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Reason #4 why the Wizard likes Bodog:
One-stop shopping
Bodog offers the triple crown of gambling: casino, poker, and sports. Many other casinos have tacked on poker as an afterthought, and many poker rooms have tacked on a casino as an afterthought, and the lack of attention shows, sometimes painfully. And very few of these sites let you make sports wagers. But Bodog doesn't just offer all three, they do each one well, and everything's integrated. It's easy to play all three off one deposit, off just one account. Another nice thing about Bodog is that you don't need a separate account to play casino games with fake money. In fact you do not even need an account for that at all, you can just click over there and play. Finally, Bodog usernames are only six or seven characters long making them possible to remember. By contrast some competitors' usernames are extremely long and cumbersome. (Visit Bodog) Jacks or Better game. One click and you're in:
No popups, no download, no registration, no B.S., just the game. |
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Home • What's New • Advice & Strategy • Ask the Wizard • Gambling online • Play for Fun |
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In Pai Gow Poker, the high hand must be greater than the low. I didn't notice a similar rule for tiles, though your Java game enforces one. Are players (not banking) allowed to set hands foul, and then forfeit, as in pai gow poker? Do you know what happens in tile tournaments? Can a player request "house way" in a tournament? — Tabby Cat from Huntington Beach
In pai gow tiles, it is always obvious which hand is higher. You don't need to know where to place the high hand. Just make any two stacks of two tiles each, and the dealer will figure it out. I have never once heard of a pai gow tiles tournament. However, the Las Vegas Hilton has an annual pai gow poker tournament. I'm not certain whether you can request the house way, but I would bet against it. It is a very strict rule in most tournaments that the dealer can not give advice of any kind. June 7, 2008
What is the standard deviation for pai gow tiles?— Doyle from Reno
0.75. March 24, 2008
I'm learning pai gow (tiles) for my next trip to Vegas. I would like to take advantage of the "banking" rules, but I have a couple of concerns, specifically banking and comps. If another player at the table shoves in a huge bet after I decide to bank, can I change my mind? Also, what happens if I don't have enough chips to cover all the bets at the table? Second, I hear that pai gow players are rated much lower than other table games per bet due to the slower pace of the game, true? Do you have an educated guess what the average bet in pai gow would have to be to equal the comp privileges of a $25/bet Blackjack player? — Uncle Mo from Parker
Your timing is good with this question. The summer of 2007 shall be referred to as my "summer of pai gow," because I am devoting a great deal of analysis to the game. About banking, yes, you can change your mind about banking, if a player makes a bet larger than you are comfortable with. It is a rule that you must have enough chips in front of you to cover all the action. My May 5, 2007 column shows that pai gow is rated at 30 hands per hour, at least by the casino that gave me the figures. If you multiply the assumed house edge and hands per hour in that table, you can see the blackjack is rated at 0.525 bet units per hour, and pai gow at 0.495, so blackjack is only slightly better at the same bet size. Although the expected loss is greater in pai gow, the standard deviation is much less. This makes pai gow a great game if you are playing for a rating, and wish to minimize risk. June 19, 2007
For pai gow poker at Mohegan Sun Casino in CT, the casino allows you to bet your commission (i.e. bet $21 to win $20). I see it as a small advantage because you are not paying commission on the extra 5% you are betting. Is it truly advantageous to do so? How does it change the house odds? - Jay R. from Shelton, CT
From my pai gow poker section, the probability of the banker winning is 29.91%. So instead of paying the usual 5% commission as player you are paying 4.76%. That will lower the house edge by 0.2991*(0.05-0.0476) = 0.07%. April 12, 2007
Great Site! Could pai gow poker be a positive expectation game if the other players bet enough while you are banking? – Michael from Knoxville, TN
Yes! The following table shows the house edge as both player and banker according to the number of other players. The last column shows the ratio of overall action as banker to player to break even. So with seven players, or six opponents, you would need to bet 13 times more as banker than player.
Thanks for teaching me Pai Gow Tiles. I had a most profitable time on my last Vegas trip. The question is that at many casinos the limit is $25. When winning, the house vig at some casinos is $1 on $25 bet equaling 4% not the 5% usually as they don't have quarters. Does this affect the house’s edge if you do not vary the amount bet or stick to odd amounts bet? – John from Raleigh, NC
You’re welcome. That was a difficult game to explain. The following table shows the house edge both ways, and the difference, assuming both player and dealer use the same house way.
I was playing pai-gow poker last week at a Las Vegas casino. The other player at the table got tired of losing to the dealer and decided to bank the next hand. Once that hand's cards were dealt he immediately picked up his hand and started to set it. I told him that since I could potentially look at his cards it wasn't a good idea to do that before I set my hand. I also added that he probably wasn't even allowed to set his hand early. The dealer said that it was in fact allowed since it could only put him at a disadvantage. I didn't look at his hand, but if I had I could have split my pair to strengthen the low hand and salvage a push. So I have two questions.
Is a banker required to wait to set his hand until after the other hands are set? If he does not do so, is it poor etiquette to use the information to the player's advantage? I would think that it is since doing so is essentially spying on the banker's hand. – Brian from Crystal, MN
Here in Vegas they always seem to tuck the cards under your bet when you bank and don’t allow you to touch them until everybody else has finished setting their hands. If you try to look at them early the dealer will give you a sharp rebuke. However in your casino I wouldn’t hesitate to try to take a peek if the banking player is setting his hand early. Just try to be discreet. I would liken it to a dealer in blackjack flashing his hole card. That is great information to have and it is perfectly legal to use it.
November 23, 2006
There's this Pai Gow Poker sidebet in Casino Niagara which pays out of a jackpot rather than at fixed odds. I'm wondering what amount the jackpot has to be at for that bet to break even (assuming one set the hand to maximize return of jackpot bet). – William from Mississauga, Ontario
The break even point is $102,680.24. I just added an analysis of this bet to my section on Pai Gow Poker side bets.
August 9, 2006
Love the site!! As mentioned in response to another question, some casinos offer a Dragon Hand in pai gow poker. My theory is to play it if I have, trips or better, preferably without the joker. Others play when they have nothing. Is there any logic to either methodology? -- Michael from Las Vegas
I never play the dragon hand myself because it always loses on copies. Regardless of what is in your hand you have the same odds of making any given hand as the dealer, assuming the same strategy. So if you must play it you may do so whenever you like.
May 18, 2006
First off, thanks for maintaining this site! I find it helpful, and also being a fellow actuary, I can appreciate the amount of detail that you put forth here, and how you can explain the math behind these games in layman (i.e. - non-actuarial) terms. Anyway, I have an etiquette question regarding Pai Gow Poker. I often play this game while in Vegas with friends, and several of them will pull back their bet and sit out a hand when a fellow player decides to be banker. I personally don't do this, being of the mindset that, (a) if I lose, I'd rather my money go to another player instead of the house, or (b) if I win, if the banking player wagering the money, and they're willing to lose it, so it's not difference to them if I get the winning or the house does. I'm curious as to what your opinion is on this practice. Thanks again for maintaining this site! Keep up the great work! -- Andy from Chicago, IL
Thanks for the kind words. I always like to hear from real actuaries out there. My opinion is that it is very bad etiquette to pull back a bet when another player is banking unless the player banking doesn’t mind. Sometimes there is collusion between players to not bank against each other, to reduce losses and volatility. Absent that, refusing to play against a player banker denies the banker the favorable odds the dealer usually enjoys. That just isn’t cool to happily give your money to the casino but not a fellow player. It would be like refusing to give somebody your luggage cart at the airport when you were done with it, even if offered the 25-cent refund.
May 2, 2006
Back in 2002 you answered a question about Washington State and commission free pai-gow, or fortune pai-gow as it's called, saying that since the house always banks, the house advantage is 1.44%. Well, they do allow player banking with commission free pai-gow, so how does that now effect the house advantage? - Michael from Marysville According to my sources in Washington state many casinos waive the 5% commission if the player makes the Fortune side bet. The most common pay table for the Fortune bet in Washington I'm told is 2/3/4/5/25/50/150/400/1000/2000/8000, which has a house edge of 5.85% less 0.93% for each additional player at the table. So the expected loss of a $5 Fortune bet is 29.25 cents less 4.75 cents for each additional player. The following table shows the breakeven point between making and not make the Fortune bet according to the number of other players at the table. For example if there are three other players you should make the Fortune bet if your pai gow poker bet is $16 or more, and not if it is $15 or less. The next table shows the overall expected return according to the number of other players and the bet amount, when not banking.
The next table shows the expected return when banking.
Note that for large bet sizes the sum of the expected return when banking and not banking is just under zero. So it would not be difficult to gain an overall advantage if some players declined to bank. March 27, 2006At the Borgata casino in AC, they have a different rule regarding commission for pai gow poker than the rest of the casinos. They only charge commissions in 50 cent increments, rather than the 25 cent norm. When I played and won a $25 hand, I only paid commission of $1. To what degree does this lower the house edge? From my pai gow poker section we have the following probabilities: I was recently in Las Vegas, and the casinos' methods for playing two pair in Pai Gow Poker vary somewhat significantly from your methodology. I was wondering whether your rules are devised to optimize he player's chances because you know how the house will play, or whether your methodology is simply a better strategy than the house method. If the answer is the former, then if a player banks, the player should play the house way instead of your way? If it is the latter, then your method should always be used. However, if it is the latter, why don't the casinos use your methodology? My two pair rule is optimized to play against the house way. However, I think it is probably just any reasonable strategy. For example, I would use it when banking against other players. The reason the casinos use a more complicated and less powerful rule is probably out of tradition. Whoever invented the game probably came up with that strategy rather arbitrarily and it since become a hard habit to break. Two other rules I find ridiculous are counting A2345 (known as "the wheel") as the second highest straight and bothering to state an exception in the house way that if the dealer has five aces with a pair of kings you should play the pair of kings in the low hand. The probability of getting this hand is 1 in 25,690,513. In my estimation this hand may have come up about 100 times in the history of the game, but has probably never affected the outcome of a hand compared to the alternative of playing a full house in the high hand. Yet every single dealer to have dealt the game had to be bothered with learning the exception. March 10, 2005 At the Trump Casino in Gary, Indiana (near Chicago) the fortune bonus in Pai Gow Poker pays out the regular bonuses for a 3 of a kind or better, but also pays 1 to 1 for 3-pair. Statistically speaking, how will this increase your chances of winning on the bonus? What percentage of the time will a player have 3-pair in their hand? The number of combinations for a three pair without the joker is combin(13,3)*10*combin(4,2)^3*4/combin(52,7) = 2,471,040. The number of combinations of a three pair with the joker being used to complete a pair of aces is 23,776. The number of combinations of a three pair with the joker as the singleton is 61,776. So, the total combinations are 2,556,592. Out of total combin(53,7)=154,143,080 possible, the probability of a three pair is 1.659%. So, changing a three pair from a loss to a win of 1 to 1 decreases the house edge by 3.32%. Assuming the standard pay table on the other hands, this would sway the odds in the player's favor with 3 or more other players. Dec. 27, 2004 You specifically mention that the A2345 is the second-highest straight. I saw one hand where the dealer had it but lost to another straight that wasn't AKQJ10. I didn't want to ask and cost a player his winnings. Is this a hard-and-fast rule that the dealer just overlooked, or do houses sometimes exclude it from their rules? Aug. 12, 2004 There are some casinos that treat A2345 (known as "the wheel") as the lowest straight but most still treat it as the second highest straight. I will make a note that this rule is a generality and not always the case. Can the player gain an advantage in Pai Gow Poker by looking at the other player's cards? I think this would put a small dent in the house edge, assuming you know how to make the correct strategy adjustments, but will not come anywhere close to overcoming it. Aug. 12, 2004 I'm a big fan of your site. I was playing some hands of Pai Gow Poker on my own and came across an unusual situation. After splitting hands, the Player had a flush: A,Q,10,8,3. The House also had a flush: A,joker,10,5,4. So who wins? The rules simply state that the joker can be used to complete a flush but does it have a rank? Can it be used as a second Ace of the flush suit? Thanks. I just asked a dealer and he confirmed that the house would win that hand because the joker would be used as a king. The general rule is the joker can substitute for any specific card not already in the same hand as long as it completes a straight, flush, or straight flush. Otherwise it is treated as a fifth-suit ace, thus allowing for the possibility of five aces. July 11, 2004 I go to Vegas once a year and enjoy playing Pai Gow poker there because all casinos near me do not allow banking. My question is: How big of an etiquette breach is it for players to pull away bets and not play a hand when someone decides to bank. This has happened to me often (usually at smaller casinos, Sahara, etc...) and usually players say "If I wanted to give another player my money I'd play in the poker room" This really bothers me and I just wanted your thoughts. This would make me furious too. While not banking it should not make any difference who is banking. I have never heard of an etiquette rule written about this situation but it falls under a breach of common courtesy in my opinion. June 25, 2004 I see on your site the house way in pai gow poker varies from one casino to another. Which is the one that gives the player the best odds? The various house ways are all very similar and only differ in rare or borderline plays. I have often heard dealer's comment that their casino uses a conservative house way that tries to balance the hands, resulting in more pushes. However, I would doubt if anyone has ever done a comparison study. April 4, 2004 At the new Seneca/Niagara Casino in Niagara Falls NY they refuse to give me a copy of their house way for pai gow poker. I would like to know the house way before I play. Do they have to provide that info? They probably don't have to. Once at the Tropicana in Atlantic City their pai gow poker rules said the house way was available upon request. So I requested it and they ran out of public copies and couldn't show me a house copy because it didn't have the Gambler's Anonymous disclaimer on it. In my opinion, the player should always have the right to know the rules of a game, but unfortunately all gaming authorities seem to think differently. Oct. 15, 2003 Which are the most and least volatile games? Pai gow poker is the least volatile and on average keno is the most. July 14, 2003 Hi, my friends were playing pai-gow and one of the other players had a royal flush with a 3 and 4, and the house also had a royal flush with a 3 and 4 (so the player lost with a royal flush, poor sucker). I was wondering, what are the chances of this happening? Thank you! I really enjoy your website. - Diane The probability of two specific players ties with a royal flush and any two other cards are about 1 in 290 billion. March 7, 2003 In Washington state some of the small non-Indian casinos offer "no-commission" pai-gow so you only lose equality on 'copies'. Without getting into the various house ways can you give some idea of how this improves the player odds? - R.S. from Seattle, US The good news in Washington State is that there is no 5% commission, as you said. The bad news is that the dealer is always the banker, thus the player always loses on copies. Overall the house edge in the Washington game is 1.44%. Nov. 28, 2002 In Stanford Wong's book, "Optimal Strategy for Pai Gow Poker", he presents an analysis of when to keep any two pairs together. Have you done a similar analysis? If not, do you think his analysis gives the optimal plays? - Mike from New York, USA Yes, I have done a similar analysis. It can be found in my pai gow poker appendix 2. There are some important difference between my strategy and his. Wong's is much more detailed, considering the highest two singletons, while mine only considers the single highest. Wong also differentiates between whether the player is banking or not. Finally Wong's book is based on the California game with no 5% commission, unlike my strategy. I do trust Wong's work and don't disagree with his table. Jan. 15, 2002 What is the probability of being dealt a natural seven card straight flush in pai gow poker? I work in a casino and just saw this for the first time in 15 years. The lucky patron won $40,000. - Michael from Southhaven, Mississippi There are 32 possible natural straight flushes (4 ranks times 8 possible spans of 7 cards). There are combin(53,7) = 154,143,080 possible ways 7 cards can be drawn out of 53. So the answer is 32/154,143,080, or 1 in 4,816,971. Nov. 23, 2001 I was recently playing Pai Gow Poker at the Barona Casino near San Diego, CA. They have different rules from Las Vegas, namely 1) They collect a commission on every hand played - $0.50 on bets between $5-$25 and $1.00 on bets between $30-$100. If every player at the table pushes, the commission is not collected for anyone on the next hand. 2) The Joker is a true "wild" card. Not only does it fill out straights and flushes, but it can be any other card needed in any case. For instance I had the Ks Kd 6c 6s 9h 9d and the Joker. I was able to put the two Kings in the low hand and keep the other 5 cards for a Full House! My question: Is this a better game for the player than the Las Vegas versions, even with the commission on every hand? (I seemed to like it. I ended up winning $142.50 after playing for 3 hours.) - Don from Racine, Wisconsin Good question. I assume player banking is still allowed. The 5% commission at the Nevada casinos costs the player 1.46%. The house edge in your game depends on how much you bet. It is lowest for a $100 bet, at 1%. I'm ignoring the rule about everybody pushing, that will lower the edge even more. Much like the card rooms in the Los Angeles area, I think there is potential to beat the house edge if you bank enough of a percentage of the action. Sept. 20, 2001 As a math/statistics instructor, I must say that your site should be required reading before anyone ventures into a casino. I like to bank when playing Pai Gow Poker in Nevada casinos. In Tahoe I can usually bank every other hand. I'm in Vegas far less often and there are more casinos to check out. Do you know which ones will allow you to bank every other hand at a full table (if no other players wish to bank)? It seems to be one in seven some places and one in twelve others. Also, some Tahoe casinos have a jackpot game based on how a players five-card hand. A sucker bet, but as a banker I like it when other players bet it. They'll often set their hand for the jackpot (paid by the house) at the expense of there standard wager (against me) by splitting two high pair to play a straight with 2 singletons, or keeping a full house together and putting two singletons up instead of 3 down, pair up. Do you have any idea which Vegas or Reno casinos do this? - Tom from Fairfield, USA Thanks for your kind words. Actually, I have been asked about teaching a course on the mathematics of gambling at UNLV. Pai gow poker is not my game so I don't follow the details very closely. I do know, as you stated, that some rotate and some zig zag the banker between the players and dealer. However, I don't keep track of who does it which way, sorry. I've also seen that progressive side bet at lots of casinos around town. Again, I don't keep track of who specifically has it. However, banking against it is a great idea, I have never thought of that. Sorry I wasn't much help. First let me say, I think your web site is really great. I have told a few people about it, and hope they will try it too. I wish you continued success with it. I also liked the link to WinPoker. I liked WinPoker enough to order it. This is a great program. I have a question I am hoping you can help me with. I have been trying to figure out the number of times each hand in 7 card stud occurs. I have a copy of your 7 card table, but I am interested in the mathematics to arrive at those numbers. I can figure out the 5 card numbers, but the 7 card just baffles me. I would like to send an Excel 2000 file with my numbers. I would also like to know how to figure the number of straights in a 53-card deck with a Joker. H E L P ! ! ! - Stan from Harahan, Louisiana Thanks for your kind words. I agree that calculating the numbers for seven-card stud is hard. That is why I do it on my computer. My program goes through all possible combinations and scores each one. The number of wild straights in pai gow poker is 11*(44-4)+10*3*(44-4)=10,332. Combined with the 10,200 natural straights the total is 20,532. May 1, 2001 In your play-for-fun pai-gow poker, if you have nothing and drop your 2nd and 3rd highest cards to the front hand, the Advice will occasionally swap the 3rd highest for the 4th highest. I haven't been able to figure out the rule -- first I thought it always did that when your back hand was ace-high, but that didn't hold up. Is it because the house way requires the dealer to drop the 2nd and 3rd highest, so if you and the dealer have equally bad hands, the front hand will be decided by your 2nd highest card but keeping the 3rd highest in the back hand has a better chance of winning? If so, why doesn't it do that all the time? I'm confounded by this. I haven't been able to see the pattern. Please enlighten me! - Sarah from Chicago, USA Sometimes the two-card hand is so bad that it is better to put the third highest card as a kicker in the five-card hand. There is no rule of thumb by which to advise exactly when to do so, but I have noticed it tends to happen when the second highest card is rather low. The logic my program uses is a large array of probabilities that each hand will win and goes with the hand with the greatest possible sum of probabilities that won't spoil the hand. Feb. 10, 2001 In your rules for pai-gow poker you state that A-2-3-4-5 is the 2nd highest straight. Why isn't 9-10-J-Q-K the 2nd highest straight. Please explain. - Gordon from Lewiston, New York I have always wondered this myself. It is probably just one of those weird things like why we spell colonel the way we do. Jan. 14, 2001 You definitely have a problem with the advice feature of this game. In circumstances where you have one pair, you play the pair in the five card hand and the next best two cards in the two card hand. In circumstances you don't have at least a pair, play the 2 & 3 highest card in two card hand. Your advice button gives bad advice. For instance: My Way: 9 Q - 2 4 6 8 A, Java: 8 Q - 2 4 6 9 A Is there something that I am missing here? Is there another strategy at play? It doesn't make sense in these circumstances to reduce the two card hand value to protect more against matching the pair with the dealer which would seem to rarely occur. Thoughts? -- Kevin The rule to put the 2nd and 3rd highest in front is a generality, but is not always the best play. In these situations the front hand is so bad that it is better to put the good kicker in back. Lets look at the following probabilities of winning the first example you sited. See my pai gow appendix for the source of these numbers. Hi, I am regular player of Pai Gow Poker, and I noticed your site has a lot of great information on the game. The other day when I was playing with a friend of mine he was dealt a 9 high hand, which I believe is the lowest hand possible. In all the time I had spent playing the game I had only seem it happen once before. Then five hands later he got the exact same hand(2-3-4-5-7-8-9). We couldn't believe it and were wondering what the odds of that happening were so we thought we would ask you. Thanks for your time and your great site. ñ Doug from Calgary, Canada There are two ways to arrange the ranks to form a 9 high hand, the one you mentioned and 2-3-4-6-7-8-9. The number of suit combinations without forming a flush is 47-4*(combin(7,5)*3^2+6*3+1) = 15,552. So, the probability of a 9 high hand is 2*15,552/combin(53,7) = 31,104/154,143,080, or 1 in 9,911. If you were to play just 5 times the probability of getting two 9-high hands would be 1 in 9,826,685. I believe that this happened due to coincidence as opposed to a fault in the random number generator or the coding of the program. Dec. 10, 2000 What is the probability of getting three pair in Pai Gow? Are the chances lesser or greater than three of a kind? - Alex of Long Beach, Mississippi Not counting a three of a kind and two pairs, the following are the ways to get a three pair and number of combinations. Great site! Is there any way I can download your pai gow practice program to preclude always having to play online? Thanks in advance. - Abraham of Ocean, New Jersey I can send the class file as an attachment to an e-mail. Let me know if this is okay. It is my policy to not send binary attachments unless specifically requested. Nov. 4, 2000 Wizard, love your site. In Pai Gow Poker should the Fortune side bet be made in your opinion. Thanks, I enjoy all your info. Eddie from West Memphis, Arkansas I was just in West Memphis in July. While visiting my cousin on the Tennessee side of Memphis, I drove over the bridge to be able to say I've been to Arkansas. Just eleven more states to go now. To answer your question, no, you should not make the Fortune side bet, or any other side bet. For more information on the Fortune side bet visit my pai gow poker section. Oct. 15, 2000 I play pai gow poker in Atlantic City. Frequently I observe a player playing two hands. My question is: does looking at 14 cards out of 53 give the player any kind of advantage. If so, what %, what kind of change in strategy does entail. Would appreciate any advice. ñ John from Baltimore, Maryland Sometimes in pai gow poker the dealer sets aside a dragon which is offered to each player in turn. This is like playing two hands and is likely what you are observing. However, when playing the dragon hand, the rules generally specify that it must be set according to the house way. If the player could set the dragon hand at will it would definitely help, assuming he could apply the information from his original hand properly. I can not give an exact percentage, this would be very complicated to determine. Sept. 26, 2000
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