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See important note about Bodog payouts & deposits. |
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On your site you show the difference in house advantage for Three
Card Poker with the Mini-Royal payout on the Pair Plus bet. At a local Casino here in Arizona the Mini-Royal plays on the Ante Bonus instead of the Pair Plus. The Ante Bonus pays as follows, 3 of a kind 6 to 1, straight flush 8 to 1, mini royal 50 to 1. What is the change in House Advantage on the Ante and Play with this pay table?
Thanks, Jesse from Scottsdale
I’ve never seen that before; thanks for the information. The house edge on the ante bet, with those ante bonuses, is 4.75%. January 13, 2008
When using a five dollar match play coupon in Three Card Poker, would the optimal strategy change on the Ante/Play portion, based on the following assumptions? The $5 match play must be placed only on the ante bet. Also, in Washington State, the match play coupon has "no monetary value," and thus is not counted when determining how much must be bet on the play portion. Thus, a $5 bet on the ante with a match play requires a $5 bet on the play portion, not a $10 bet. Thank you. – Richard from Bremerton, WA
I assume if the dealer doesn’t qualify, then the player wins $10. In this case, the player should always raise. According to my calculations, the value of this coupon is $2.57. September 30, 2007
With regards to your California Three Card Poker section, there is a casino in Oceanside that offers the game with similar rules. The casino shows one card, but in order to win your ante bet the dealer hand does not have to beat the player's hand. What is the house edge in this game? – Joshua K. from Oceanside
That rule change is worth 2.49% in the player's favor, lowering the house edge from 4.30% to 1.80%. The subraction is not exactly 2.5% less, due to rounding. September 1, 2007
When playing Three Card Poker, and spotting a dealer card, I am aware the edge is 3.48%, played properly. However, the game I play has the 1, 3, 4 Ante Bonus table. I am curious as to the effect this has on my edge over the game, as well as my edge if I only identify ace/paint/non-paint.
p.s. I only play this game because of your book and when one of my sloppy blackjack dealers is dealing Three Card Poker. First time I played I got a straight flush, and the reaction from the table "experts" tearing into me for not playing pair plus was worth the 40 to 1 bet I didn't win. Ignorance is bliss I suppose. – Brock W. from Bible Hill, N.S.
Thank you for buying my book. I heard somebody out there bought a copy. The difference in house edge between the usual 1/4/5 and the 1/3/4 pay tables is 0.46%. So that would lower the player advantage from 3.48% to 3.02% if you can tell the dealer's rank exactly, and 1.95% if you can only tell paint/no paint. I’ve suffered in silence the Pairplus lecture many times, so I know how you feel. July 25, 2007
I went to Vegas last month and played Three Card Poker for the first time. I got a straight flush, and was so excited to win that I didn't notice that the dealer only paid out 20 to 1 instead of 40 to 1. I lost a few hands and left the table to go cash in, then realized what had happened. My question is, if I notice an error in the future, what should I do? I'm assuming after I left the table it was way too late, but what is the rule if I'm still at the table? If I don't point out an error before the next hand begins, is it too late? – Scott from San Diego
Ideally, you should challenge the hand before it is over, while it is still easy to run back the cards. It doesn’t hurt to ask later than that, but you are not entitled to anything. This is getting outside my area of expertise, but the decision whether or not to review the tape would likely depend on the amount of money involved and your value as a player. July 17, 2007
Why does the dealer have an advantage in Three Card Poker? First, it is three random cards vs. three random cards. Second, even if the dealer beats you, he has to qualify, so wouldn't that give YOU the player the advantage? I know, it's stupid but my brain can't comprehend. — Chris from Coon Rapids
Much as in blackjack, the dealer has the advantage because he gets to act last. If both the player and dealer in blackjack bust, the player loses. In Three Card Poker, if both the player and dealer have lousy hands, the player will fold first, and lose. June 2, 2007
As a dealer, I can help with the Three Card Poker positioning of the toke bet question. A smart dealer will position the bet between the pair plus and ante spots and then can take advantage of either bet winning. Shhhhhhhhhh, don’t tell on me. – Name withheld from Niagara Falls
Don’t worry, I won’t give your name. March 18, 2007
Three Card Poker toking: If a player tokes on the ANTE bet, but does not toke on the dealer's play bet, then the toke bet is technically "surrendered," - just as if the player had refused to make his own PLAY bet to play out the hand, technically. However, most dealers ignore the absence of a matching PLAY dealer's bet, and are loath to petition a generous player for fear of appearing selfish, so just pay the ANTE dealer's bet. Of course, the PLAYER must ALWAYS make a PLAY bet to match his ANTE bet if he wants to play out his Three Card Poker hand. Is there an unfair dealer's toke edge to this practice, or is it similar to surrendering after double down for less? I think it's unimportant, as since the player's hand is active, then the toke is active, and the risk versus reward are simply cut in half for both the dealer and the house, - no harm done. The wizard's view would be GREATLY appreciated by this dealer. Regards, Dan from Las Vegas
You're right. If the player makes an ante bet for the dealer then he doesn't seem required to match it with a raise bet if he raises his own bet. The optimal strategy on the tip is to raise with K/Q/10 or better. To keep it simple, this is almost the same as ace high. Anything less and the raise portion of the tip is a bad bet. Following this strategy will result in an advantage of 26.09% on the combined tip bets.
January 18, 2007
Hi, Wizard. The casino here allows players to take over another player's hand in Three Card Poker if he wishes to fold. The player taking over the hand must put up the play bet himself. Should I take over his hand if I know that one of the dealer's cards is 2 to J (low rank card)? What is the player edge? Thanks for your reply. - James from Genting, Malaysia
Yes, you should. If you see the dealer has a 2 to jack the odds favor raising on anything. Using this strategy does result in a player advantage. I get into the details in my book Gambling 102.
December 26, 2006
I deal 3 Card Poker and I like to play my tip bets on the ante. Will I win more money for myself on the ante or should I be going for the long shot on the pairs plus bet? Thanks! – Tim from Deadwood
If you can trust the player to make the raise bet when he raises his own bet then you should put the tip on the ante. However, if the player will never make the raise bet for you, then the tip would carry a 10.11% house edge, making the Pairplus the much better bet.
October 4, 2006
I have begun playing 3-card guts online for play money (they do offer live games). My question is....
Where can I find a guide for what would be a medium starting hand in a 10 handed game...9 handed..8 handed , and so on. The hand rankings are the same as three card poker.
I have found the probabilities for three card poker on your site.
But I do not know how to go deeper to find the medium expected hand.
Can you help? – Annie from Prior Lake
Following is the median high hand according to the number of players. This is based on an assumption of independence between hands, which is not the case, but the table should still be a very close estimate.
Last night, a fellow player at a 3-Card Poker table
dropped his cards on the floor. After the cards were dealt, he had picked them up and was opening them up with one hand while showing them to his son who was a "spectator" behind him. Somehow he fumbled them and all 3 fell to the floor. I had already looked at my two hands ( a flush and a straight!) and placed my bets. The floorman told everyone all their hands were "dead". When I asked for the supervisor, he came over, thought about it for a few seconds, and also agreed it was a "dead" hand. Is this the standard rule on this type of occurance? Should all hands have been disqualified, or just the offender's (who, by the way, had a Q,6,5). I was betting $10 per spot, so my loss was $150 in winnings (I am assuming that I beat the dealer - he never did show his cards). Should I have asked for a copy of the written rule on this? Should I have not given in after the supervisor's ruling?
- Linda from Atlantic City I forwarded this story to Brian, who is a former gaming regulator and current operator. Here is what he wrote. All of the table limit signs usually have the caveat "management decision is final" - not much comfort to the player, but they'll fall back on this for justification. In the scenario described, I would have allowed the hand to continue especially if all of the cards were already out. If I had concerns, I would change the deck out after the hand. Many casinos won't allow 3CP players to even look at their hands until all cards are dealt. This was cutting into my hands per hour so I changed the procedures. Since the potential appeasement payout for a person that receives a good hand and then the shuffler dies is relatively small, I'm willing to take the risk. In Caribbean Stud, no one touches the cards until they are all on the table. April 19, 2006If you have a sloppy Three Card Poker dealer who shows one of their cards, how does this change the house advantage? For instance, you are holding a Q-8-6 and you see that the dealer is holding a Queen or higher, the player would most likely fold the hand thereby affecting basic strategy and the house advantage. If the dealer exposes one of his cards, which happens frequently, the player has a 3.48% advantage if the information is used properly. I explain the proper strategy in my book Gambling 102. However, to answer your question, you would fold Q86 against a queen. Sept. 4, 2005 What is the standard deviation on the Ante & Play bets in Three Card Poker? 1.64 Jan. 16, 2005 I'm a croupier working in a UK casino and just thought I'd point out that our version of Three Card Poker has a slightly different paytable than any of the ones listed on your page.. We pay 35-1 for a straight flush, and 33-1 for three of a kind (then 6-1, 4-1 and 1-1 for the other 3). - Richard T. The house edge of that pay table is 2.70%. Jan. 16, 2005 Assume there are 7 players plus the dealer in a game of Three Card Poker and that the Players only wager the BET if they have Queen/Six/Four or better. Let's assume that I do not have Queen/Six/Four but delay in making my decision until the other six players have made their bets and assume I notice that the other 6 players all wager the BET on the hand. Are my chances significantly improved that the dealer will not Qualify - so that I should wager the BET? You sure make a lot of assumptions. Yes, if you see the other six players raise then there are probably a disproportionate number of kings and aces out of the deck. That would leave the remaining deck rich in smaller cards, making it more likely the dealer will not qualify. So if you had a hand just under Q64 and everyone raised then it would make sense to raise also. However, I have never studied at exactly what point you should. You could improve your odds much more by switching to a game with a lesser house edge. Nov. 28, 2004 First off, I love your site. I occasionally play Three Card Poker at Grand Victoria Casino in Elgin, IL. They have a Pairs Plus Pay Table that isn't listed in your Three Card Section: Pair 1:1 Thanks. This pay table has a house edge of 5.10%. May 30, 2004 Hi wizard - thanks for a great site! The basic Three Card Poker strategy is to play Q-6-4 or better to minimize the house edge. But what is the best strategy to minimize the element of risk (given '5-4-1' rules)? Your site reads that playing Q-6-3 loses 1.00255 units; but then betting that hand will dilute the element of risk, since the bet is suffering a house advantage of only 0.255% (which is less than the 2.01% element of risk). You're welcome. To minimize the element of risk you should raise until the point where the expected value of raising is less than the element of risk for the entire game. The expected loss by raising on Q62 is 1.24% and on Q54 is 2.10% to 2.15% (depending on how the cards are suited). So, to minimize the element of risk you should raise on Q62 or higher. April 22, 2004 Is there an optimal strategy for the amount of the Pair Plus bet in relationship to the Ante? (i.e. should the Pair Plus bet be 2x, 5x or some other increment of the ante to maximize potential return?) Bet 100% on the Ante, because the ante has the lower element of risk. March 6, 2004 Good Day. May I say that I have thoroughly enjoyed looking through your web site. Can the house advantage on any particular game be affected by the Limit/Maximum being too high (i.e. over $5000 on the pair plus), especially with three card poker? Best regards, John (London, England) Thank you. No, the house edge is not affected by the table minimum and maximum. The greater the spread between minimum and maximum bet the greater the volatility, but in the long run results will keep getting closer to the house edge. Some people incorrectly believe that setting a maximum bet increases the house edge, but it does not. March 6, 2004 What is the optimum ratio between the Pairplus and Ante bet in Three Card Poker? - Mark Snyder from Jacksonville, Florida 100% Ante and 0% Pairplus. The reason is the Ante bet has a lower element of risk. The house edge is defined as the ratio of the expected loss to the initial wager. The element of risk is defined as the ratio of the expected loss to the average total wager. Although the Pairplus has the lower house edge, I believe when comparing one game against another the element of risk should be used. The element of risk on the Pairplus is the same as the house edge, 2.32%, and on the Ante bet the element of risk is 2.01%, assuming full pay rules. Casinos that offer less than full pay take much more from the Pairplus bet, making the Ante even better by comparison. So don't waste any money on the Pairplus, although the other players will think you're crazy as a loon. May 26, 2003 What are the odds of getting the same hand as the dealer in Three Card Poker, and how did you got your answer. Sincerely, Darcy J. Ahenakew The probability is about 1 in 1 in 903.76 but the solution is too involved to explain. March 7, 2003 Hi, I just have a general question. It is about the Poker Table Games. Why is it that almost every casino carries "Let it Ride", "Caribbean Stud Poker", and "3 card poker"? Some of those other Poker games I was reading about on your website sound cool, but they aren't around at the Atlantic City locations. Is it because the above games are more popular, or just because the casino makes more money on them? Just wondering since Bally's and Caesars in Atlantic City are testing the Boston 5 Poker game, and I like that game the best so far. i hope they keep it there. It is nice when the dealer doesn't have to qualify (the reason why I try to avoid Caribbean stud poker) Thanks for your time, Joe Ultimately, the games that you see in the casinos are the ones that make the most money for the casinos. For a game to make money, the players have to like it. So these games you mention are what players find the most fun. It also helps that they are owned by big gaming companies that have the resources to get them out there in the first place. March 7, 2003 Playing 3 Card Poker and using a Shufflemaster, I received 2 consecutive hands with the same cards, same suit (from the same deck). I was sitting at first base, so these were the first cards out both times. What are the odds of this occurring on consecutive hands? - Larry from Silverdale, Washington There are combin(52,3) = 22,100 ways to arrange 3 cards out of 52. So the probability of any given hand exactly matching the previous one is 1 in 22,100. Why is a straight a higher hand than a flush in the new casino game 3 card poker? - Joe from Sloatsburg, USA The probability of a straight is less than a flush with 3 cards. The number of ways to form a flush is 4*(combin(13,3)-12) = 1,096. The number of ways to form a straight is 12*(43-4) = 720. Sept. 24, 2002 In your Table of probabilities in Three Card Poker you state the number of combinations as 9720 for Queen to Ace high and Jack high or less as 6720. I'm trying to calculate these probabilities myself and have failed to do so. I would be obliged if I you could let me see your calculations. Much obliged. - Paul Wood from Bradford, England The probability of any hand less than a pair is the product of the number of ways to pick 3 different ranks out of 13, less 12 for the consecutive ranks that result in a straight, and the number of ways to pick a suit 3 different times, less 4 for picking the same suit each time. So the total combinations for ace-high or less is (combin(13,3)-12)*(43-4) = 16,440. When playing Three Card Poker what is the optimal ratio of the Pairplus bet to the ante/play bet? (Since if you have a Q/6/4 or better but no-pair and the dealer does not qualify - you lose the Pairplus bet but win the Ante. In this case a equal bet on both with be a push - but doubling the Pairplus bet on the Ante - would give you a win of the Pairplus bet amount) - Arthur Bocian from West Orange, New Jersey The optimal ratio is to bet 100% on the ante and 0% on the Pairplus. Assuming full pay rules the element of risk is 2.01% on the Ante and 3.37% on Pairplus. Your goal should be to minimize the element or risk as much as possible. Be warned that every other player will bet on the Pairplus and will ridicule those who don't go along. Once I bet $50 on the Ante only and got a straight flush, which would have paid $2,000 on the Pairplus. The other players had a good laugh at my expense but I had no regrets. June 28, 2002 In Three Card Poker which is the better bet, the Pairplus or the Ante & Play? - Mark Snyder from Jacksonville, Florida I asked this very question on one of my homework assignments for my casino math class at UNLV. Although the house edge is generally higher on the Ante, it is the better bet. The reason is that it has a lower element of risk (the ratio of expected loss to the total amount bet). May 8, 2002 Wizard -What is the advantage in Three Card Poker in playing two hands versus one, if there is one? Some casinos allow you to play two, playing the first hand before looking at and making a decision on the second hand. Some casinos will only let you play the second hand blind, which I'm sure is no advantage to the player. Thank you - Ruby DeVos from Tacoma, USA Good question. In Stanley Ko's booklet "Mastering Three Card Poker", he says that if you had a concealed computer to take maximum advantage of the information then seeing the first hand would lower the house edge from 3.37% to 3.31% on the second hand. Even if you could see all seven hands at the table the house edge would still be 2.32%. Mar. 6, 2002 Wizard, I have just read an article on another site that was talking about Three Card Poker. The author called the "Pair Plus " bet a sucker bet ,compared to the "ante" bet. Of the two bets , I thought the "ante" bet was more of a sucker bet because of its higher house edge. Also, what is the element of risk in Three Card Poker , compared to Let it Ride , assuming the player is starting with $5 bets in the three betting circles for Let It Ride, and $5 in the Pair plus and ante bet in Three Card Poker? - Eddie Garrett from West Memphis, Arkansas Good question. In full play Three Card Poker the house edge on Pairplus is 2.32% and on Ante & Play is 3.37%. However, the element of risk on Pairplus is still 2.32% while in Ante & Play it is 2.01%. I believe if comparing one game to another the element of risk is more appropriate. In other words, comparing the expected loss to the total amount bet. In this case, Ante & Play has the lower element of risk and is thus the better bet. So I would disagree with the writer of the article you mention. According to my house edge index the element of risk in Let it Ride is 2.85% higher than that of Ante & Play. Feb. 11, 2002 My question is a very basic one. Are the odds for slots and the payoff tables for games like Caribbean Poker, Three Card Poker and Let It Ride typically lowered on board the cruise ships from major cruise lines? - Paul Robinson from Novi, Michigan I'm not sure. The only cruise I ever took was from Florida to the Bahamas and it only lasted about eight hours. This was before I started this web site so I didn't pay close attention to the rules. However, I do recall that the blackjack rules were stingy, and that I lost a lot! Other things I have read corroborate that cruise ships casinos are tight. After all, where else can you play? However, the games you mention already have rather high house edges so perhaps they won't mess with them. I also know that Caribbean Stud Poker has a more generous paytable in Europe and Africa, so maybe they use that one. Jan. 15, 2002 What is the probability of getting two identical straight flushes (in both ranks and suit) two hands in a row in Three Card Poker? - Ralph Harpster The probability of getting a straight flush on the first hand is 4*12/combin(52,3) = 48/22,100 =~ 0.0022. The probability that the next hand will be exactly the same is 1/22,100. So the answer is (48/22,100)*(1/22,100) = 48/488,410,000, or 1 in 10,175,208. This is a 1.37 more likely than hitting a 6/49 lottery, which has a probability of 1 in 13,983,816. Jan. 15, 2002 I was playing 3 card poker at the Venetian this weekend and a friend of mine drew 3 Queens in the same suit in 2 consecutively dealt hands. Was very curious as to what the odds are of that happening? - Bruce Keene from Williston, Vermont The probability of getting three queens in one hand is combin(4,3)/combin(52,3) = 0.000181. The probability of doing it twice in a row is 0.0001812, or 1 in 30,525,625. The probability of them being the same three suits both times is 0.0001812/4, or 1 in 122,102,500. [Bluejay notes: The odds of hitting the Megabucks slot jackpot are only about 1 in 50 million!] Nov. 23, 2001 In Three Card Poker would it be prudent to increase your bet after say 5 or 6 losses? I know the Martingale system is bad news but since in Three Card Poker you have bonus payouts for better hands I thought it might be worth a chance. Please think about this for a minute before you answer. - John Cameron from Crestwood, Illinois In the long run it doesn't matter what you do. As I have said numerous times, measured by long term results, all betting systems are equally worthless. Systems in which you chase loses with bigger bets increase the probability of a modest short term win but at the cost of even bigger losses when your luck is at it's worst. June 29, 2001 Ever wonder why Three Card Poker is not available online? - Bob Beck from Houston, Texas It is still not as popular as Let it Ride and Caribbean Stud. I speculate that the software developers either don't understand it or don't think it is popular enough. However, I get asked about Three Card Poker online all the time. The first online casino to offer the game is going to be very glad they did, I predict. (p.s. Since this question was published Three Card Poker became available at most Internet casinos) Nov. 11, 2000 First, let me congratulate you on your great website. I tell everyone I know that if they are going to gamble to make sure that they visit your site first! My question is on Three Card Poker ante & play. If you know one of the dealer's three cards how should you change your basic strategy and could you obtain an advantage over the house and by how much? -- G.M. from Monmouth County, New Jersey Are you friends with Brian Widdowson (see above)? In "Mastering the Game of Three Card Poker" by Stanley Ko, a section is devoted to this topic. He explains when to raise and fold on a queen high hand, based on the cards of other players you are able to see. According to Ko, if you had perfect knowledge of all cards in a seven-player game and could make perfect use of this information it would cut the house edge from 3.37% to 2.32%. You can find this booklet at the Gambler's Book Club. Thanks for the compliment on my site. Nov. 11, 2000 What online casinos have Three Card Poker to bet on? ñ Stacy from the USA None that I know of have Three Card Poker. Sept. 10, 2000 How is the house edge derived in Three Card Poker (ante/play bet)?? I haven't played yet, but my guess is that the edge comes from the fact that the player must decide whether to fold before the dealer. If the player folds and the dealer does not qualify, does the player get paid on the ante anyway?? Otherwise, it would seem an even game (which is obviously not the case). Thanks in advance. ñ T.T. from Clarkston, Michigan The house edge lies in the rule that if the player folds he loses, even if the dealer doesn't qualify. Sept. 3, 2000 Do any of the online casinos offer three card poker? ñ Bill from Birmingham, Alabama I don't think so. I have never seen it myself. July 9, 2000 How do you go about working out the separate probabilities for getting: (1) queen high, (2) king high, and (3) ace high in three card poker? - Paul Goodchild I'll just work out the king high first and briefly show the formula for the other two. The probability will be the number of king high hands divided by the total number of hands. The number of ranks less than king is 11. The king high hand must have 2 different of these ranks. The number of ways to arrange 2 out of 11 is combin(11,2) = 55. However, one of these combinations is king-queen-jack, resulting in a straight, so subtracting that combination there are 54 left that do not form a straight. Next there are 4 suits for each rank, or 43=64 possible combinations of suits. However, 4 of these 64 result in a flush so there are 64-4=60 combinations of suits left. So the total number of king high combinations is 54*60 = 3,240. There are a total of combin(52,3)=22,100 to arrange 3 cards out of 52. So the probability of forming a king high is 3,240/22,100 = 0.1466063 . I noticed on your page for three card poker you advise to stay with Q/6/4. A dealer in Tunica told me Q/J. Why the difference and is the Q/6/4 suggestion based on actual computer generated odds? Seems a pretty good game with low house odds, no skill involved. What do you think? - Weintraut from ? I have no doubt that Q64 is the optimal strategy for three card poker. Stanley Ko independently came up with the same advice. This strategy is based on a computer program which analyzes all 22,100 possible combinations of the player's three cards and for each one the remaining 18,424 possible combinations of the dealer's three cards. If you follow the dealer's strategy you will be folding on some hands which have an expected return of more than -1 (the return by folding). Overall, however, it shoudn't make a big difference. For a game of little skill three card poker is actually not that bad when comparing the house edge to most other games. Mar. 25, 2000
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