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Fortune Pai Gow Poker Side Bet.

Introduction

"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.

Following are pay tables that I am aware of, based on the player's own hand. Wins are on a "to one" basis.

Fortune Pay TablesExpand

Hand Pay Table
1 2 3 4 5 6 7 8
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 8000 to 1 1000 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 2000 to 1 750 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 1000 to 1 500 to 1
5 Aces 250 to 1 400 to 1 400 to 1 250 to 1 400 to 1 300 to 1 400 to 1 250 to 1
Royal Flush 100 to 1 150 to 1 150 to 1 125 to 1 150 to 1 110 to 1 100 to 1 150 to 1
Straight Flush 50 to 1 50 to 1 50 to 1 50 to 1 50 to 1 45 to 1 30 to 1 50 to 1
4 of a Kind 20 to 1 25 to 1 25 to 1 25 to 1 25 to 1 25 to 1 20 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 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 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 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 2 to 1 2 to 1
Three Pair Push Loss Loss Loss Loss Loss Loss 1 to 1

The next table shows the Envy Bonus for each paytable.

Fortune Envy BonusesExpand

Hand Pay Table
1 2 3 4 5 6 7 8
Natural 7 Card S/F $1000 $5000 $3000 $1000 $2500 $2500 $5000 $500
Royal Flush + R/M $250 $1000 $1000 $750 $500 $500 $1000 $250
Wild 7 Card S/F $100 $500 $500 $250 $250 $250 $500 $150
5 Aces $50 $250 $250 $100 $150 $150 $250 $100
Royal Flush $25 $50 $50 $50 $55 $55 $50 $50
Straight Flush $10 $20 $20 $20 $25 $25 $20 $20
4 of a Kind $5 $5 $5 $5 $6 $6 $5 $5

The next table shows the number of combinations, probability, and contribution to the return for each hand, under pay table 2, which I believe to be the most popular. The lower left cell shows a house edge of 7.77% before considering the Envy Bonus.

Pay Table 2 -- Return Table

Hand Pays Combinations Probability Return
Natural seven-card straight flush 8,000 32 0.00000021 0.00166079
Royal Flush + R/M 2,000 72 0.00000047 0.00093420
Wild seven-card straight flush 1,000 196 0.00000127 0.00127155
Five Aces 400 1,128 0.00000732 0.00292715
Royal Flush 150 26,020 0.00016880 0.02532063
Straight flush 50 184,644 0.00119787 0.05989370
Four of a Kind 25 307,472 0.00199472 0.04986795
Full house 5 4,188,528 0.02717299 0.13586494
Flush 4 6,172,088 0.04004129 0.16016517
Three of a kind 3 7,672,500 0.04977518 0.14932555
Straight 2 11,034,204 0.07158417 0.14316833
Three pair -1 2,862,000 0.01856717 -0.01856717
All other -1 121,694,196 0.78948855 -0.78948855
Total 0 154,143,080 1.00000000 -0.07765575

The next table shows the return table for the Envy Bonus under pay table 2, based on a $5 bet. 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 equals 0.04634162/b, where b is the amount bet.

Envy Return Table -- Paytable 2

Hand Pays Combinations Probability Return
Natural seven-card straight flush $5,000 32 0.00000021 0.00020760
Royal Flush + R/M $1,000 72 0.00000047 0.00009342
Wild seven-card straight flush $500 196 0.00000127 0.00012715
Five Aces $250 1,128 0.00000732 0.00036589
Royal Flush $50 26,020 0.00016880 0.00168804
Straight flush $20 184,644 0.00119787 0.00479150
Four of a Kind $5 307,472 0.00199472 0.00199472
Total   519,564 0.00337066 0.00926832

The next table shows the contribution for each hand under all seven pay tables, before considering the Envy Bonus.

Fortune Pai Gow Poker Return — Expected ReturnsExpand

Hand Pay Table
1 2 3 4 5 6 7 8
7 Card Straight Flush 0.001038 0.001661 0.001038 0.000519 0.001038 0.001038 0.001661 0.000208
Royal Flush + Royal Match 0.000467 0.000934 0.000934 0.000467 0.000934 0.000467 0.000934 0.00035
7 Card Straight Flush with Joker 0.000954 0.001272 0.001272 0.000954 0.001272 0.000636 0.001272 0.000636
5 Aces 0.001829 0.002927 0.002927 0.001829 0.002927 0.002195 0.002927 0.001829
Royal Flush 0.01688 0.025321 0.025321 0.021101 0.025321 0.018568 0.01688 0.025321
Straight Flush 0.059894 0.059894 0.059894 0.059894 0.059894 0.053904 0.035936 0.059894
4 of a Kind 0.039894 0.049868 0.049868 0.049868 0.049868 0.049868 0.039894 0.049868
Full House 0.135865 0.135865 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 0.160165 0.160165
3 of a Kind 0.149326 0.149326 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 0.143168 0.143168
Three Pair 0 -0.018567 -0.018567 -0.018567 -0.018567 -0.018567 -0.018567 0.018567
All Other -0.789489 -0.789489 -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 -0.120027 -0.044292

 

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 Envy Bonus — Expected ReturnsExpand

Hand Pay Table
1 2 3 4 5 6 7 8
7 Card Straight Flush 0.000042 0.000208 0.000125 0.000042 0.000104 0.000104 0.000208 0.000021
Royal Flush + Royal Match 0.000023 0.000093 0.000093 0.00007 0.000047 0.000047 0.000093 0.000023
7 Card Straight Flush with Joker 0.000025 0.000127 0.000127 0.000064 0.000064 0.000064 0.000127 0.000038
5 Aces 0.000073 0.000366 0.000366 0.000146 0.00022 0.00022 0.000366 0.000146
Royal Flush 0.000844 0.001688 0.001688 0.001688 0.001857 0.001857 0.001688 0.001688
Straight Flush 0.002396 0.004791 0.004791 0.004791 0.005989 0.005989 0.004791 0.004791
4 of a Kind 0.001995 0.001995 0.001995 0.001995 0.002394 0.002394 0.001995 0.001995
Total 0.005398 0.009268 0.009185 0.008796 0.010674 0.010674 0.009268 0.008703
 

The next table shows the house edge for each pay table by total players (including yourself).

Fortune Bet Overall House EdgeExpand

Total
Players		 Pay Table
1 2 3 4 5 6 7 8
6 5.30% 3.13% 3.24% 4.09% 2.49% 3.95% 7.37% 0.08%
5 5.84% 4.06% 4.15% 4.97% 3.56% 5.02% 8.30% 0.95%
4 6.38% 4.99% 5.07% 5.85% 4.63% 6.08% 9.22% 1.82%
3 6.92% 5.91% 5.99% 6.73% 5.69% 7.15% 10.15% 2.69%
2 7.46% 6.84% 6.91% 7.61% 6.76% 8.22% 11.08% 3.56%
1 8.00% 7.77% 7.83% 8.49% 7.83% 9.29% 12.00% 4.43%
 

Fortune Pai Gow Poker Progressive -- Version 1

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 break-even 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

 

Fortune Pai Gow Poker Progressive - Version 2

This is a $1 progressive jackpot bet I have seen at the Wynn, Rampart, Golden Nugget, and Suncoast casinos. Wins are paid on a "for one" basis, in other words the player doesn't get his bet back if he wins. The return column shows the return for only fixed wins. In other words, not including the top two awards, the player can expect to get back 46.27% of his money back.

Fortune Pai Gow Poker House Edge

Event Pays Combinations Probability Return
Seven-card straight flush Jackpot 228 0.000001 ?
Five aces 10% of jackpot 1,128 0.000007 ?
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
Loser $0 149,434,988 0.969456 0.000000
Total   154,143,080 1.000000 0.462719

The value of the jackpot is 2.21% for each $10,000 in the meter. The break-even meter (where there house edge is exactly zero) is $243,011.06. I have yet to see a jackpot get anywhere near this high.

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Written by: Michael Shackleford