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Pai Gow Poker Side Bets

Last update: Sep. 23, 2009

This sections contains my analysis of the following pai gow poker side bets:

Fortune Pai Gow Poker

"Fortune" is a side bet in Pai Gow Poker that pays based on the value of the player's seven cards. It doesn't not matter how the player sets his hand. In addition, if another player has a four of a kind or better the player making the Fortune bet will get an "Envy Bonus." At every table I have seen there is a $5 minimum and the Envy Bonus is a fixed amount.

According to Shuffle Master literature there are six pay tables available as follows.

Fortune Pai Gow Poker Return Paytables
Hand Paytable 1 Paytable 2 Paytable 3 Paytable 4 Paytable 5 Paytable 6
Natural 7 Card S/F 5,000 to 1 8,000 to 1 5,000 to 1 2,500 to 1 5,000 to 1 5,000 to 1
Royal Flush + R/M 1,000 to 1 2,000 to 1 2,000 to 1 1,000 to 1 2,000 to 1 1,000 to 1
Wild 7 Card S/F 750 to 1 1,000 to 1 1,000 to 1 750 to 1 1,000 to 1 500 to 1
5 Aces 250 to 1 400 to 1 400 to 1 250 to 1 400 to 1 300 to 1
Royal Flush 100 to 1 150 to 1 150 to 1 125 to 1 150 to 1 110 to 1
Straight Flush 50 to 1 50 to 1 50 to 1 50 to 1 50 to 1 45 to 1
4 of a Kind 20 to 1 25 to 1 25 to 1 25 to 1 25 to 1 25 to 1
Full House 5 to 1 5 to 1 5 to 1 5 to 1 5 to 1 5 to 1
Flush 4 to 1 4 to 1 4 to 1 4 to 1 4 to 1 4 to 1
3 of a Kind 3 to 1 3 to 1 3 to 1 3 to 1 3 to 1 3 to 1
Straight 2 to 1 2 to 1 2 to 1 2 to 1 2 to 1 2 to 1
Three Pair Push Loss Loss Loss Loss Loss
All Other Loss Loss Loss Loss Loss Loss

The next table shows the Envy Bonus for each paytable.

Fortune Pai Gow Poker Envy Bonuses
Hand Paytable 1 Paytable 2 Paytable 3 Paytable 4 Paytable 5 Paytable 6
7 Card Straight Flush $1000 $5000 $3000 $1000 $2500 $2500
Royal Flush + Royal Match $250 $1000 $1000 $750 $500 $500
7 Card Straight Flush with Joker $100 $500 $500 $250 $250 $250
5 Aces $50 $250 $250 $100 $150 $150
Royal Flush $25 $50 $50 $50 $55 $55
Straight Flush $10 $20 $20 $20 $25 $25
4 of a Kind $5 $5 $5 $5 $6 $6

In my experience Paytable 2 is the most common, at least here in Las Vegas. The next table shows the number of combinations, probability, and contribution to the return for each hand. The lower left cell shows a house edge of 7.77% before considering the Envy Bonus.

Fortune Pai Gow Poker Detailed Return Table for Paytable 2
Event Pays Combinations Probability Return
7 Card Straight Flush 8,000 to 1 32 0.00000021 0.00166079
Royal Flush + Royal Match 2,000 to 1 72 0.00000047 0.0009342
7 Card Straight Flush with Joker 1,000 to 1 196 0.00000127 0.00127155
5 Aces 400 to 1 1128 0.00000732 0.00292715
Royal Flush 150 to 1 26020 0.0001688 0.02532063
Straight Flush 50 to 1 184644 0.00119787 0.0598937
4 of a Kind 25 to 1 307472 0.00199472 0.04986795
Full House 5 to 1 4188528 0.02717299 0.13586494
Flush 4 to 1 6172088 0.04004129 0.16016517
3 of a Kind 3 to 1 7672500 0.04977518 0.14932555
Straight 2 to 1 11034204 0.07158417 0.14316833
Three Pair Loss 2862000 0.01856717 -0.01856717
All Other Loss 121694196 0.78948855 -0.78948855
Total 154143080 1 -0.07765575

The next table shows the return table for the Envy Bonus under paytable 2. The lower right cell shows that each additional player at the table is worth 0.93%, based on a $5 bet. If the player bets more than $5 the value of the Envy Bonus is 0.0463/b, where b is the amount bet.

Fortune Pai Gow Poker Detailed Return Table Paytable 2 Envy Bonus
Event Pays Combinations Probability Return
7 Card Straight Flush 1000 to 1 32 0.00000021 0.0002076
Royal Flush + Royal Match 200 to 1 72 0.00000047 0.00009342
7 Card Straight Flush with Joker 100 to 1 196 0.00000127 0.00012715
5 Aces 50 to 1 1128 0.00000732 0.00036589
Royal Flush 10 to 1 26020 0.0001688 0.00168804
Straight Flush 4 to 1 184644 0.00119787 0.0047915
4 of a Kind 1 to 1 307472 0.00199472 0.00199472
All Other Loss 153623516 0.99662934 0
Total 154143080 1 0.00926832

The next table shows the contribution for each hand under all six pay tables. The bottom row shows the player's expected return before factoring in the Envy Bonus.

Fortune Pai Gow Poker Return Tables for Paytables 1 to 6
Hand Paytable 1 Paytable 2 Paytable 3 Paytable 4 Paytable 5 Paytable 6
7 Card Straight Flush 0.001038 0.001661 0.001038 0.000519 0.001038 0.001038
Royal Flush + Royal Match 0.000467 0.000934 0.000934 0.000467 0.000934 0.000467
7 Card Straight Flush with Joker 0.000954 0.001272 0.001272 0.000954 0.001272 0.000636
5 Aces 0.001829 0.002927 0.002927 0.001829 0.002927 0.002195
Royal Flush 0.01688 0.025321 0.025321 0.021101 0.025321 0.018568
Straight Flush 0.059894 0.059894 0.059894 0.059894 0.059894 0.053904
4 of a Kind 0.039894 0.049868 0.049868 0.049868 0.049868 0.049868
Full House 0.135865 0.135865 0.135865 0.135865 0.135865 0.135865
Flush 0.160165 0.160165 0.160165 0.160165 0.160165 0.160165
3 of a Kind 0.149326 0.149326 0.149326 0.149326 0.149326 0.149326
Straight 0.143168 0.143168 0.143168 0.143168 0.143168 0.143168
Three Pair 0 -0.018567 -0.018567 -0.018567 -0.018567 -0.018567
All Other -0.789489 -0.789489 -0.789489 -0.789489 -0.789489 -0.789489
Total -0.080008 -0.077656 -0.078279 -0.0849 -0.078279 -0.092855

The next table shows the return table for the Envy Bonus, based on a $5 bet. The bottom row shows how much the house edge is reduced for each other player at the table.

Fortune Pai Gow Poker Return Tables for Envy Bonus
Hand Paytable 1 Paytable 2 Paytable 3 Paytable 4 Paytable 5 Paytable 6
7 Card Straight Flush 0.000042 0.000208 0.000125 0.000042 0.000104 0.000104
Royal Flush + Royal Match 0.000023 0.000093 0.000093 0.00007 0.000047 0.000047
7 Card Straight Flush with Joker 0.000025 0.000127 0.000127 0.000064 0.000064 0.000064
5 Aces 0.000073 0.000366 0.000366 0.000146 0.00022 0.00022
Royal Flush 0.000844 0.001688 0.001688 0.001688 0.001857 0.001857
Straight Flush 0.002396 0.004791 0.004791 0.004791 0.005989 0.005989
4 of a Kind 0.001995 0.001995 0.001995 0.001995 0.002394 0.002394
Total 0.005398 0.009268 0.009185 0.008796 0.010674 0.010674

The next table shows the overall house edge according to both the paytable and the number of players (including yourself).

Fortune Pai Gow Poker House Edge
Players Paytable 1 Paytable 2 Paytable 3 Paytable 4 Paytable 5 Paytable 6
6 5.3% 3.13% 3.24% 4.09% 2.49% 3.95%
5 5.84% 4.06% 4.15% 4.97% 3.56% 5.02%
4 6.38% 4.99% 5.07% 5.85% 4.63% 6.08%
3 6.92% 5.91% 5.99% 6.73% 5.69% 7.15%
2 7.46% 6.84% 6.91% 7.61% 6.76% 8.22%
1 8% 7.77% 7.83% 8.49% 7.83% 9.29%

Fortune Pai Gow Poker Progressive

I have an unconfirmed report that the following pay table is offered in Washington State. The bet amount is $1, nd there is no Envy Bonus. The following return table shows the return from the fixed wins only is 48.45%. For every $10,000 in the meter, the return will go up by 0.76%. The breakeven meter (when there is no house edge) is $679,171.90

Fortune Pai Gow Poker House Edge
Event Pays Combinations Probability Return
7 Card Straight Flush 100% of meter 32 0.00000021 0
Royal Flush + Royal Match 50% of meter 72 0.00000047 0
7 Card Straight Flush with Joker 25% of meter 196 0.00000127 0
5 Aces 2500 1128 0.00000732 0.01829469
Royal Flush 200 26020 0.0001688 0.03376084
Straight Flush 100 184644 0.00119787 0.11978741
4 of a Kind 75 307472 0.00199472 0.14960386
Full House 6 4188528 0.02717299 0.16303793
All Other 0 149434988 0.96945635 0
Total 154143080 1 0.48448473

Jackpot Pai Gow Poker

"Jackpot" is a side bet I noticed at the Rio in November 2005. The game was closed at the time so the top prize was not evident, but according to the Shufflemaster web site it is alternatively $25,000; $50,000; or $100,000.

The following table shows the probability and return for each possible event. A $100,000 for the top win is assumed and a $5 bet, for a win of 20,000 to one. The table also assumes the player will always set his hand to maximize the value of the side bet, at the possible cost of his pai gow poker bet. The lower left cell shows a house edge of 2.21%, which for a side bet is pretty good.

Jackpot Pai Gow Poker Return Table
Event Pays Combinations Probability Return
Natural Royal plus Pair of Aces* 20000 12 0.00000008 0.001557
Five Aces plus Pair 400 72 0.00000047 0.000187
Royal Flush plus Pair 200 1560 0.00001012 0.002024
Five Aces 200 1056 0.00000685 0.00137
Royal Flush 100 24560 0.00015933 0.015933
Straight Flush plus Pair 60 11748 0.00007621 0.004573
Four of a Kind plus Pair 40 57648 0.00037399 0.01496
Straight Flush 30 173084 0.00112288 0.033686
Four of a Kind 20 249824 0.00162073 0.032415
Full House plus Pair 12 150480 0.00097624 0.011715
Flush plus Pair 8 489260 0.00317406 0.025393
Straight plus Pair 6 1155536 0.00749652 0.044979
Full House 6 4024560 0.02610925 0.156655
Flush 4 5631420 0.03653372 0.146135
Straight 3 10145388 0.06581799 0.197454
Three of a kind 2 7470676 0.04846585 0.096932
Nothing -1 124556196 0.80805571 -0.808056
Total 154143080 1 -0.022088

* Both royal flush and pair of aces must be natural (no joker) for highest win.

If the top prize is less than $100,000, or the player bets more than $5 on the side bet, the return will be slightly less. The next table shows the house edge according to various other wins for a natural royal plus pair of aces according to the win on a to one basis.

House Edge by Highest Win
Natural Royal plus Aces Pays House Edge
20000 2.21%
10000 2.29%
5000 2.33%
4000 2.33%
3000 2.34%
2000 2.35%
1000 2.36%

Emperor's Challenge

Emperor's Challenge is a side bet I noticed at Hooter's Casino in Las Vegas in April, 2006. The following return table shows the probability and return of all possible outcomes. The lower right cell shows a house edge of 4.171%.

Emperor's Challenge Return Table
Event Pays Combinations Probability Return
Natural 7-card straight flush 5000 32 0.00000021 0.001038
Wild 7-card straight flush 1000 196 0.00000127 0.001272
Five aces 500 1128 0.00000732 0.003659
Royal Flush 150 26092 0.00016927 0.025391
Straight Flush 50 184644 0.00119787 0.059894
Four of a Kind 25 307472 0.00199472 0.049868
Full House 5 4188528 0.02717299 0.135865
Flush 4 6172088 0.04004129 0.160165
Three of a kind 3 7672500 0.04977518 0.149326
Straight 2 11034204 0.07158417 0.143168
9 high pai gow 40 31080 0.00020163 0.008065
10 high pai gow 5 248640 0.00161305 0.008065
J high pai gow 2 963480 0.00625056 0.012501
Nonpaying hand -1 123312996 0.79999048 -0.79999
Total 154143080 1 -0.041714

I hear that in Washington State the player must bet at least $5 to qualify for the pai gow hands. See the Washington State Gaming Commission dealing procedures for more information.

Progressive Pai Gow Poker

The Falls View casino in Niagara Falls Ontario offers "Progressive Pai Gow Poker". This is basic pai gow poker with an added $5 side bet. They have an online rule card for the game.

The following table shows the return table based on a breakeven meter of 20536.05 bet units, which for a $5 bet is $102,680.24. The house edge at all other times is 11.5428% less 1.1242% for every $10,000 in the meter.

Progressive Pai Gow Poker Return Table
Event Pays Combinations Probability Return
Natural Royal Flush or Five Aces + pair 20536.05 336 0.000002 0.044764
Wild Royal Flush + pair 200 1260 0.000008 0.001635
Straight Flush + pair 50 11748 0.000076 0.003811
Four of a Kind + pair 40 57648 0.000374 0.01496
Full House + pair 12 150480 0.000976 0.011715
Flush + pair 8 489260 0.003174 0.025393
Straight + pair 4 1117388 0.007249 0.028996
Natural Royal Flush or Five Aces 2053.6 5304 0.000034 0.070664
Wild Royal Flush 100 20360 0.000132 0.013209
Straight Flush 25 173084 0.001123 0.028072
Four of a Kind 20 249824 0.001621 0.032415
Full House 6 4030416 0.026147 0.156883
Flush 4 5663712 0.036743 0.146973
Straight 2 10071516 0.065339 0.130677
Three of a kind 2 7544548 0.048945 0.09789
Nothing -1 124556196 0.808056 -0.808056
Total 154143080 1 0

Pai Gow Insurance

Pai gow “insurance” is a side bet I noticed at the Red Rock casino in August, 2008. It appeared along with the Emperor’s Challenge side bet. A “pai gow” in pai gow poker is a hand with seven singletons, where no straight or flush is possible. This side bet wins if the player had a pai gow, the lower the highest card, the more it pays. The following return table shows the details. The lower right cell shows a house edge of 7.35%.

Pai Gow Insurance
Event Pays Combinations Probability Return
9 high pai gow 100 31080 0.000202 0.020163
10 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
Loser -1 129362660 0.839238 -0.839238
Total 154143080 1 -0.073457

Jokolor

The Jokolor is a side bet mentioned on page 85 in the a document titled Rules of casino games in Great Britain (1124K). The side bet wins if the player has a joker and/or all cards of the same color. The following table shows the house edge is 3.90%.
Jokolor
Event Pays Combinations Probability Return
Six cards same color plus joker 30 460460 0.002987 0.089617
Seven cards same color, without joker 10 1315600 0.008535 0.085349
Any hand with joker 5 19898060 0.129088 0.645441
Loser -1 132468960 0.85939 -0.85939
Total 154143080 1 -0.038982

My Pai Gow Poker coverage

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