 1 | -0.070066 |
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. The following table shows what each event pays, the probability, and contribution to the return. The lower right cell shows a house edge of 2.68%.
Protection Return Table
| Event | 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
The Queen's Dragon pays if the dealer has exactly a queen-high pai gow hand. Winning bets may pay 45 or 50 to 1, depending on how generous/stingy casino management is. The following two return tables show the house edge is 18.84% at 45 to 1, and 10.02% at 50 to 1.
Queen's Dragon — 45 to 1
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Queen-high pai gow | 45 | 2,719,500 | 0.017643 | 0.793921 |
| Lose | -1 | 151,423,580 | 0.982357 | -0.982357 |
| Total | 154,143,080 | 1.000000 | -0.188436 |
Queen's Dragon — 50 to 1
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Queen-high pai gow | 50 | 2,719,500 | 0.017643 | 0.882135 |
| Lose | -1 | 151,423,580 | 0.982357 | -0.982357 |
| Total | 154,143,080 | 1.000000 | -0.100222 |
Progressive Pai Gow
This is a progressive side bet found with G3 electronic betting units. The player may bet $1 to $25. All jackpot wins are the same, regardless of bet size, so I would never bet more than $1. As usual with progressive bets, wins are on a "for one" basis. That means you don't get your original bet back, even if you win. To be consistent with other pages on this site, the following page is on a "return basis," meaning what the player can expect to get back for his bet, based on a $1 bet.
Progressive Pai Gow
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| 7-card Straight Flush | Jackpot | $228 | 0.000001 | 0.000000 |
| Five Aces | 0.1×Jackpot | $1,128 | 0.000007 | 0.000000 |
| Royal Flush | $500 | $26,092 | 0.000169 | 0.084636 |
| Straight Flush | $100 | $184,644 | 0.001198 | 0.119787 |
| Four of a Kind | $75 | $307,472 | 0.001995 | 0.149604 |
| Full House | $4 | $4,188,528 | 0.027173 | 0.108692 |
| All other | 0 | $149,434,988 | 0.969456 | 0.000000 |
| Total | 154,143,080 | 1.000000 | 0.462719 |
The bottom right corner shows a return of 46.27% on all fixed wins. The value of the progressive is 22.11% for each $100,000 in the meter. To reach 100% the meter would need to be $243,011.06. When I saw this bet at the Rampart casino on March 17, 2011, the meter was at $207,361, for a return of 92.12%. This was probably unusually high, because the Rampart has had a truck with a big sign in the back drive around Summerlin promoting the large jackpot.
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.