Pai Gow Poker Odds Calculator
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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
German translation of this page.
Pai-Gow poker--also known as double-hand poker--was invented in the 1980s, but its roots stretch back much further. That's because the game takes inspiration from the popular Chinese domino game known as pai gow, which came into being sometime around 960 AD.
The purpose of this article is to familiarize you with the basics of the game, from the rules of pai gow poker to various forms of real-money strategy. While the house will always maintain an edge over the player, an increased knowledge of the game should give you the best odds of walking away with a profit.
The Joker in Pai-Gow Poker
In addition to the usual 52 cards, the deck used in pai-gow poker also includes a single joker. The joker may substitute for any card in order to complete a straight, flush, or straight flush. Otherwise, it counts as an ace.
Pai-Gow Hand Rankings
While most of the rankings in double-hand poker are the same as regular poker, there are a few minor differences.
Five of a Kind - The highest possible pai gow poker hand, it's comprised of four aces and a joker.
Royal Flush - Made up of the following cards in the same suit: A, K, Q, J, 10.
Straight Flush - Five cards of the same suit in consecutive order. Example: 6H, 7H, 8H, 9H, 10H.
Four of a Kind - Four cards made up of the same rank. For example: 7H, 7D, 7C, 7S.
Full House - A hand comprised of one pair and three of a kind. Example: 4H, 4D, 4S, 6S, 6H.
Flush - Five cards made up of the same suit. Example: 2H, 4H, 5H, 8H, 10H.
Straight - Five consecutive cards of different suits. Example: 7H, 8S, 9C, 10C, JD.
Three of a Kind - Three cards of the same rank. Example: 2S, 2D, 2H.
Two Pair - Two individual pairs, each made up of a different rank. Example: 4C, 4D, 9H, 9C.
One Pair - Two cards of the same rank. Example: 4S, 4D.
High Card - When the hand contains none of the above combinations, the highest card is used to determine the hand's value.
How to Play Pai-Gow Poker for Real Money
Now that we've looked at the purpose of the joker and the hand rankings, let's examine the specific rules of pai-gow poker. Keep in mind that the player is competing only against the dealer.
The game begins when the player makes a wager. Betting requirements differ from one casino to another, so make sure you check before starting play.
After the player has made their bet, they will be provided with seven cards. The dealer also receives seven cards face-down.
The player examines his hand and separates it into a five-card ('high') and two-card ('low') hand. The five-card option must be superior to the two-card hand (see the hand rankings listed above). The two-card hand can only achieve a pair or high card ranking.
Casino near santa clara ca. Once the player has set his hand, the dealer turns his cards over and also arranges them into 5-card and 2-card sets. In both land-based and online casinos, the house has specific rules for how this is done, which prevents the dealer from having to employ any kind of strategy. This is known as the 'house way.'
The hands are now compared against one another. Here are the results:
- If both the player's hands are superior, he is declared the winner and receives even money on his payout, minus a 5% commission.
- If the player and dealer each win a hand, then the bet is considered a push.
- If the dealer wins both hands, the player loses his bet. Please note that a dealer wins any ties.
Hand Odds in Pai-Gow Poker
The following list shows the probability of achieving various hands in a game of double-hand poker.
- Five Aces - 0.00000732
- Royal Flush/Straight - 0.00136862
- Four of a Kind - 0.00199472
- Full House - 0.02717299
- Flush - 0.04004129
- Straight - 0.07289350
- Three of a Kind - 0.04846585
- Two Pair - 0.23065464
- One Pair - 0.41663862
- Anything Else - 0.16076246
Pai Gow Poker Betting Strategy
Winning Strategies for Real-Money Pai-Gow Poker
If you're looking for an edge during your next pai gow poker session, give these tips a try. While you may still lose some hands, you should see your overall success rate improve.
Pai Gow Strategy
- Avoid Bonus Bets - These side bets are far more common at land-based casinos, but even if you find an online establishment that offers them, they are to be avoided. Casinos take in more money from bonus bets than they do from the 5% commission charged to winning player hands.
- If you're lucky enough to get five aces, you should keep three in the high hand and move the others to the low hand. The only exception is when you have a pair of kings. In this case, move the kings to the low hand.
- When you have four of a kind, the following strategy should be employed. Keep the four cards together if their ranks are six or lower. If the ranks are seven through 10, split the cards unless you also have an ace or better to move to the low hand. Unless you have another pair to use in the low hand, four of a kind with face cards should always be split.
- Three of a kind should almost always be kept together. The only exception is when the cards are aces. In this case, use a pair of aces in the high hand and the remaining ace (along with your next highest card) in the low hand.
- If you have three pair after the initial deal, the highest pair should be moved to the low hand.
- If you find yourself with no pairs, flushes, or straights, leave the best card in the high hand and move the two cards with the next highest value to the low hand.
- When you draw a full house, move the pair to the low hand. If you happen to draw an additional pair, then use the higher of the pairs for the low hand.
- It is best to keep straights and flushes in the high hand. If, however, you have a pair of tens or better and an ace/king to move to the low hand, then you might consider splitting up a flush or straight.
- If you have two pair, and one of the pairs is comprised of aces, then you should split. The same goes for two pair with a pair of kings (unless the other is a pair of deuces). If the latter occurs, play the pairs together in the high hand and move the next best cards to the low hand.
- If you have two pair with jacks though aces, split the pairs and leave the best one in the high hand.