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Fortune Pai Gow Poker Side Bet.

Introduction

"Fortune\" represents a side wager in Pai Gow Poker that rewards players based on the strength of their seven cards. The arrangement of cards does not impact the payout. Furthermore, if another participant achieves a four of a kind or higher, the player who placed the Fortune bet qualifies for an 'Envy Bonus.' Typically, there is a minimum bet of $5 at every table, and the Envy Bonus is a predetermined sum.

Here are some payout tables that reflect outcomes based on the player's hand. The wins are expressed 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 subsequent table illustrates the Envy Bonus for each specific payout table.

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 following table details the number of combinations, their probabilities, and the expected contribution to the player’s return for each hand according to pay table 2, which is commonly favored. The lower left section indicates a house edge of 7.77% before taking the Envy Bonus into account.

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 presents the return expectations for the Envy Bonus based on a $5 wager. It shows that the presence of each additional player at the table contributes an additional 0.93% value based on this $5 stake. Should the player wager more than $5, the value of the Envy Bonus equates to 0.04634162 divided by the total wagered amount.

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

This table provides an overview of the contribution for each hand across all seven payout structures, not factoring in the Envy Bonus.

Fortune Pai Gow Poker Return — Anticipated 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 following table outlines expected returns for the Envy Bonus based on a $5 bet, highlighting the reduction in the house edge as more players join the table.

Fortune Pai Gow Poker Envy Bonus — Anticipated 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

This table reveals the house edge corresponding to each payout structure, accounting for the total number of players at the table (including the bettor).

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 — Option 1

I have received an unofficial report suggesting that a specific payout table is available in Washington State, with a $1 minimum bet. Notably, this version does not include an Envy Bonus. According to the return table, the fixed wins yield a return of 48.45%. The return increases by 0.76% for every $10,000 accumulated in the meter, setting a break-even point at $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 — Option 2

This pertains to a $1 progressive jackpot bet encountered at casinos such as Wynn, Rampart, Golden Nugget, and Suncoast. The wins are disbursed on a 'for one' basis, meaning the player does not have their original bet refunded upon winning. The return column indicates the payout from fixed wins only; therefore, excluding the top two prizes, the player can anticipate a return of 46.27% of their wager.

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 jackpot value increases by 2.21% for every $10,000 in the meter, with a breakeven point established at $243,011.06. I have yet to witness a jackpot reach such heights.

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Written by: Michael Shackleford