Pai Gow Poker Side Bets
Last update: Mar. 20, 2008
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 |
My Pai Gow Poker coverage
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