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Pai Gow Poker - FAQ
I enjoy playing pai gow poker in Atlantic City. I often notice a player managing two hands simultaneously. I'm curious: does having the ability to see 14 cards from a total of 53 provide any sort of advantage? If it does, to what extent and how would this alter their strategy? I'd appreciate any insights.
In pai gow poker, there's a scenario where the dealer sets aside a dragon hand that is given to players one by one. This might resemble the situation you're observing where players are effectively playing two hands. However, the rules state that this dragon hand must be arranged following the house's guidelines.
Even if a player could utilize information from 14 cards to optimize their hand, I doubt that this would yield a significant benefit, as applying this information correctly would be quite challenging.
I really appreciate your website. In your view, should one consider placing the Fortune side bet in Pai Gow Poker? Thank you for all the valuable information you provide.
It's advisable not to make the Fortune side bet or similar side bets, as they are generally designed to favor the house with a significant edge. For further information about the Fortune side bet, please refer to my analysis of pai gow poker. side bets section .
Do the odds in table games fluctuate with the number of participants? In other words, if more hands are dealt, do the odds shift? If they don’t, is there any significant relevance concerning the number of players engaged in a specific game? This would clarify a betting concern.
Typically, the odds remain constant regardless of the number of players. The only notable exception comes from certain side bets, such as those in Pai Gow Poker that include an envy bonus and therefore improve payouts based on player numbers. Fortune What are the chances of being dealt three pairs in Pai Gow Poker? Are these odds lower or higher than those of getting three of a kind?
Excluding three of a kind and two pairs, the potential methods for achieving three pairs and the associated combinations are as follows.
Using a wild card to complement a pair of aces results in: combin(12,2)*10*6.
No wild card: combin(13,3)*10*63*4 =2471040
Employing a wild card as a single ace gives: combin(12,3)*6.2*42= 380,160
The total number of combinations for getting three pairs amounts to 2,898,720. This figure is significantly less than the 7,470,676 combinations possible for three of a kind.3= 47,520
I've gone through all your insights on the Fortune side bet, but I remain uncertain if playing it is completely foolish or not. I recognize the odds are long, but there's an element of fun in a 'what if' bet. If you have any perspectives on this, I'd love to hear them.
Gambling is intended for enjoyment, so if you feel like you get around 39.5 cents worth of entertainment for every $5 wagered, then it might be worth playing. That's the amount you will sacrifice to the house edge, given no other players are involved.
Hello, as a frequent player of Pai Gow Poker, I find your site filled with excellent insights about the game. Recently, while playing with a friend, he was dealt a 9-high hand, which I think is the lowest possible. In my entire experience, I’ve only seen it happen once before. To our surprise, just five hands later, he received the exact same hand (2-3-4-5-7-8-9). We were amazed and curious about the likelihood of this occurrence, so we decided to reach out to you. Thank you for your attention and for maintaining such a great website.
For a 9-high hand, there are two arrangements possible, including the one you mentioned and 2-3-4-6-7-8-9. The combinations of suits that avoid forming a flush are calculated as 4 - 4 * (combin(7,5) * 3^2 + 6 * 3 + 1) = 15,552. Subsequently, the probability of getting a 9-high hand is 2 * 15,552 / combin(53,7) = 31,104 / 154,143,080, which simplifies to about 1 in 9,911. If you were to play just five hands, the odds of being dealt two 9-high hands would be approximately 1 in 9,826,685. This occurrence appears to be purely coincidental rather than indicative of an issue with the random number generator or the program's code.
According to your pai gow poker rules, you claim that A-2-3-4-5 is the second-highest straight. Why isn’t 9-10-J-Q-K considered the second-highest straight? Could you clarify this matter?7This has always piqued my curiosity as well. It likely falls into that category of quirky exceptions, similar to the peculiar spelling of 'colonel'.
In your practice version of pai gow poker, if you hold no noteworthy hands and move your second and third highest cards to the front hand, the system will occasionally swap your third highest card with the fourth highest. I haven't been able to pinpoint the reasoning—initially, I thought it was consistent when your back hand was ace-high, but that hasn't proven true. Is it possible that the house rules dictate the dealer should drop the second and third highest cards, which means if you and the dealer end up with comparably weak hands, the second highest card will determine your front hand while keeping the third highest in the back hand offers a better winning chance? If that's the case, why doesn't it happen uniformly? I'm puzzled and haven't identified a consistent pattern. Please clarify!
At times, the two-card hand may be so weak that placing the third highest card as a kicker in the five-card hand proves more beneficial. There isn’t a universal guideline to dictate exactly when to execute this, but I've noticed it tends to occur when the second-highest card is relatively low. The logic applied by my program relies on a comprehensive array of probabilities that dictate the potential for each hand to win, opting for the hand that offers the greatest cumulative odds without compromising the overall hand.
As a mathematics and statistics instructor, I believe your website should be considered essential reading before anyone steps into a casino. When engaging in Pai Gow Poker in Nevada casinos, I prefer to bank. While in Tahoe, I can usually manage to bank every other hand. My visits to Vegas are less frequent, and there are more casinos to explore. Do you know which establishments permit banking every other hand at a full table, provided no other players intend to bank? It seems to vary, with some places allowing every seventh hand and others every twelfth.
Furthermore, certain casinos in Tahoe feature jackpot games linked to the ranking of a player's five-card hand. Though it’s a less favorable bet, as a banker, I appreciate when others choose to play it. Typically, they configure their hands in a manner that optimally positions them for the jackpot (financed by the house), often at the expense of their main bets (against me) by splitting two high pairs to create a straight with two singletons, or retaining a full house while deploying only two singletons instead of three down with a pair. Are you aware of any casinos in Vegas or Reno that implement this?
Thank you for your kind remarks. In fact, I've been approached regarding the possibility of teaching a course focused on the mathematics of gambling at UNLV.
This isn’t a game I follow closely, so I don’t have all the specifics memorized. However, I am aware, as you mentioned, that some casinos rotate the banker while others execute a zig-zag pattern between players and dealer. Unfortunately, I don't track who utilizes which system, and I have observed that the progressive side bet is available in many casinos throughout town. It's a terrific notion to bank against it; I’d never considered that before. Regrettably, I don't have much additional information to offer.
Recently, while playing Pai Gow Poker at the Barona Casino near San Diego, CA, I discovered they have differing rules compared to Las Vegas. For instance, 1) they charge a commission on each hand played - $0.50 for bets ranging from $5 to $25 and $1.00 for bets from $30 to $100. If all players at the table push, the commission isn’t collected on the subsequent hand. 2) The Joker is a complete 'wild' card, which means it can fill straights and flushes and can represent any card needed at any time. For example, I was dealt Ks Kd 6c 6s 9h 9d along with the Joker, allowing me to use the two Kings for my low hand while keeping the other five cards for a Full House! My question is: does this version of the game offer a better opportunity for the player than the Las Vegas variants, despite the commission? (I had a positive experience and ended up winning $142.50 after playing for three hours.) pai gow poker That’s an interesting question. I assume player banking remains permissible. In Nevada casinos, the 5% commission translates to an effective 1.46% cost for the player. The house edge in your game hinges on the bet size, being at its lowest with a $100 wager, which has an edge of 1%. I’m not factoring in the pushing rule, which could decrease the edge further. Similar to the card rooms in the Los Angeles area, I think there's a distinct possibility of overcoming the house edge by banking a sufficient share of the action.
What are the chances of being dealt a natural seven-card straight flush in pai gow poker? I work in a casino and witnessed this occur for the first time in 15 years. The fortunate player won $40,000.
There exist 32 possible natural straight flushes (four ranks times eight configurations of seven cards). The total number of ways to draw seven cards from a deck of 53 is combin(53,7) = 154,143,080. Thus, the probability is 32/154,143,080, equating to roughly 1 in 4,816,971.
In Stanford Wong’s book, 'Optimal Strategy for Pai Gow Poker', he delves into the analysis of when to keep pairs together. Have you conducted similar research? If not, do you believe his analysis offers the best strategies?
Indeed, I have performed a similar analysis, which you can find in my own resources. Although there are noteworthy differences between my strategy and his. Wong's method is more intricate, taking into account the two highest single cards, while I only consider the highest single card. Wong also separates strategies based on whether the player is banking or not. Moreover, Wong’s analysis addresses the California game without the 5% commission, unlike my strategy. I have faith in Wong’s work and do not dispute his findings.
Hello, my friends were engaging in a game of pai gow, and one of the players held a royal flush with a 3 and 4, while the house also had a royal flush with a 3 and 4 (resulting in the player losing despite having a royal flush—poor guy). I'm curious about the odds of such a scenario happening. Thank you! I truly appreciate your website.
The likelihood of two individual players tying with a royal flush while holding any two additional cards is approximately 1 in 290 billion. pai gow poker appendix 2 What are the games recognized as the most and least volatile?
Pai gow poker exhibits the least volatility, while Keno generally ranks as the most volatile.
At the location where I play pai gow poker, the commission for a $25 bet stands at $1, which translates to a 4% cost. What effect does this have on reducing the house edge?
A commission rate of 4% results in a reduction of the house edge by 0.29%.
At the newly opened Seneca/Niagara Casino in Niagara Falls, NY, they have declined my request for a copy of their house rules for pai gow poker. I would really like to understand their house rules before I engage in play. Are they obligated to disclose this information?
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I frequently engage in pai gow poker at Atlantic City. Often, I see someone managing two hands at once. I'm curious: does examining 14 cards out of a total of 53 provide any sort of strategic advantage? If so, how significant is it, and what adjustments to their strategy might it require? Any insights would be greatly appreciated.
In pai gow poker, the dealer sometimes sets aside a 'dragon' card to offer to each player in succession. This is akin to playing dual hands and is likely what you've witnessed. However, the rules typically dictate that when playing the dragon hand, it must be configured according to the house rules.
Even if a player could benefit from the information available from 14 cards when forming their hand, I doubt the advantage would be substantial as effectively utilizing that information would be quite complex.
Wizard, I admire your website. In your opinion, is it advisable to make the Fortune side bet in Pai Gow Poker? I appreciate all the information you share.
No, you should refrain from making the Fortune side bet, or any side bets for that matter. In general, these types of bets are often unfavorable, as they tend to have a high house edge. For more details about the Fortune side bet, take a look at my analysis on pai gow poker.
Does the probability in table games fluctuate with the number of participants? Specifically, if more hands are dealt, are the odds affected? If they remain unchanged, is there any critical information regarding how the number of players impacts the game's odds? This would help clarify a prevailing debate.
Typically, the odds remain consistent regardless of player count. The only notable exception is with side bets that include features like an envy bonus, which may offer better payouts based on participant numbers.
What are the likelihoods of securing a three pair in Pai Gow Poker? Is it more or less probable than achieving a three of a kind?
Excluding a three of a kind with two pairs, let's explore how one can attain a three pair and the various combinations to achieve this.
Using a wild card to complete a pair of aces: combin(12,2)*10*6
Using a wild card as a single ace: combin(12,3)*6
The total number of possible combinations stands at 2,898,720, which is significantly lower than the 7,470,676 combinations available for achieving a three of a kind.
I've reviewed everything you've written about the Fortune side bet, but I'm still torn on whether it's purely foolish to pursue it. While I understand the odds aren't in my favor, the allure of a 'what if' scenario makes it intriguing. I'd love to hear your perspective on this.
Gambling should primarily be about enjoyment. If you believe you're getting 39.5 cents in entertainment value for every $5 wagered, then I encourage you to go for it. That's essentially the house edge you're accepting under the circumstances.
Hello, I'm a frequent player of Pai Gow Poker and I've found your website to be a fantastic resource on the game. Recently, while playing with a friend, he ended up with a 9-high hand, which I understand to be the weakest hand possible. In all my time playing, I've only witnessed that once before. To our astonishment, just five hands later, he was dealt the exact same weakest hand (2-3-4-5-7-8-9). We were stunned and curious about the odds of such an occurrence, so we thought of reaching out to you. Thank you for your time and for maintaining such a great site.
There are two distinct ways to establish a 9-high hand, namely the one you mentioned and 2-3-4-6-7-8-9. The combinations of suits that do not result in a flush amount to 4
-4*(combin(7,5)*3^2+6*3+1) = 15,552. Therefore, the probability of forming a 9-high hand is 2*15,552/combin(53,7) = 31,104/154,143,080, which translates to approximately 1 in 9,911. If you were to play merely five times, the likelihood of being dealt two 9-high hands would be 1 in 9,826,685. I believe what occurred was merely a coincidence, rather than an issue with the random number generator or program code.
According to your pai gow poker rules, A-2-3-4-5 is classified as the second highest straight. Why isn't 9-10-J-Q-K recognized as the second highest straight? Please clarify.
This has always struck me as peculiar. It seems to be one of those oddities, similar to why we spell 'colonel' the way we do. combin In your casual pai gow poker games, if you have a worthless set of cards and move your second and third highest cards to the front hand, it seems the game occasionally replaces the third highest card with the fourth highest. I've yet to decode the logic behind this -- at first, I assumed this always occurred when your back hand was ace-high, but that wasn't always the case. Is this adjustment due to the house rules that dictate the dealer drop the second and third highest? And in instances of equally poor hands, does the decision for the front hand hinge on the second highest card while retaining the third highest in the back hand for a better shot at winning? If so, what justifies it not happening consistently? I'm thoroughly puzzled and would greatly appreciate some clarity!
In certain situations where the two-card hand is particularly weak, it might be strategic to use the third highest card as a kicker in the five-card hand. There's no definitive guideline about when to do so, but I have observed that it often occurs when the second highest card is relatively low. The strategy my program employs is based on a comprehensive array of probabilities estimating each hand's chances of winning and selects the configuration with the highest potential probability without compromising the hand integrity.
As a math/statistics instructor, I strongly believe that your website should be a prerequisite study for anyone planning to step into a casino. I tend to bank while playing Pai Gow Poker at Nevada casinos. In Tahoe, I can usually bank every second hand, although my visits to Vegas are less frequent, and I explore various casinos. Are you aware of any casinos that facilitate banking every other hand at a full table, provided no other players want to bank? It appears to vary between one in seven at some venues and one in twelve at others.
Additionally, several casinos in Tahoe feature a jackpot game linked to how a player's five-card hand performs. It's not the most advisable bet, but as a banker, I appreciate when other players join in. They often configure their hands for the jackpot (covered by the house) at the expense of their primary wager (against me) by rearranging two high pairs to aim for a straight with two solo cards or keeping a full house intact while opting for two singletons up instead of three down. Do you know of any Vegas or Reno casinos that implement this?
Thank you for your encouraging comments. Interestingly, I've been approached about teaching a course focused on the mathematics behind gambling at UNLV.
Player wins both 28.61%
Tie 41.48%
Banker wins both 29.91%
This isn't my area of expertise, so I don't meticulously follow every nuance. However, I understand, as you pointed out, that some casinos adopt a rotating or zig-zag method for the banker between players and the dealer. Regrettably, I don't keep track of which casinos employ which methods. I've also observed the progressive side bet at numerous establishments around town, but again, I don't have specific details. Nevertheless, I appreciate your idea of banking against it; that's a perspective I hadn't considered.
Recently, I was playing Pai Gow Poker at the Barona Casino close to San Diego, CA. Their rules differ from those in Las Vegas: 1) They impose a commission on every hand played - $0.50 for bets between $5-$25 and $1.00 for bets from $30-$100. If all players at the table push, the next hand incurs no commission for anyone. 2) The Joker acts as an authentic 'wild' card. It not only completes straights and flushes but can represent any card required in any scenario. For example, I had Ks Kd 6c 6s 9h 9d along with the Joker. This allowed me to arrange the two Kings as the low hand while reserving the other five cards for a Full House! Is this version more advantageous for players compared to the Las Vegas variants, despite the every-hand commission? (I found it enjoyable, ending up with a $142.50 win after three hours of play.)
That's an excellent question. I assume player banking remains permitted. The 5% commission at Nevada casinos ultimately costs a player about 1.46%. The house edge in your game depends on your betting size. For a $100 wager, the edge is at its lowest, sitting at around 1%. I'm not factoring in the rule concerning all players pushing, which could further decrease that edge. Similar to the card rooms in the Los Angeles area, I see a potential to overcome the house edge if you manage a percentage of the action effectively. Pai Gow poker What are the odds of being handed a natural seven card straight flush in pai gow poker? I work in a casino and just witnessed this occurrence for the first time in 15 years, with a fortunate player winning $40,000.
There are 32 possible natural straight flushes (4 ranks multiplied by 8 possible spans of 7 cards). The number of different ways to draw 7 cards from a total of 53 is combin(53,7) = 154143080. Therefore, the probability stands at 32/154143080, or about 1 in 4,816,971.
In Stanford Wong's book, \"Optimal Strategy for Pai Gow Poker\", he conducts an analysis on when it's best to keep any two pairs together. Have you performed a similar evaluation? If not, do you believe his findings yield the best strategies? Fortune Bonus Pai Gow Yes, I have indeed conducted a comparable analysis, and you can find it in my resources. There are some key differences between my approach and his. Wong's strategy is more expansive, taking into account the highest two singletons, whereas mine considers only the top singleton. Furthermore, Wong differentiates based on whether the player is banking or not. Finally, his book is based on the California game without a 5% commission, contrasting with my strategy. I respect Wong's expertise and hold his work in high regard.
Hi, my friends were engaged in pai-gow, and one of the other players managed to have a royal flush featuring a 3 and 4, while the house also achieved the same royal flush with a 3 and 4 (resulting in the player losing despite having a royal flush – what a letdown!). I'm curious about the odds of such an incident occurring. Thank you! I genuinely enjoy your website.
No joker: combin (13,3)*10*combin(4,2)3*4 = 2,471,040
Joker used in a pair of aces: combin(12,2)*10*42*combin(4,2)2= 380,160
The odds of two specific players tying with a royal flush along with any two additional cards are approximately 1 in 290 billion.3= 61,776
What are the games with the highest and lowest volatility?
Back in 2002 Pai gow poker demonstrates the least volatility, whereas keno typically ranks as the most volatile game on average.
In the location where I play pai gow poker, the commission on a $25 bet stands at $1, which translates to 4%. How does this influence the house edge? Fortune side bet A 4% commission effectively reduces the house edge by 0.29%.
- 1 player: $27.36
- 2 players: $23.63
- 3 players: $19.90
- 4 players: $16.17
- 5 players: $12.44
- 6 players: $8.71
- 6 players: $4.98
At the new Seneca/Niagara Casino in Niagara Falls, NY, they are unwilling to provide me with a copy of their house rules for pai gow poker. I want to understand the house rules before I decide to play. Are they obligated to disclose this information?
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Engage in Slot Tournaments with Incredible Prize Pools pai gow poker In Atlantic City, I often participate in pai gow poker sessions. I've noticed players occasionally play with two hands. I'm curious: does observing 14 cards out of 53 provide any kind of strategic edge? If so, what sort of adjustments to their strategy could that imply? I would appreciate any insights.
In pai gow poker, there are instances when the dealer sets aside a dragon hand, which is offered to players sequentially. This scenario resembles playing with two hands, and it's likely what you've observed. However, rules dictate that when utilizing the dragon hand, it must be arranged according to the house's standard procedures.
Despite the potential to consider 14 cards when arranging a hand, I'm skeptical about the significant advantage it might confer. Properly leveraging that information could be quite complex.
Wizard, I truly appreciate your website's content. In your view, is it advisable to place the Fortune side bet in Pai Gow Poker? Thank you, as I greatly value the information you share. Pai Gow Poker side bets .
No, it's generally advisable to avoid the Fortune side bet or any similar side bets. They are typically considered poor bets due to their high house edge. For additional details on the Fortune side wager, please refer to my analysis on pai gow poker.
Do the odds change in table games based on the number of players participating? Specifically, if there's a greater number of hands dealt, does this affect the odds? If not, what's the relevance of the player count in a particular game in terms of odds? This could clarify a bet we've been discussing.
Typically, the odds remain consistent regardless of the number of players at the table. The only notable exception would be certain side bets like those in Pai Gow Poker that offer envy bonuses and thus adjust payouts based on player numbers.
What are the chances of being dealt a three pair in Pai Gow Poker? Is it more or less likely than getting three of a kind?
Excluding the combinations of three of a kind paired with two pairs, there are several ways to achieve three pairs, and here are their corresponding combination amounts.
Wildcard utilized to compete against a pair of aces: combin(12,2)*10*6
Wildcard employed as a singleton ace: combin(12,3)*6
| Players | House Edge Banker |
House Edge Player |
Breakeven Ratio |
| 2 | 0.2% | 2.73% | N/A |
| 3 | -0.02% | 2.73% | 136.5 |
| 4 | -0.1% | 2.73% | 27.3 |
| 5 | -0.15% | 2.73% | 18.2 |
| 6 | -0.19% | 2.73% | 14.4 |
| 7 | -0.21% | 2.73% | 13 |
The total number of possible combinations adds up to 2,898,720, which is significantly less than the 7,470,676 combinations available for obtaining three of a kind.
From my pai gow poker section I have thoroughly examined your insights regarding the Fortune side bet, but I'm still unsure whether it's completely unwise to engage in it. While I acknowledge the odds are not favorable, I find it adds a fun element of speculation. I would appreciate your thoughts on this.
Gambling should be an enjoyable experience, so if you believe you're gaining around 39.5 cents worth of excitement for every $5 bet, then it might be worth it to you. That amount represents the potential loss due to the house edge, assuming no other players are involved. tiles , though your Java game Hello, I'm an avid player of Pai Gow Poker, and I've found your site to be a treasure trove of valuable game-related information. Recently, while playing with a friend, he was dealt a 9-high hand, which I understand is the lowest possible hand. In my extensive playing experience, I've only encountered it once before. Remarkably, just five hands later, he received the identical hand (2-3-4-5-7-8-9). We were astonished and wondered about the likelihood of this occurrence, so we wanted to ask you. Thank you for your time and amazing site.
To create a 9 high hand, there are two rank arrangements: the one you mentioned and 2-3-4-6-7-8-9. The number of suit combinations that avoid forming a flush equals 4
While playing Fortune Bonus Pai Gow -4*(combin(7,5)*3^2+6*3+1) = 15,552. Thus, the probability of receiving a 9 high hand is calculated as 2*15,552/combin(53,7) = 31,104/154,143,080, approximately 1 in 9,911. If you were to play just five rounds, the odds of being dealt 2 9-high hands would be about 1 in 9,826,685. I believe this occurrence is simply coincidental and not indicative of any issues with the random number generator or programming.
Your Pai Gow Poker rules indicate that A-2-3-4-5 is the second highest straight. I'm confused as to why 9-10-J-Q-K isn't regarded as the second highest straight. Can you clarify?7No joker: combin (13,3)*10*combin(4,2)
I've often pondered this question myself. It seems to be one of those peculiar conventions, similar to why we spell 'colonel' the way we do. *4 = 2,471,040 In your play-for-fun pai gow poker mode, if you lack a strong hand and place your second and third highest cards in the front hand, the system sometimes substitutes the third highest with the fourth highest. I can't seem to grasp this rule—it appeared to follow a pattern when my back hand was an ace-high, but that hasn't always proven consistent. Is this swap due to the house way requiring the dealer to drop the second and third highest cards? If so, when both you and the dealer have weak hands, would your second highest card in the front hand outweigh the chance of winning by retaining the third highest in the back? Why is this not a constant rule? I'm struggling to understand this and could use some clarity.
At times, the two-card hand is so inadequate that it makes more sense to use the third highest card as a kicker for the five-card hand. There's no set rule for when this should occur, but it seems to happen more frequently when the second highest card is relatively low. The logic behind my program involves a vast array of probabilities forecasting the potential success of each hand, opting for the hand configuration likely to yield the best outcomes without compromising the overall hand strength.
As a mathematics and statistics educator, I believe your site should be essential reading prior to anyone entering a casino. I prefer to act as the banker when playing Pai Gow Poker in Nevada casinos. In Tahoe, I'm able to take on the role of banker during roughly every other hand. However, my visits to Vegas are less frequent, and I'd like to explore more casinos. Do you know which establishments permit banking every other hand at a full table, provided other players aren't interested in banking? I've noticed a variation, with some places allowing it about once in seven hands and others roughly once in twelve. *combin(4,2) .
Furthermore, select casinos in Tahoe feature a jackpot game based on the value of a player's five-card hand. While this is a risky bet, as a banker, I appreciate when other players opt for it. They may set up their hands for the jackpot (which is covered by the house) at the cost of their standard wager against me—like splitting two high pairs to pursue a straight with two singletons, or maintaining a full house while allowing two singletons to play instead of three down paired up. Any idea which casinos in Vegas or Reno follow this practice?
Thank you for your encouraging feedback. In fact, I have been approached about the possibility of offering a course on gambling mathematics at UNLV.
It’s not a game I focus on closely, so I don’t keep track of the finer details. However, I am aware that some casinos use alternating banks while others employ a zig-zag method between players and the dealer. Unfortunately, I can’t specify which casinos go which route. I've also seen that progressive side bet at numerous locations, but again, I don't maintain a record of their specifics. The concept of banking against it is intriguing—I've never considered that before. Apologies for not providing more assistance.
Recently, I played Pai Gow Poker at Barona Casino near San Diego, CA, which has different rules compared to those in Las Vegas. For instance, 1) they charge a commission on every hand - $0.50 on bets ranging from $5-$25 and $1.00 on bets from $30-$100. If all players push, the commission is waived for everyone on the next hand. 2) The Joker acts as a true wild card, functioning not just to complete straights and flushes, but also as any other needed card. For example, I had Ks Kd 6c 6s 9h 9d, along with the Joker. This allowed me to use the two Kings as a low hand and keep the other 5 cards for a Full House! Is this variation more favorable for players compared to the traditional Las Vegas games, despite the commission on every hand? (I found it enjoyable, winning $142.50 after three hours of play.)
That's an interesting question. I assume player banking is still permissible. The 5% commission at Nevada casinos equates to a loss of approximately 1.46% for the player. The house edge in your game varies with bet size, with the lowest edge occurring on a $100 wager, around 1%. I won't factor in the pushing rule, which could further diminish the edge. Similar to the card rooms in Los Angeles, there's potential to reduce the house edge if you maintain a good percentage of the action.
What are the chances of being dealt a natural seven-card straight flush in Pai Gow Poker? I work at a casino and just witnessed this after 15 years—one fortunate player took home $40,000.
There are 32 distinct natural straight flush combinations (calculated by multiplying 4 ranks by 8 possible 7-card spans). Given that the total combinations for drawing 7 cards from 53 is combin(53,7) = 154143080, the probability of this event is 32/154143080, equating to approximately 1 in 4,816,971.
In Stanford Wong's book titled 'Optimal Strategy for Pai Gow Poker,' he provides an analysis on when to retain pairs together. Have you conducted a similar investigation? If you haven't, do you believe his findings yield the most beneficial strategies? = 61,776 .
Yes, I've carried out a comparable analysis, which you can find in my work. There are notable differences between my strategy and his. While Wong's methods are more intricate, involving the two highest singletons, mine focuses solely on the highest singleton. Additionally, Wong distinguishes between players banking and not banking. Furthermore, his analysis is based on the California game without the 5% commission, unlike my approach. I have confidence in Wong's conclusions and do not dispute his findings.
Hi, while playing Pai Gow with friends, an opponent showcased a royal flush featuring a 3 and 4, while the house also held a similar royal flush with a 3 and 4 (so the player lost despite having a royal flush, unfortunate for them). I'm curious about the likelihood of this situation arising. Thank you, I genuinely appreciate your website.
The probability of two specific players tying with royal flushes, using any two other cards, is estimated to be around 1 in 290 billion.
Which games have the highest and lowest volatility?
In Stanford Wong's book titled 'Optimal Strategy for Pai Gow Poker,' he provides an analysis on when to retain pairs together. Have you conducted a similar investigation? If you haven't, do you believe his findings yield the most beneficial strategies? Michael from Marysville .
Pai Gow Poker is known for its low volatility, whereas Keno typically exhibits the highest volatility.Fortune side bet1 player: $27.36
- 2 players: $23.63
- 3 players: $19.90
5 players: $12.44 6 players: $8.71 At my Pai Gow Poker venue, a $25 bet incurs a $1 commission, resulting in a 4% cost. How does this impact the house edge?
6 players: $4.98
| Andy from Chicago, IL | pai gow poker | Michael from Las Vegas | William from Mississauga, Ontario | Pai Gow Poker side bets | Brian from Crystal, MN |
|---|---|---|---|---|---|
| Michael from Knoxville, TN | Players | 0.452967 | 0.999507 | 1.452474 | 0.416162 |
| House | Edge | 0.989071 | 0.821870 | 1.810941 | 0.765667 |
In Stanford Wong's book titled 'Optimal Strategy for Pai Gow Poker,' he provides an analysis on when to retain pairs together. Have you conducted a similar investigation? If you haven't, do you believe his findings yield the most beneficial strategies? Banker .
A 4% commission effectively reduces the house edge by 0.29%.
At the new Seneca/Niagara Casino in Niagara Falls, NY, they are unwilling to share their pai gow poker house way with me. I'd like to know their rules before I play. Are they obligated to disclose this information?
It seems that they may not be obligated to provide it. I remember a time at the Tropicana in Atlantic City when the rules for pai gow poker mentioned that the house way could be shared if requested. When I made that request, however, they informed me that they had run out of available copies and were unable to show me a house version due to it lacking the necessary Gambler’s Anonymous disclaimer. Personally, I believe that players have a right to understand the rules of the game, but it appears that the gaming authorities hold a different perspective.
On your website, I've noticed that the house way for pai gow poker can differ significantly between casinos. Could you tell me which casino version offers the most favorable odds for players? Player Although the various house ways are quite similar, the differences typically arise in unusual or borderline hands. I've frequently heard dealers mention that their casino adopts a more conservative house way, which aims for balance in the hands and often leads to more pushes. However, I question whether anyone has carried out a study comparing these approaches.
I make an annual trip to Las Vegas and I really enjoy playing Pai Gow poker there because the local casinos I frequent do not permit banking. My question revolves around the etiquette: how significant is it for players to withdraw their bets and refrain from playing a hand when another player opts to bank? This situation has occurred to me multiple times, mainly at smaller casinos like the Sahara, and I often hear players say things like, 'If I wanted to donate to another player, I’d play in the poker room.' This behavior really irritates me, and I'd appreciate your perspective on this matter.
I can certainly understand your frustration. The notion of banking shouldn't dictate player behavior at the table. While I haven't encountered a specific etiquette rule regarding this issue, I believe it definitely touches upon a breach of common courtesy.
In Washington State, there are several clubs that offer a modified payout structure for Fortune Pai Gow. These clubs provide lower payouts (for example, a Royal Flush paying 125-1 instead of 150-1) but also apply a push on three pairs. What impact does this have on the house edge for the side bet?
Players experience a 0.42% loss due to the decreased royal flush payout. However, the probability of achieving three pairs is about 1.88%. Altogether, these adjustments actually reduce the house edge by 1.46%. Breakeven I'm a strong supporter of your website. During a solo session of Pai Gow Poker, I encountered an unusual scenario. After splitting my hands, I ended up with a flush: A, Q, 10, 8, 3, whereas the dealer had a flush himself consisting of A, joker, 10, 5, 4. Who is the winner here? While the rules state that a joker can be utilized to form a flush, does it carry any rank? Can it be treated as an additional Ace in the flush?
Thank you for your response. I consulted with a dealer who confirmed that the house wins that hand because the joker assumes the role of a king. The general rule is that a joker can take the place of any specific card not already included in the same hand if it finalizes a straight, flush, or straight flush. Otherwise, it is considered a fifth-suit ace, which opens up the chance for five aces in total.
In Stanford Wong's book titled 'Optimal Strategy for Pai Gow Poker,' he provides an analysis on when to retain pairs together. Have you conducted a similar investigation? If you haven't, do you believe his findings yield the most beneficial strategies? N/A .
I genuinely appreciate your website! I love engaging in casino games, but I usually only have a modest budget (less than $100 per session). Which game would you suggest to extend my budget and improve the likelihood of a successful gaming experience?
Thank you! In terms of balancing winning odds and preserving your bankroll, I would recommend either blackjack (which tends to favor victories) or pai gow poker (which is better for bankroll protection). If you can locate a $5 blackjack table, I would opt for that. If the minimum is $10, then I would advise playing pai gow poker instead.
-0.1%
Is there an opportunity for a player to gain an edge in Pai Gow Poker by observing the cards of their opponents? -0.15% I believe this could slightly diminish the house edge, provided that you are aware of the proper strategy adjustments to make, but it won't come close to overcoming it. -0.19% In Las Vegas, the majority of casinos where I've played require a $100 bet in blackjack for four hours daily to receive a complimentary room. Based on the rules of S17, RSA, DOA, and LSR, and assuming 100 hands per hour, this amounts to a cost of $120 daily if I employ basic strategy. Is there another game that could help minimize my losses? I'm particularly interested in how much I could lose in Pai Gow if I'm not banking and wagering $100 a hand for four hours each day. However, I thought you might know of a game that would be even less costly for me.
-0.21%
As a general principle regarding comps, casinos typically return a percentage, often around one-third. Therefore, if your aim is to secure the room while minimizing expected losses, you should choose the game with the lowest house edge. This way, you're likely to earn your complimentary room more quickly and with less fluctuation in your bankroll by playing pai gow or pai gow poker. However, bear in mind that the house edge is typically higher, so your expected losses will be greater compared to blackjack. Personally, I advise playing whatever game you would enjoy if there were no comps involved. Then, treat any comps you receive as a nice bonus.
I encountered a curious situation in Reno a couple of years ago that seemingly no one else has reported. During a game of pai gow poker, the dealer set her cards, which included a Jack and a Ten in her two-card hand, as well as a flush in her five-card hand. It appeared that the dealer overlooked the presence of a higher straight with a two-card hand but still proceeded to set her cards and dealt with four players before the pit boss intervened. He pointed out the error, instructed her to reset the hand, and they went to the discard tray to analyze the hands anew. This caused two of the players to transition from a push to a loss. The pit boss even went to the players' stacks to collect their funds after reviewing the videotape to verify the bets. We were all instructed to remain at the table until the confusion was resolved, but afterward, despite not knowing each other, we all chose to leave both the table and the casino entirely. It leaves me wondering: once a hand is established and the results of the first hand are settled, shouldn't there be no further alterations? From a public relations standpoint, that pit boss lost my business permanently over a situation that cost the casino $20. What are your thoughts?
In Stanford Wong's book titled 'Optimal Strategy for Pai Gow Poker,' he provides an analysis on when to retain pairs together. Have you conducted a similar investigation? If you haven't, do you believe his findings yield the most beneficial strategies? Jay R. from Shelton, CT .
The casino had the right to take those measures. However, I would argue that it was a poor business choice. Not only did the casino waste time sorting out this issue, but, as you've observed, it left all the players feeling quite discontented. This incident underscores the shortcomings of strictly adhering to rules. Personally, I believe rules should be contextualized within common sense.
At the Trump Casino in Gary, Indiana (close to Chicago), the fortune bonus in Pai Gow Poker offers the regular bonuses for three of a kind or better, but also provides a 1 to 1 payout for three pairs. Statistically, how does this enhance the chances of winning on the bonus? What percentage of time is a player likely to end up with three pairs?
pai gow poker section
| tiles | , though your | Java game | Tabby Cat from Huntington Beach |
|---|---|---|---|
| While playing | 0.95 | 0.383010 | 0.363860 |
| Fortune Bonus Pai Gow | 0 | 0.413936 | 0.000000 |
| Greg | No joker: | 0.203054 | combin |
| (13,3)*10*combin(4,2) | 1.000000 | 0.160806 |
*4 = 2,471,040 Joker used in a pair of aces: combin(12,2)*10*4 For a three pair combination without the use of a joker, the number of possible combinations is calculated as follows: *combin(4,2) (13,3)*10*combin(4,2)^3*4/combin(52,7) = 2,471,040. When using a joker to build a pair of aces, we find 23,776 possible combinations. If the joker is taken as the singleton card, there are 61,776 combinations. Therefore, the overall total is 2,556,592. Out of the total combin(53,7) = 154,143,080 possibilities, the probability of achieving a three pair is 1.659%. Changing a three pair from being a loss to a win at 1 to 1 reduces the house edge by 3.32%. Assuming a standard payout structure on the other hands, this gives the player favorable odds, particularly when there are three or more other players.
I recently found myself in Las Vegas, and the approach taken by the casinos regarding two pair in Pai Gow Poker differs quite a bit from the method you've shared. I am curious whether your rules are designed to maximize the player's opportunities based on knowledge of how the house operates, or if your methodology simply presents a superior strategy compared to the house's approach. If it leans towards the former, would it be better for a player who is banking to adopt the house way over yours? Conversely, if your strategy is indeed superior, then it should always be used. However, if that's the case, why don't the casinos implement your methodology?
My two pair rule is crafted to counter the house way. Nevertheless, I believe it represents just about any reasonable strategic approach. For instance, I would apply it when banking against fellow players. The reason the casinos stick with a more archaic and less effective rule likely stems from tradition. The original creator of the game probably devised that strategy somewhat arbitrarily, which has led it to become an ingrained habit. I also find two other rules to be quite nonsensical: counting A2345 (known as 'the wheel') as the second-highest straight and insisting that there be an exception in the house way which states that if the dealer has five aces combined with a pair of kings, the kings should play as the low hand. The odds of landing this hand are 1 in 25,690,513. In my experience, this scenario has probably occurred about 100 times throughout the game's history, but it likely has never influenced the outcome of a hand compared to opting to play a full house for the high hand. Yet, every dealer who has dealt the game must tedious learn this exception.
At the Borgata casino in Atlantic City, they implement a unique rule regarding the commission structure for pai gow poker which differs from other establishments. They charge commissions in increments of 50 cents rather than the standard 25 cents typically seen. During my play, I won a hand for $25 and was charged just $1 in commission. How much does this affect the house edge?
| = 61,776 | Back in | Michael from Marysville Fortune side bet |
1 player: $27.36 2 players: $23.63 |
|---|---|---|---|
| 3 players: $19.90 | 0.018868 | 0.257773 | 0.004864 |
| 4 players: $16.17 | 0.075472 | 0.136483 | 0.010301 |
| 5 players: $12.44 | 0.075472 | 0.038914 | 0.002937 |
| 6 players: $8.71 | 0.075472 | 0.000534 | 0.000040 |
| 6 players: $4.98 | 0.754717 | 0.000000 | 0.000000 |
| Andy from Chicago, IL | 1.000000 | 0.018141 |
From my analysis of the pai gow poker section, here are the resulting probabilities.
In this case, you are benefiting from a 4% reduced commission. As a player, your expected value for payouts is .2861*0.96 - .2991 = -2.44%. When acting as the banker (in a one-on-one scenario), the expected value adjusts to .2991*0.96 - .2861 = 0.001036. Thus, a 4% commission leads to a decrease in the house edge by approximately 0.3%.
P.S. In May 2008, a reader reported that the Borgata does indeed use quarters in pai gow poker and mandates bets to be in increments of $5.
| pai gow poker | Michael from Las Vegas | William from Mississauga, Ontario Pai Gow Poker side bets |
Brian from Crystal, MN Michael from Knoxville, TN |
|---|---|---|---|
| Players | 0.018868 | 0.257773 | 0.004864 |
| House | 0.075472 | 0.136483 | 0.010301 |
| Edge | 0.075472 | 0.038914 | 0.002937 |
| Banker | 0.830189 | 0.000000 | 0.000000 |
| House | 1.000000 | 0.018101 |
My girlfriend and I often visit the casino together to play.
I’m curious whether it’s statistically more beneficial for us to each gamble half of our money, or if one of us should stake it all; do both methods yield the same odds?
The probabilities are equivalent. Nevertheless, playing at half the bet size would make the experience less volatile for both of you.
| Edge | Player | Breakeven Ratio |
N/A -0.02% |
|---|---|---|---|
| -0.1% | 0.018868 | 0.257773 | 0.004864 |
| -0.15% | 0.075472 | 0.136483 | 0.010301 |
| -0.19% | 0.905660 | 0.000000 | 0.000000 |
| -0.21% | 1.000000 | 0.015164 |
First and foremost, thank you for creating such an engaging and informative website. I have a brief question regarding...
I'm aware that the fortune bonus bet isn't the best option since it pays out less than 20% of the time. Still, I enjoy playing it for the chance of hitting a big win. At the Trump Casino located in Gary, Indiana, which is near Chicago, they offer a fortune bonus that not only provides regular payouts for three of a kind or higher but also gives a 1 to 1 payout for having three pairs. From a statistical viewpoint, how does this impact your winning probabilities with the bonus? What are the chances of a player ending up with three pairs in their hand? Thank you once more. Jay R. from Shelton, CT .
You're very welcome! Here's the breakdown of how to obtain a three pair:
Using the joker as a standalone card: combin(13,3)*combin(4,2)
The overall number of different combinations adds up to combin(53,7), which equals 154,143,080. Hence, the likelihood of forming a three pair is (2,471,040 + 380,160 + 61,776) divided by 154,143,080, resulting in a probability of 0.0189. Consequently, reclassifying a three pair from a loss to a 1 to 1 push would lower the house advantage by 1.89%.
You previously addressed a query about Washington State's commission-free pai-gow, sometimes referred to as fortune pai-gow, noting that since the house always serves as the banker, they maintain a 1.44% advantage. However, in commission-free pai-gow, players are permitted to be bankers. How does this change the house’s advantage?
- From what I've gathered about Washington State, numerous casinos choose to forgo the usual 5% commission if a player opts to bank. The typical pay table for the Fortune bet in Washington appears to be 2/3/4/5/25/50/150/400/1000/2000/8000. This layout has a house edge of 7.83%, reduced by 1.07% for each additional player at the table. Therefore, the expected loss on a $5 Fortune wager amounts to 39.14 cents, decreasing by 5.34 cents for each added player. Below is a table showing the break-even point for making or not making the Fortune bet dependent on the number of players present, including yourself.
- For instance, if there are four individuals (yourself included), it's advisable to make the Fortune bet if your pai gow poker wager is $17 or greater, and to refrain when the bet is $16 or lower.
- First and foremost, thank you for maintaining this website! I find it incredibly useful, and as someone who also works in the field of actuarial science, I can appreciate the depth of detail you provide and your ability to explain the mathematics behind these games in simpler terms for those who aren't actuaries. I do have a question related to etiquette in Pai Gow Poker. When I play this game in Vegas with friends, some of them tend to withdraw their bets and avoid participating in a hand when another player decides to bank. Personally, I don’t follow that practice, as I believe that (a) if I incur a loss, I'd prefer my money to go to another player rather than the house, or (b) if I win, the player serving as banker has willingly taken that risk, so it shouldn't matter if the winning goes to me or the casino. I'd love to hear your thoughts on this practice. Thank you once more for the fantastic content on your site! Keep it up!
I genuinely appreciate your kind words. It's always great to hear from fellow actuaries. In my view, it's quite rude to retract a bet when another player is acting as the banker, unless that player has explicitly indicated they don't mind. Occasionally, players may work together to avoid banking against each other to lessen losses and fluctuations. Without such collaboration, refusing to bet against a player banker essentially denies them the favorable odds that the dealer typically enjoys. It's not fair to happily hand your money over to the casino while withholding it from a fellow gambler. It’s somewhat akin to refusing to share your luggage cart at the airport once you're done with it, despite being offered the option of a 25-cent refund.
I absolutely love the site!! As I mentioned in response to another inquiry, some casinos present a Dragon Hand option in their game. My personal strategy is to engage with it only if I possess trips or better, ideally without employing the joker. Conversely, others seem to bet on it even if they have no strong hand. Is there any rationale behind either of these approaches? pai gow poker section Personally, I refrain from playing the dragon hand because it consistently loses in duplicate situations. Irrespective of what you're holding, you have identical odds of achieving any hand as the dealer if both of you follow the same strategy. Therefore, if you feel the need to play it, go ahead whenever you prefer.
In Casino Niagara, there is a side bet available in Pai Gow Poker that is based on a jackpot payout rather than fixed odds. I'm curious about the threshold that the jackpot must reach for that side bet to be considered break-even, assuming one effectively plays to maximize the return on that jackpot side bet. tiles The break-even point is established at $102,680.24. I've recently completed an analysis pertaining to this bet and added it to my section on the topic.
During my recent visit to a Las Vegas casino, I was playing pai-gow poker when another player, frustrated by their persistent losses to the dealer, decided to assume the role of banker for the next hand. After the cards for that hand were dealt, he hastily picked up his hand to set it. I instructed him that, since I could potentially glimpse his cards, it wasn't wise to do that prior to my own hand being set. I also pointed out that he likely wasn’t permitted to set his hand early. However, the dealer chimed in, confirming that it was indeed acceptable as it could only disadvantage him. While I didn't look at his cards, had I done so, I could have split my pair to strengthen the weaker hand and at least achieve a push. Therefore, I have a couple of inquiries.
Is it obligatory for a banker to wait to set their hand until after the other players have set theirs?
If they do not comply with this, is it considered bad etiquette to capitalize on the information to one's advantage? I'd assume it is, as that would be akin to snooping on the banker’s hand. Low Power Rating In Las Vegas, the dealers typically position the cards beneath your bet when you are banking, prohibiting you from touching them until all other players have completed setting their hands. If you attempt to view them prematurely, you will receive a stern admonishment from the dealer. In contrast, at your casino, I wouldn’t hesitate to take a quick peek if the banker sets their hand early. Just remember to be discreet about it. I would equate it to a blackjack dealer accidentally revealing their hole card. That's valuable information, and using it is entirely within the rules.
Fantastic site! Is it possible for Pai Gow Poker to become a game with a positive expectation if the other players place sufficient bets while you are banking?
Absolutely! The table below illustrates the house edge for both the player and banker, dependent on the number of opposing players. The final column indicates the necessary proportion of total action while banking compared to playing to break even. For instance, with seven players, or six competitors, you'd need to wager 13 times more as the banker than as a player.
Banker Ratio Required to Break Even in Pai Gow Poker
At Mohegan Sun Casino in Connecticut, players are permitted to wager their commission (for example, betting $21 to win $20). I perceive this as a slight edge since you’re not incurring commission on the additional 5% of your bet. Is there a real advantage to this? How does this influence the house's odds? High Power Rating When banking, the probability of winning is pegged at 29.91%. Thus, instead of the standard 5% commission for players, you are effectively paying 4.76%. This alteration will decrease the house edge by 0.2991*(0.05-0.0476) = 0.07%.
In Pai Gow Poker, the stronger hand must exceed the lesser hand's value. However, I didn’t detect a similar requirement in the game.
Are players, who are not banking, allowed to set their hands incorrectly and then forfeit their turn, similar to what happens in Pai Gow Poker? Are you aware of the procedures in tile tournaments? Is it permissible for a player to ask for 'house way' during a tournament?
In Pai Gow tiles, the superior hand is always clearly identifiable. You don't need to determine where to position the high hand. Just create any two stacks of two tiles each, and the dealer will resolve the rest. I’ve never encountered a Pai Gow tiles tournament. Nonetheless, the Las Vegas Hilton organizes an annual Pai Gow Poker tournament. I'm not certain if requesting the house way is allowed, but I would bet against it. Most tournaments enforce strict regulations that prevent the dealer from offering any advice. Total Power Rating .
The hand I was dealt in Pai Gow was quite poor. Interestingly, the dealer ended up with the exact same numeric cards, meaning I lost my $5 wager. The dealer commented that she had never seen that happen before, and the pit boss affirmed her statement. What are the odds of encountering a double copy when a player holds a pai gow?
For clarity to other readers, a 'pai gow' hand consists of seven distinct cards, making it impossible to have a straight or flush. The chances of the dealer having the same seven ranks, excluding the joker, stand at 3.
- KQ
- Royal flush
- AA
- KKQQJ
- Wizard of Vegas
- Cary L.
pai gow poker page Shuffle Master Occasionally in Washington State, they waive the 5% commission in this particular game. The profit comes from the banker’s edge and voluntary side bets. How does this impact the odds?
Without the commission, the banker enjoys a 1.3% advantage, while all others face a 1.3% disadvantage, provided that players adhere to the casino's house way. If a player banks half the time, then the overall house edge balances out to exactly 0%. If a player banks 1 out of 7 hands, the total house edge is 0.93%. When a player banks 1 out of 14 hands, the overall house edge stands at 1.11%. If we denote the fraction of hands that a player banks as 'b', then the overall house edge will be expressed as 1.2% - 2.4% multiplied by 'b'.
- sugabush26
- Wizard of Vegas
- Paigowdan
- (1) AAAAW/KK (W=wild)
In some instances in Washington, the player may need to place the Fortune side bet in order to avoid incurring a commission. I cover this regulation in my work.
Regarding Pai Gow and Pai Gow Poker, is it correct that there are no limits on bets made between players when one player is serving as the banker? What occurs if a player or a group of players wagers more than the banker is able to cover?
To answer your second question first, the banker is obligated to have enough chips on the table to accommodate all wagers. If they do not, the dealer will offer them the choice to purchase additional chips or forfeit their opportunity to serve as the banker.
As for your first question, the table limits still apply, even while someone is banking. It would seem like sound business practice to permit any wager, as the casino would benefit from a 5% cut of a higher total. I made inquiries at three different casinos, and here’s a summary of what I was told, in order of my questions: combin .