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Pai Gow Poker
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Introduction
Pai Gow Poker is based on an adaptation of the traditional Chinese domino game. pai gow This game is characterized by a leisurely pace of play and frequent ties, making it a low-risk option. While it involves skill, most hands have clear strategic plays, and learning the correct tactics for the remaining hands is relatively straightforward. Every participant competes against the same dealer hand, leading to scenarios where the entire table wins or loses together, contributing to an enjoyable and sociable gaming experience.
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History
The concept of Pai Gow Poker originated in 1985 thanks to Sam Torosian, who was the proprietor of the Bell card club in Southern California. However, many people are unaware of his contributions. In contrast to others who have earned millions through their card game innovations, Sam followed poor legal advice, believing that card games couldn't be patented and thus failed to file for one for his creation. Subsequently, when his game gained popularity at his venue, there was nothing stopping rival casinos from offering it too, resulting in Sam not receiving any compensation.
Source: Casino Owner Unable to Profit from His Own Game Creation — Los Angeles Times, Nov. 3, 2002.
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The Rules
A single 53-card deck is used, consisting of the usual 52 cards, plus one joker.- The joker card acts as a semi-wild card. It can substitute for an ace or help complete a straight, flush, straight flush, or even a royal flush. Once a player places a bet, the dealer distributes seven cards to both the player and themselves.
- The game adheres to standard poker hand rankings, with one unusual caveat — the A2345 straight, commonly referred to as 'the wheel,' is ranked as the second highest straight. While some casinos choose to disregard this quirky rule, the majority still uphold it.
- Players will organize their seven cards into a high hand consisting of five cards and a low hand with two cards. The five-card hand must possess a higher poker value than the two-card hand.
- The five-card hand is evaluated according to conventional poker hand rankings. The only hand permissible in the two-card hand is either a pair or no pair, with the value determined by the individual cards.
- After the player has arranged their hand, the dealer reveals their cards and organizes their hand in a similar fashion by following rules known as the 'house way.'
- The high hands will be compared against one another, just as the low hands will be, with the hand showing greater poker value winning. If there’s a tie, for example when both two-card hands consist of an ace and a king, the tie favors the 'banker.'
- If the player wins in both high and low comparisons, they will receive even money on their wager, minus a 5% commission. If they win one and lose one, their bet will remain unchanged. If they lose or tie both hands, the player will forfeit their bet.
- Unlike many other casino games, in pai gow poker, players have the ability to bet against the dealer and other participants. This practice is known as 'banking.'
- Typically, the role of the banker is intended to rotate around the table; however, in various casinos this may alternate between the dealer and each player in sequence.
- Players always have the option to decline the banking role (which is common), in which case the opportunity passes to the next player or the dealer.
Strategy
I'm very proud to present my pai gow strategy page This section includes strategies for various levels — beginner, intermediate, and advanced — for those playing as the banker, competing against the banker, and combining strategies. My assistant JB dedicated months to assembling this information, and I strongly encourage you to take a look.
For your ease, I also have a concise one-page summary. simple pai gow poker strategy (PDF).
House Edge
The house edge in Pai Gow Poker is influenced not just by your skill in forming hands but also by how much action you opt to bank. I plan to release updates regarding pai gow poker strategies in January 2014. In the meantime, the tables below illustrate the likelihood of different outcomes and the expected values across four scenarios — whether you employ the house way or an optimal strategy, and whether you are banking or the dealer is taking that role.
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 table provided outlines the expected values across all four scenarios. The 'difference' row and column indicate that banking, when compared to not banking, lifts the expected value by 2.47%. The disparity between following the house way and a theoretical optimal strategy, which is likely unknown to most, 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
In Washington State, casinos often do not impose the 5% fee on banker wins. Instead, they profit from the banker’s advantage and side bets alone. Without the commission, the banker enjoys a 1.30% advantage, while all opponents against the banker face a similar disadvantage.
Banking Against Yourself
Occasionally, when a player decides to take on the banking role, other players may want to engage with a side bet but prefer not to wager against one another on the main game. This can also be done in an attempt to 'change the fortunes' at the table. In such instances, non-banking players might establish an agreement with the banking player that the one who wins will reimburse the other, excluding a 5% commission. This arrangement effectively allows players to bank against themselves through a mutual agreement. The dealer is not involved in any way. Some casinos explicitly prohibit this practice, though it may be challenging to enforce, especially if players converse in a language unfamiliar to the dealer. I mention this as a caution that you could be approached for such an arrangement if you decide to bank. Ultimately, it’s your choice on how to respond, but declining might create some tension at the table.
A discussion regarding this can be found within my forum at Wizard of Vegas .
The House Way
The house way refers to the established method the dealer uses to arrange their own hand. This can differ from one location to another, but the variations are usually minor and quite rare. The house way is applicable at the following casinos:
- Bally's (Atlantic City)
- Barona (San Diego)
- British Columbia (Canada)
- Canterbury Park (Minnesota)
- Claridge (Atlantic City)
- Flamingo Hilton (Las Vegas)
- Four Queens (Las Vegas)
- Foxwoods (Connecticut)
- Golden Nugget (Las Vegas)
- Great Britain (1124K PDF; see page 80)
- MGM Grand (Las Vegas)
- Santa Ana Star (New Mexico)
- Texas Station (Las Vegas)
- Trump Plaza (Atlantic City)
- Real Time Gaming
- Silver Dollar (Washington)
- IGW (Software providers for Arrow's Edge Internet casinos)
Pai Gow Poker Probabilities
The table below illustrates the probability associated with forming any specific poker hand. These probabilities take into account all seven cards without considering how a player might choose to play their 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 total number of combinations for a Royal Flush is 26,132; comprising 21,620 wild combinations and 4,512 natural ones.
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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 : Provides a statistical probability of the dealer forming any specified hand or less. This is valuable for strategic decision-making.
- When to split Two Pair : My advice on when to split two pair.
- Side Bets : Covers the various side bets such as Fortune, Jackpot, and Emperor's Challenge.
- No Push Pai Gow Poker : My analysis regarding this variant of Pai Gow Poker.
- Pai Gow Mania : My analysis.
- Play Online Pai Gow Poker - Free, No Download
- Face Up Pai Gow Poker — A version in which the dealer's cards are dealt face up.
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