Last Updated: September 11, 2019

# 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:

1. There is no commission.
2. 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.
3. Most casinos do not allow player banking. If they do, then the rules revert to normal pai gow poker for that hand.
4. 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.

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