Mar 23, 2016 Pai Gow Poker Betting Systems If there’s one thing gamblers love, it’s their betting systems. The idea is that systematizing their bets, both the amounts wagered and their timing, can improve their odds of making a profit over the long run. Beating the House – Overcoming the Pai Gow House Edge Playing Pai Gow Poker offers gamblers the opportunity to enjoy a casino game with a relatively low house edge of approximately 2.9%. In fact, the house edge in Pai Gow Poker is just slightly more than that of the much loved casino classic; blackjack. Beating Pai Gow Poker at your local casino isn't as tough as you think! Although there are books on the subject like Sanford Wong's Optimal Strategy for Pai Gow Poker, there are some simple things you can do to increase your chance of winning without reading a 150-page book!
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Introduction
This section contains my analysis of the following pai gow poker side bets:
Dealer Bonus
Please see my page on the Dealer Bonus for information on that side bet.
Fortune Pai Gow Poker
Please see my page on the Fortune side bet for information on that side bet.
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.
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.
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 that 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 |
Lucky 8's
Please see my page on the Lucky 8's for information on that side bet.
Pai Gow'd
Pai Gow'd is a side bet I noticed at the Four Queens on December 26, 2011. It is exactly like Pai Gow Insurance, explained above, but with a modified pay table. The lower right corner of the odds table below shows a house edge of 6.44%.
Pai Gow'd
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| 9 high pai gow | 100 | 31080 | 0.000202 | 0.020163 |
| 10 high pai gow | 50 | 248640 | 0.001613 | 0.080652 |
| J high pai gow | 10 | 963480 | 0.006251 | 0.062506 |
| 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 | -0.064384 |
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 |
This side bet is paired with pai gow poker games, including EZ Pai Gow, 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% |
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.
G3 Progressive
| 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.
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On This Page
Introduction
Pai Gow Poker is a variation of the Chinese domino game pai gow. The game is known for a slow rate of play and lots of pushes, resulting in low risk game. While a game of skill, most hands are obvious how to play, and it is not difficult to learn proper strategy for the rest of them. Every player plays against the same dealer hand, which causes the table to often win and lose together, resulting in a fun and social game.
History
Pai Gow Poker was invented in 1985 by Sam Torosian, owner of the Bell card club in southern California. However, his is a name few people recognize. While other have made millions inventing casino games, Sam received some bad legal advice that card games were not patentable, and never filed one for his game. When his game was a success at his own casino there was nothing to prevent competing casinos from offering the game as well, and they didn't have to pay Sam a dime.
Source: Casino Boss Can't Cash In on Game He Developed — Los Angeles Times, Nov. 3, 2002.
The Rules
- A single 53-card deck is used, consisting of the usual 52 cards, plus one joker.
- The joker is semi-wild. It may be used as an ace, or to complete a straight, flush, or straight flush, or royal flush. After the player makes a bet, the dealer will deal the player and himself seven cards each.
- Standard poker ranking rules are followed with one strange exception — the A2345 straight (known as 'the wheel') is considered the second highest straight. Some casinos have dropped this ridiculous rule, but most still cling to it.
- The player will separate his seven cards into a five-card high hand, and two-card low hand. The high hand must be of higher poker value than the low hand.
- The five-card hand is ranked according to conventional poker rules. The only poker hand in the two-card hand is a pair or no pair, after which the individual cards determine the value.
- After the player has set his hand, the dealer will turn over his cards and divide his hand in the same manner, according to specified rules known as the 'house way.'
- The two high hands will be compared, and the two low hands, the hand with the higher poker value winnings. If the event of a tie, for example both two-card hands are ace/king, then the tie has go to the 'banker.'
- If the player wins both comparisons, then the player will win even money on his bet, less a 5% commission. If the player wins one and loses one, then the bet shall push. If the player loses or ties both, then the player shall lose his wager.
- Unlike most casino games, the player may bet against the dealer, and other players in pai gow poker. This is known as 'banking.'
- The turn to act as banker is supposed to rotate around the table, but at some casinos it zig-zags between the dealer and each player in turn.
- The player may always decline to bank (which usually happens), in which case the option will revert to the next player, or dealer.
Strategy
I'm very proud to present my pai gow strategy page. It contains simple, intermediate, and advanced strategies for both playing as the banker, against the banker, and combined. This page took months for my assistant JB to create so I hope you'll have a look.
For your convenience, I also have my one-page simple pai gow poker strategy (PDF).
House Edge
The house advantage in Pai Gow Poker depends on partially on your skill setting hands but more on how much of the action you bank. I plan to publish some pai gow poker strategy in January, 2014. Until then, the following tables show the probability of each possible outcome and the expected value four ways — whether using the house way or optimal strategy and whether banking or the dealer is banking.
House way Strategy — Dealer Banker
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Win | 0.95 | 2,402,491,783,820,756 | 0.291195 | 0.276635 |
| Push | 0 | 3,341,087,256,920,524 | 0.404958 | 0.000000 |
| Loss | -1 | 2,506,879,990,473,120 | 0.303847 | -0.303847 |
| Total | 8,250,459,031,214,390 | 1.000000 | -0.027212 | |
House Way Strategy — Player Banker
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Win | 0.95 | 2,506,879,990,473,120 | 0.303847 | 0.288655 |
| Push | 0 | 3,341,087,256,920,524 | 0.404958 | 0.000000 |
| Loss | -1 | 2,402,491,783,820,756 | 0.291195 | -0.291195 |
| Total | 8,250,459,031,214,390 | 1.000000 | -0.002540 | |
Optimal Strategy — Dealer Banker
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Win | 0.95 | 2,413,147,766,131,848 | 0.292486 | 0.277862 |
| Push | 0 | 3,337,551,044,510,696 | 0.404529 | 0.000000 |
| Loss | -1 | 2,499,760,220,571,856 | 0.302984 | -0.302984 |
| Total | 8,250,459,031,214,400 | 1.000000 | -0.025122 | |
Optimal Strategy — Player Banker
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Win | 0.95 | 2,521,011,760,499,300 | 0.305560 | 0.290282 |
| Push | 0 | 3,330,840,908,447,708 | 0.403716 | 0.000000 |
| Loss | -1 | 2,398,606,362,267,392 | 0.290724 | -0.290724 |
| Total | 8,250,459,031,214,390 | 1.000000 | -0.000442 | |
The following table summarizes the expected value under all four scenarios. The 'difference' row and column show that banking, compare to not banking, increases expected value by 2.47%. The difference between following the house way and the theoretical optimal strategy, which I'm quite sure nobody knows, is 0.21%.
Summary
| Banker | House Way | Optimal | Difference |
|---|---|---|---|
| Player | -0.002540 | -0.000442 | 0.002098 |
| Dealer | -0.027212 | -0.025122 | 0.002090 |
| Difference | 0.024672 | 0.024680 |
Commission Free Pai Gow Poker
Often in Washington State the casino will not charge the 5% commission on banker wins. They make a profit on the banker's advantage and side bets only. With no commission, the banker has a 1.30% advantage, and all others playing against the banker a 1.30% disadvantage.
Banking Against Yourself
Sometimes, when a player invokes his right to bank, the other players will want a shot at whatever the side bet is, but dislike betting against another player on the primary wager. Another reason this might be done is to 'change the luck' at the table. In this case, non-banking players may make a deal with the banking player that if one beats the other, the winner will refund the loser, less the 5% commission. It is essentially banking against yourself through a gentleman's agreement with the banker. The dealer will have nothing to do with it. In some casinos, they will overtly not allow it, although it may be hard to prevent, especially if the deal is made in a foreign language the dealer doesn't know. I mention this as a warning that you may be asked to do this, if you choose to bank. How you respond is up to you, but I will say it may cause some ill-will at the table if you say 'no.'
There is a discussion of this in my forum at Wizard of Vegas.
The House Way
The house way is how the dealer arranges their own hand. It can vary from place to place the differences are marginal and happen infrequently. The house way is available for the following casinos:
- Great Britain (1124K PDF; see page 80)
- Silver Dollar (Washington)
- IGW (Software for Arrow's Edge Internet casinos)
Pai Gow Poker Probabilities
The following table shows the probability of forming any specified poker hand. These probabilities consider all seven cards and without regard to how the player may play the hand.
Probabilities in Pai Gow Poker
| Hand | Combinations | Probability |
|---|---|---|
| Five Aces | 1,128 | 0.00000732 |
| Straight/Royal Flush | 210,964 | 0.00136862 |
| Four of a Kind | 307,472 | 0.00199472 |
| Full House | 4,188,528 | 0.02717299 |
| Flush | 6,172,088 | 0.04004129 |
| Straight | 11,236,028 | 0.07289350 |
| Three of a Kind | 7,470,676 | 0.04846585 |
| Two Pair | 35,553,816 | 0.23065464 |
| One Pair | 64,221,960 | 0.41663862 |
| All Other | 24,780,420 | 0.16076246 |
| Total | 154,143,080 | 1 |
Note: The number of combinations for a Royal Flush is 26,132; 21,620 wild and 4,512 natural.
Internal Links
- pai gow strategy page.
- pai gow poker simple strategy (PDF).
- Ask the Wizard questions about Pai Gow Poker.
- EZ Pai Gow Poker.
- Commission Free Pai Gow Poker.
- Dealer Probabilities: Shows the probability the dealer will form any given hand or less. Useful for making accurate strategy decisions.
- When to split Two Pair: My advice on when to split two pair.
- Side Bets: Analysis of various side bets such as Fortune, Jackpot, and Emperor's Challenge.
- No Push Pai Gow Poker: My analysis of this Pai Gow Poker variant.
- Pai Gow Mania: My analysis.
- Play Pai Gow Poker. Play my Pai Gow Poker game.
- Face Up Pai Gow Poker — Variant where the dealer's cards are dealt face up.
External Links
Pai Gow Poker Betting System Reviews
German translation of this page.