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EZ Pai Gow Poker (featuring a Partially Wild Joker)
Introduction
In EZ Pai Gow Poker, there are no commissions involved. Pai Gow Poker This game variant eliminates the usual 5% commission. Instead, if the dealer showcases a queen-high hand consisting of five cards, the round will end in a tie or push. Additionally, players can place bets on four different side wagers. Furthermore, there’s a Fully-wild joker version Is available to play in California.
Rules
The gameplay follows the same principles as traditional pai gow poker, with a few distinctions:
- There is no commission.
- A hand will be deemed a push if the dealer has a five-card hand that is only queen-high.
- Typically, players are not permitted to act as the banker in most casinos; however, if this option is available, standard rules will apply. Pai Gow Poker For that hand.
- There are multiple side bets that can be made, which are explained in detail below.
Strategy
The strategic insights I provide align with those applicable to Conventional Pai Gow Poker If you're pressed for time and unsure about the best move, it’s advisable to let the dealer arrange your hand in the house-specific manner.
Analysis
The table below illustrates the probabilities and potential returns associated with each possible outcome, showing a house edge of 2.47% in the bottom right corner.
EZ Pai Gow Poker Return Table — Featuring 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
Casino operators may offer various side bets that complement EZ Pai Gow Poker. Here are several examples that I am aware of, but you might not encounter all of these at the same table – typically, just two or three.
Dynasty Bonus
Similar to the Fortune Bonus In traditional pai gow, the Dynasty Bonus rewards players if their best five-card hand includes at least three of a kind. The player's hand setting does not matter. Should another player obtain four of a kind or a better hand, they will receive an 'Envy Bonus.' The next table outlines the payouts for both the player’s hand and the Envy Bonus. The bottom row of the second to last column reveals a house edge of 8.16%, excluding the effects of the Envy Bonus. Additionally, every extra player reduces the house edge by 0.90% due to the Envy Bonus.
Version 1
For this variant, players need to place a minimum bet of $1 to be eligible 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 subsequent table depicts the overall house edge depending on the number of players involved, including yourself, and the various stake amounts. It's noteworthy that the highest edge is the lowest at a bet of $1, as the payout for the Envy Bonus remains constant, independent of the player's wager amount.
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 iteration, players are required to place a bet of $5 to qualify for the Envy Bonus, which is typically five times larger than the bonuses available 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 subsequent table depicts the overall house edge depending on the number of players involved, including yourself, and the various stake amounts. It's noteworthy that the highest edge is the lowest at a bet of $1, as the payout for the Envy Bonus remains constant, independent of the player's wager amount.
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 closely related to the Dynasty Bonus and is often associated with games offering G3 electronic side bets. In the Rampart casino, this offering is simply referred to as 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 subsequent table depicts the overall house edge depending on the number of players involved, including yourself, and the various stake amounts. It's noteworthy that the highest edge is the lowest at a bet of $1, as the payout for the Envy Bonus remains constant, independent of the player's wager amount.
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 out when the best hand of the player is ace-high or lower. The table below details each potential payout, the associated probabilities, and their contribution towards the potential return. The lower right cell illustrates 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 result in a win if the selected color predominates among the player's cards; therefore, at least four cards of the chosen color are needed to secure a victory. It's important to note that the joker does not count for either color. The following table outlines the payouts, probabilities, and contributions to the return, with a house edge of 2.68% shown in the lower right corner.
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 win occurs if the dealer possesses a pai gow hand that is exactly queen-high. Successful bets can yield payouts of either 45 to 1 or 50 to 1, depending on the casino's payout policies. The next two return tables indicate a house edge of 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 progressive side bet is available through G3 electronic betting units, with stakes ranging from $1 to $25. All jackpot payouts are the same irrespective of the stake size, so I would suggest only wagering $1. Standard practice with progressive bets indicates that wins are awarded on a 'for one' basis, meaning the original stake will not be returned even on winning bets. For consistency with other site pages, the upcoming section is presented on a 'return basis' to highlight what players can anticipate receiving back from their bets, assuming a $1 stake.
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 lower right corner reveals a return rate of 46.27% for all fixed wins. The value attached to the progressive bet is 22.11% for each $100,000 reflected in the meter. To achieve a complete return of 100%, the meter would need to reach a total of $243,011.06. When I observed this wager at Rampart casino on March 17, 2011, the meter was displayed at $207,361, yielding a return rate of 92.12%. This amount was likely inflated, as Rampart has promoted this large jackpot with a mobile advertisement.
Acknowledgement
I extend my gratitude to the game's creator, Dan Lubin, and mathematician Charles Mousseau of Future Sight Gaming for sharing the mathematical analysis report of this game, which serves as the foundation for this information.