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Home • What's New • Advice & Strategy • Ask the Wizard • Gambling online • Play for Fun • Site Map • About Us • Colors |
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In baccarat, the cut card is placed in front of the last 13 cards in the shoe, and one hand is dealt following the hand the cut card came out on. If the cut card came out after the first player card was dealt, and both the player and banker draw a card, only 8 cards will remain in the shoe for the last hand. If you are tracking the cards, and know the last 8 cards are all 0-value cards, a table max bet on tie would net you a huge profit. My question is, what are the odds that the last 8, 9, or 10 cards in an 8 deck shoe are all 10 value? Also if you knew exactly what the last 8 cards were, could you use a formula or program to figure the odds that the next hand will be banker, player, or tie? — Mike S. from Michigan City
To answer your first question, the probability that the last 8 cards in an 8-deck shoe are all 0-valued cards is combin(128,8)/combin(416,8) = 0.0000687746. So, it isn’t something to wait around for. I know of no easy formula for what to bet in other situations. If you could find a casino that would allow you to use a computer, the advantages would sometimes be huge towards the end of the shoe, especially on the tie. October 7, 2008
Hi, Wizard. Let’s say I have $300 to gamble with, and can accept a 25% risk of ruin. What should I do to maximize my upside? Thanks! — Jerry T from Hertford I would make the banker bet in baccarat. My betting advice would be to do what is known as a two-step progression. First, bet 1/3 of your bankroll. If that wins, walk away. If that loses, then bet the other 2/3. Again, if you win, walk. With any tie, just bet again until the bet is resolved. Here are the probabilities in baccarat:
Banker: 45.86% The probability of a banker win, given that the bet is resolved is 45.86%/(45.86%+44.62%) = 50.68%. The probability of losing both steps of the progression is (1-0.5068)2 = 24.32%. The banker bet pays 19 to 20, so you will have a 75.68% chance of winning $95, and a 24.32% chance of losing $300. June 7, 2008
I was playing a baccarat game in Asia, where the house paid 150 to 1 for bets on a 1 to 1 tie. What are the odds on that bet? Your site rocks, thanks for all the great work. — Jim from Las Vegas
Thank you for the kind words. My baccarat appendix shows the probability of a 1-1 tie is 0.004101. That is the most infrequent outcome in baccarat, I might add. Fair odds would be (1/p)-1 to 1, where p is the probability of winning, which comes to 242.84 to one. An easy formula for the house edge is (t-a)/(t+1), where t is the true odds, and a is the actual odds. At an actual win of only 150 to 1, the house edge is (242.84-150)/(242.84+1) = 38.1% (ouch!). May 26, 2008
On two recent visits to the baccarat tables the results were definitely player biased. Please tell me if these results would be considered within two standard deviations of the expected results for bank and player. I have eliminated tie hands.
Session I
Session II
From my baccarat page, we see the probabilities in the usual 8-deck game are:
Banker: 45.86% Skipping the ties, the probabilities for the banker and player are:
Banker: 45.68%/(45.68%+44.62%) = 50.68%. The total number of hands in session I was 282+214 = 496. In session I the expected number of player wins is 49.32% × 496 = 244.62. The actual total of 282 exceeds expectations by 282-244.62 = 37.38. The variance for a series of win/lose events is n × p × q, where n is the number is the sample size, p is the probability of winning, and q is the probability of losing. In this case, the variance is 496 × 0.5068 × 0.4932 = 123.98. The standard deviation is the square root of that, which is 11.13. So, the total player wins exceeded expectations by 37.38/11.13 = 3.36 standard deviations. The probability of results that skewed, or more, is 0.000393, or 1 in 2,544. Using the math method for sample II, the probability is 0.042234. If you combine the two samples into one, the probability is 0.000932. About 0.1% is not enough to be "definitely player biased." If you still think the game isn't fair, I would collect more data, for a larger sample size. May 13, 2008
All Books I have seen regarding Baccarat say the banker wins more often than the player. None of them explain why this is. Common sense would make it seem that each side has an equal chance over the long run.
Your explanation will be appreciated. – Al from Mississauga, Ontario Canada
Briefly, it is because the banker gets to act last. If the player got a third card that is likely to help, the banker will hit. If the player’s third card is likely to make the player hand worse, the banker will stand. September 30, 2007
Great site! My question is related to the game of baccarat. In baccarat the casino typically offers somewhere in the region of 20 to 40 times between the minimum and the maximum bet. If a casino, for promotion purposes, decides to offer a bigger spread between min/max and for example offer 100 times between the min/max, what advantage does the player get from such promotion and what mathematical disadvantage or risk, if any, is the Casino taken from such promotion? – Frank from Copenhagen
I have answered this about roulette, and my answer is the same in baccarat. The house edge is exactly the same regardless of the bet spread allowed. I have asked casino executives a few times why they keep the spread as small as they do. For example, if the casino will take a $150,000 baccarat bet in the high-limit room, why a $5,000 maximum in the main casino? The consensus answer is that casinos like to corral their big players into the high limit areas. The reason I get for this is the service and game security is better in those areas. The reason is definitely not to foil system players. September 11, 2007
For baccarat, if you found a casino that allowed a player to bet both player and banker at the same time, is there any advantage to do that? How about if they rated you for the total of both bets? (I.E. - bet $25 on Banker, $25 on Player and be rated for $50) – William R. from Las Vegas
I asked Barney Vinson this question, author of Ask Barney: An Insider's Guide to Las Vegas. He said the casino would likely only rate one of the bets, in your case $25. An advantage to doing that is that it certainly lowers risk. This might be a good play if you needed to put in a lot of action, for example to qualify for an event you were invited to, and didn't have much money to lose. However I think that if large bets were involved ($100 or over) it would set off a red flag, and you probably wouldn't be invited to the next event. July 17, 2007
First of all, thanks for the wonderful site. I recently saw a set of bonus bets in Baccarat called 4-5-6, on the total number of cards between the player and banker hands. The odds they offer at the Atlantic City Hilton are 3 to 2 for 4 cards, 2 to 1 for 5 cards, and I believe 3 to 1 for 6 cards if I remember correctly. That means we should see more hands that end with 4 cards. What are the odds on all three bets? — Ray from Egg Harbor Township You’re welcome, thanks for the compliment. Without knowing anything about the probabilities, if those were the payoffs, then there would exist a player advantage on at least one bet. The way you can tell is to take the sum of 1/(1+x), where x is what the bet pays on a "to one" basis, over all the bets. If this sum is less than 1, then at least one bet has a player edge. In this case, according to your odds, this sum would be 1/2.5 + 1/3 + 1/4 = 0.9833. This trick may come in handy, for example, if you see an amateur putting up sports betting futures. What is probably the case here is that six cards pays 2 to 1. Based on that assumption, and six decks, the house edge is 5.27% on four cards, 8.94% on five cards, and 4.74% on six cards. For more information see my baccarat appendix 5.June 19, 2007
I have just returned from a gambling trip to Niagara Falls, Ontario. Interestingly, Casino Niagara has a Mini-Baccarat table (a 9-seater) where the bank wager is rounded down to the nearest $20 for the purpose of calculating the commission. Thus, a $35 winning bet is only charged a $1 commission. This places the commission percentage on that wager at 2.86%! If I am not mistaken, this means that there is no house edge on bank wagers, but actually a player edge!
Do you agree? – Darryl from Longueuil, QC
As I quoted in an earlier question the probabilities in 8-deck baccarat are:
So the expected value on the banker bet is 45.8597%×(1-(1/35)) + 44.6274%×-1 = -0.00075. So the house still has an edge of 0.075%. The breakeven commission on the banker bet is 2.693%. If you could bet $37.14 the odds would swing to your favor. November 23, 2006
I was recently presented with numbers for the house advantage for Baccarat (Banker=1.17%; Player=1.36%). The problem is the calculations were done without taking the tie wager into consideration. In the past I had seen these numbers in a book though I don’t remember where. My question is, why would someone do the calculations like that? Is there some reason I am missing? It seems to me that this is a flawed method for presenting the house advantage. What is the best way to present to them how/why this is flawed (if it indeed is flawed). – Bill from Las Vegas The reason some sources differ on the house edge in baccarat has mostly to do with how the house edge is defined. I prefer to define the house edge as the ratio of the expected casino win to the initial wager. Other gambling writers define it as the ratio of the expected casino win to bet resolved. The difference is in whether or not ties are considered as a possible outcome. In an eight-deck game the following are the probabilities in baccarat:
Here is how I calculate the expected return on each bet by counting ties.
So I get a house edge of 1.24% on the player, 1.06% on the banker, and 14.36% on the tie. Other gambling writers prefer to think of ties as a non-event, in other words leaving the bet up until it is resolved. The probability of a banker or player win is 45.8597% + 44.6274% = 90.4844%. The probability the next bet resolved will be a player win is 44.6274%/90.4844% = 49.3175%. The probability the next bet resolved will be a banker win is 45.8597%/90.4844% = 50.6825%. The way the other camp would calculate the expected return on the player bet is 49.3175%×1 + 50.6825%×-1 = -1.3650%. The expected return on the banker bet, ignoring ties, is 49.3175%×-1 + 50.6825%×0.95 = -1.1692%. Thus the house edge ignoring ties is 1.36% on the player and 1.17% on the banker. One reason I think counting ties is appropriate is that it gives the player an accurate measure of expected losses over time. For example if a player bet $100 a hand on the banker in baccarat for 4 hours, and the casino’s average rate of play was 80 hands per hour, then the expected player loss is $100×4×80×0.0106=$339.20. No need to worry about the probability of a tie in the calculation. If a casino used the 1.17% house edge for the banker it would be overestimating expected loss, and perhaps over-comp the player as a result. Another reason I count ties is all the major blackjack and video poker experts count ties in the analysis of those games. For example if you ignored ties in 9/6 Jacks or better, when getting a pair of jacks to aces, then the return would be 99.4193%. Never once have I seen such a figure quoted for 9/6 jacks; it is firmly held that it is 99.5439% with optimal strategy. Finally, here is a table of some gambling books and the figures used for baccarat.
Casino Math by Robert C. Hannum and Anthony N. Cabot lists the house edge both ways. November 23, 2006
In baccarat, how much edge does a player get if the first card showing (accident by the dealer) is 9. I saw it happens twice in the casino and everyone bet a huge amount (including me) on player hand and lost both times. My basic math tell me that 50% of the time the player hand will stand on 6 points or higher and will have a about 70 percent chance of winning. Is it a good time to max out my bet? Is it just bad luck or the advantage is not that great for an all in bet? – Davis Q form San Diego
I hope you’re happy, I just made an entire section to answer this question on flashing dealers in baccarat.
September 22, 2006
Love the site. Regarding Baccarat, what is the house edge if one bets less than $5.00 per hand on the Banker? Some mini-baccarat tables used to have a $3.00 minimum. The commission would be calculated as 5% of the nearest $5.00 (so, $0.25 on a $3.00 wager, rather than $0.15.) Thanks for your consideration. – Gary from Albuquerque
Thanks. Paying a 25-cent commission on a $3 bet amounts to an 8.33% commission. Assuming you only play as the player, you will win both bets 28.61% of the time. So the normal cost of the 5% commission rule is 0.2861×0.05=1.43%. The losing on copies rule costs the player 1.30%, for a total house edge of 1.43%+1.30% = 2.73% normally. In the case of this game, the cost of the commission is 0.2861×0.0833=2.38%. So the total house edge is 2.38%+1.30%=3.68%.
September 13, 2006
I looked in your Baccarat appendices and did not find odds for a "Super 6" that paid 12-to-1 as found the Casino Filipino Online. In sum they state: In general, winning hands are paid even money. If the final count of the Banker is 6 while Player has less than 6, bets on the Banker and Super 6 win and the game is a Super 6. In this case, Banker bets are paid 0.5-to-1, while Super 6 bets are paid 12-to-1. The Super 6 bet is based on the proposition that a particular deal would result in a Super 6. Bets on the Super 6 lose when the deal results in a Draw, or any other outcome that is not a Super 6. I was wondering how bad this game could be. Thanks. - Bob from Largo The same game without the side bet was once played in Atlantic City and is analyzed in my baccarat appendix 6. There it shows that the probability of a Super 6 is 5.3864%. So the house edge at 12 to 1 would be 29.977% (ouch!). Sept. 25, 2005 Recently I was watching an episode of the new "reality" show, The Casino. In one scene, the show featured a "high-roller" playing, I believe, blackjack. Apparently this gentleman hit a rather bad losing streak because as he started to lose more and more, he would tear up the cards! I would have thought this a severe breach of etiquette, if not some actual gaming commission regulation, but when asked to stop, he was insulted that they would ask him! Is this sort of thing generally tolerated and I've just never seen it, or is this guy just used to being allowed to get away with that sort of thing because he's losing tons of money, or something else entirely? Baccarat (at the big tables) is the only casino game in which players are allowed to damage the cards. An explanation I heard is that Asian players bend the cards anyway as they slowly peak at them so that they only use each card once. Therefore, as long as the dealer is replacing the cards after one usage, the casino may as well let the players do anything with them. Being able to identify cards is of little value to baccarat players anyway because the dealer doesn't take a hole card (as the dealer does in blackjack) and the player has no choice as to whether to hit or stand. However, there are also gaming regulations that stipulate that the tapes must show all the cards in case of a dispute, which isn't possible if the player tears them up first. In the show you mention, the player didn't know this and I think both parties handled it badly, which led to the hard feelings that the show captured. Had I been the casino manager I would have explained what I just said and then asked the player to lay the card face-up on the table before ripping it into tiny pieces. I am just learning how to play Baccarat and since every player can bet on either player and banker and are not really playing each other, I was wondering what game is played in the James Bond movies? For example, In Dr. No it seems as if Bond is against a woman and he is winning her money? Is there something I am missing or is it a different game? Thank you for your time. Fortunately I am a big James Bond fan and have all the Bond movies on DVD. I checked Dr. No and it seems he is playing Chemin De Fer. The scene was spoken in French, which doesn't help me. There is a similar scene in For Your Eyes Only. In that movie it looks like Bond is playing baccarat, acting as the banker, but after the player acts he pauses and another character tells Bond, "The odds favor standing pat". This would imply that Bond had free will in whether to take a third card, an option you don't have in baccarat. As I understand my gambling history, the American version of baccarat is a simplified version of Chemin De Fer, in which the drawing rules are predetermined. Incidentally, according to www.casino-info.com American baccarat originated at the Capri Casino in Havana, Cuba. Feb. 21, 2005 On baccarat, are the odds perpetual (as in dice and roulette) or do the odds change as cards are dealt out of the shoe (as in blackjack)? I know that it is not at all probable, but is it mathematically possible for the Banker to win every single hand in the baccarat shoe? In an effort to debunk betting systems I used to say that the past does not matter in gambling. However once in a while somebody would rebuke me by saying that the past does matter for card counters, which is true. So now I say that in games of independent trials, like roulette and craps, the past does not matter. As I show in my baccarat appendix 2 a shoe rich in small cards favors the player and a shoe rich in large cards favors the banker. Thus, in baccarat, there is an extremely slight disposition that the next outcome will be the opposite of the last. So, yes, the odds do change in baccarat as the cards play out, but only to a very small extent. For all practicable purposes the game is not countable. I do not know if the banker could win every hand but I speculate that the answer is yes. Nov. 28, 2004 Can you please, please, please put me out of my misery and answer a question that's been plaguing me for months and I just can't seem to find an answer to. I play baccarat mostly for leisure, and have created my own decision rules for when to bet Banker or Player, betting only 1 unit per hand (no betting systems for me). Out of curiosity I tried my decision rules on the both Zumma books (a total of 1600 shoes) and returned a tidy profit (betting an average of 60 hands per shoe). Zumma states that when betting this many hands, his shoes are enough to validate a strategy on a conceptual basis. Yet I've have read that 1600 shoes are not deemed a significant sample size given the large number of possible B/P combinations in a baccarat shoe. I thought about the effect of large populations when selecting sample size (where at a certain level increasing the population does not materially increase the required sample size), and after using different on-line sample size calculators, get around 2,400 shoes as being a significant enough sample for a population as large as the baccarat BP combinations (4,998,398,275,503,360 according to your calculations). So is it 2,400 or 1,000,000+? - Suzanne. P.S. Learning so much from your site, definitely the best I've found. There is no magic number at which you enter the long run or to determine when a sample size is big enough to prove a hypothesis. It is always a matter of degree. However we can say the standard deviation of the sample mean is inversely proportional to the square root of the sample size. Your question is rather vague so let me rephrase it: what is the sample size required so that the sample mean will be within 1% of the actual mean with 95% probability? From my house edge section we see the standard deviation of the banker bet is 0.93 and of the player bet is 0.95. Since you go back and forth we'll use the average of 0.94. Now I'll wave my hands and get an answer of 33,944 hands. At 60 hands per shoe that comes to 566 shoes. In Holland there is a version of baccarat in which the banker bet pays even money, except a winning 5 pays 1 to 2. What is the house edge on this variation? The house edge is 0.93%. More details can be found in my baccarat appendix 6. Aug. 23, 2004 There is a story today about a British man who will bet his life savings on one roulette roll. My friend and I have been debating about what the best casino bet is for this type of wager. If you can only place one bet, and you wish to maximize your odds, what is the best game to play and what is the best bet? First, let me say this guy was a fool. He bet $138,000 on a normal American roulette wheel which has two zeros and a house edge of 5.26%. This amounted to an expected loss of $7,263. However had he taken a 10 minute ride to the Bellagio, Mirage, or Aladdin he could have made the bet on a single zero wheel which follows the European rule of giving half an even money bet back if the ball lands in zero. He planned to make an even money bet anyway. So, at these wheels with full European rules his house edge would have been only 1.35%, for an expected loss of only $1865. Dear Wizard, Great site! I'm a devoted fan who only bets on games with a small house edge. I was surprised to find on the Nevada Gaming Control Board's website, that the statewide casino win percentage for baccarat in 2003 was 19.62% and for mini baccarat, the casinos kept 13.81%. Why such a difference if the two games have the same house edge? By comparison, nickel slots (considered to have a lousy house edge) kept only 7.89% statewide! Why would slot machines (with a high house edge) keep less money than table games (with a low house edge)? Thanks, Andy. Thanks for the kind words. You are far from the only person to be confused about this. The reason is you are comparing the house advantage to the hold. The house advantage is the percentage you will lose, on average, of each dollar bet. The hold is the ratio of money the casino wins to chips purchased. This is going to be much higher than the house edge because in table games players circulate through the same chips for a while. So that baccarat figure is saying that of all the money dropped in the box in baccarat the casino won 19.62% and gave the players back the other 80.38%. Meanwhile the nickel slot figure is saying that of the total amount bet, the casino kept 7.89% and gave the players back 92.11%. To make a long answer short, you are comparing apples and oranges. March 6, 2004 Recently I played at one MG casino (Viper version) High Limit Baccarat and by betting on Banker only, I get an awful result as follows: Player 44 (64.7%) What's the chance of this happening? I appreciate your reply if you can, and hopefully with the formula so that I can calculate it myself next time. It is bad practice to look back at past play and ask about the odds. Rather, I prefer to state a hypothesis and then gather data to prove or disprove it. However, if we must, I would phrase your question this way: "I played the banker bet 68 times and lost 25.95 units (44-0.95×19). What is the probability of losing this much or more?" Hello, Wiz. Really great site. Thanks for all the valuable information that saves us readers countless money on sucker bets. The society needs more people like you to educate us common folks. I come from southern California, and instead of charging 5% on winning, the local casinos here charge commission by each hand you play ($1 for every $100 bet). My question is, what's the house edge for both banker and player in this case? Thanks for the compliment. As I state in my pai gow poker section, the probability of a banker win is 29.98%, a player win is 28.55%, and a tie is 41.47%. So if you are charged 1% the expected return as banker in a head to head game would be .2998-.2885-0.01 = 0.0013, or a player advantage of 0.13%. As player, the expected return is .2855-.2998-0.01 = -0.0243, or a house edge of 2.43%. Jan. 4, 2004 Can you recommend a free baccarat game for the Mac? My webmaster Michael Bluejay is a loyal Mac user and has a helpful page about Macintosh casino games. Sept. 26, 2003 Where I play pai gow poker the commission on a $25 bet is $1, or 4%. How much does this reduce the house edge? A 4% commission lowers the house edge by 0.29%. Aug. 2003 dear sir, i've read your FAQs with great interest.I've a question of my own. In the game of baccarat how man times on average,can u expect a B/P winning streak of nine times in a row.Can u show the mathematics of it. Thank you. The probability of a single banker win is 0.50682483 and the probability of a single player win is 0.49317517, ignoring ties. So the probability that the next 8 hands will be banker win, skipping ties, is 0.506824838 = 0.004353746 . The probability of the same thing on the player is 0.493175178 = 0.003499529. March 21, 2003 Mabuhay!! Great site!!! Ive learned a lot from you! Had I not learned the math behind the casino games, I probably would be a compulsive gambler by now. I used to gamble to win, but after learning that one cannot beat the house, I learned how to play for fun. I'm not sure if you are familiar with Super 6. Its a commissionless baccarat that pays 1:2 on a winning 6. What is the house edge (for banker and player) on this? Also, there's this side bet which pays 12-1 on a winning 6, would this be a sucker's bet? Thanks. - Thefamousv, Manila Thanks for the nice words. I already address commission free baccarat in my baccarat section. Yes, the winning 6 is a sucker bet. The probability of the banker having a winning 6 is 5.39% and the probability of the player having a winning 6 is 6.26%. The house edge on the banker is 30.00% and on the player is 18.68%. March 21, 2003 We have a casino here offer zero commission for the baccarat game. But pay 1/2 if banker win on 8. Is this a favorable edge for the house ,compare to the 5 % commission? - Clint from Singapore The house edge on the banker bet is 4.07%. Nov. 28, 2002 In 500 hands of baccarat betting only on banker, what percent of the time will player win over 46% of the decisions. Thanks - Haig First I'm going to assume you want me to ignore ties. From my baccarat section we see the probability of a player win is 49.32%, given that there wasn't a tie. We'll use the normal approximation to the binomial distribution for this problem. The expected number of player wins is 500×0.4932 = 246.58. 46% of 500 decisions equals 230. The standard deviation is (500×(0.4932)×(1-0.4932))1/2 = 11.18. So... I have two friends that have a bet on which game (craps or baccarat) have the best odds for the player. Could you help me settle this. They are both casino workers and are sure they are right. - Charline from Las Vegas It depends on how the games are played. If optimal strategy is compared to optimal strategy then craps is better. By betting only the line bets and taking maximum odds the combined house edge in craps is well under 1%. The best you can do in baccarat is bet on the banker at a house edge of 1.06%. However, it wouldn't surprise me if the actual house edge in craps is higher due to all the sucker bets players make. Sept. 24, 2002 In an 8 deck baccarat, what is the probability of getting an Ace and an 8 of Diamonds for both the player and the banker in a same deal? - Emi Mungcal from Manila, Philippines (82/combin(416,2))× (72/combin(414,2)) = 0.00000043, or 1 in 2308093 Mar. 6, 2002 Is there a progressive wagering system for baccarat? Is there a specific site for this? - Emi Mungcal from Manila, Philippines There are lots of them and they are all worthless. Mar. 6, 2002 What table game has the best odds for winning and is user friendly for a novice gambler? Thanks in advance. - Dave Holcomb from Port St. Lucie, USA For the person with no casino gambling experience who puts an emphasis on something easy to play, I would start with baccarat. Just bet on the banker every time. Nov. 11, 2001 I was just reading Peter Griffin's Theory of Blackjack and found something in the back of the book that caught my attention. In his analysis of a baccarat count system in order to get true count he divided the running count by the number of cards remaining rather then the number of decks remaining. Is that correct? Thanks for your attention. - Ted Whiting from Las Vegas, USA It is more accurate to divide by the exact number of cards remaining. He was trying to show that for all practical purposes baccarat was not countable, even for a computer perfect counter. Therefore, there was no need to devise a more practical count. If baccarat isn't worth playing for a perfect counter then it certainly isn't worth playing for a mere mortal. Sept. 13, 2001 What is the house edge for baccarat with 10% commission on a winning banker? - Denis The probability of the banker winning is 45.86% and the probability of the player winning is 44.62%. So the house edge would be 44.62%-.9×45.86%=3.346%. Aug. 6, 2001 In Baccarat, you address the question of counting to zero the house edge. But what about the (true) count (for 'player') necessary to make 'player' the better bet than 'dealer'? According to your table in Appendix 2, removing cards 5 through 9 increases the relative probability of a 'player' win. In an 8-deck shoe, is there a point at which the house edge on 'player' falls below that on 'dealer,' even though the edge on both may remain positive? Where is that point? - Richard Conover from Glendora, USA No, unless you are card counting, the banker is the best bet at all points in the shoe. June 6, 2001 I agree with you that there are no system that can beat a negative expectation game. Anyway, I take a look at the cancellation system and keep wondering ... what about using it in a bet like the banker in baccarat, where you have a POSITIVE expectation outcome? In which extension would the commission payed to the house erode your gains in the long run? I apologize for my shady English. - M·rcio from S„o Paulo, Brazil No betting system can beat a negative expectation game. No exceptions. Betting on the banker in baccarat, you may actually cancel out all the numbers and still lose because of the 5% commission you will have paid all along. May 1, 2001 I am thinking of taking the following strategies to play mini baccarat. I only bet after either the Banker or Player has appeared 4 times in a roll. I double my money if I don't win the first time. However, if the second time I don't win, I stop betting for the time being until the next 4 continuous appearance coming again. Once I win, I also stop betting until the next 4 continuous appearance coming. Please evaluate my strategy. Thank you! - Mandy from Gold Coast, Australia Waiting for streaks of four in a row is not going to help. The cards do not have a memory. Doubling after a loss is also not going to help. I would recommend betting on the banker every time. Skipping hands is fine; in fact, not playing at all is the best possible strategy. Feb. 10, 2001 Fantastic site Wiz. This is the best gaming resource I've found in 5 years on the net. However your baccarat probability tables have shaken my belief that 4s favour the player hand. "The Money Spinners" by Jacques Black (!) suggests that low cards (1 to 4) favour the player, and that the 4 is in fact the best card for the player, since it improves every player hand where the 2 card total is 5 or less. Black also suggests that the 6 is the banker's best card, yet your table indicates that it is the 5.I have trialled a simple hi-lo count for baccarat, tracking low cards (1-4) as favouring player, and high cards (5-8) favouring the banker. Should this be revised? ñ Alex of Auckland, New Zealand Thanks for the compliment. The source you cite is correct. I made a formatting mistake in the table. My baccarat appendix 2 should be correct now. My index numbers are in proportion to Peter Griffin's in "The Theory of Blackjack". Thanks for asking about this; otherwise I wouldn't have noticed my error. Dec. 2, 2000 Enjoy your site more than any other gambling site. I am curious about how realistic the randomness of your Java baccarat game is. I've played it for many hours and have been using a strategy that appears to win every time now. I am fearful to try my strategy at a casino though, because I'm unsure of how random your game is. The strategy is to begin with a $5 bet on Banker and with each loss bet one more unit and with every win subtract one more unit. I've only been down about $300 at the most, but usually will get to $1,100 or $1,500 within about 200 hands. What are your thoughts? ñ Michael Andrews of Fort Worth, Texas My Java games are based on the random number generator that comes with Visual J++. For personal play it should be quite fair. I speculate that any bias would only show up over millions of hands. Your results are not the result of a biased random number generator but of both luck and a progressive betting system. Nov. 19, 2000 My question concerns baccarat, is a 1,2,3,5,8,13,21,etc. progression a profitable method of play? I add the previous two bets and bet the sum on a loss and subtract one level of the progression on a win. Any two wins in a row and I go back to 1 unit. i always bet on banker. I've tried this online in several casinos (as well as your site's baccarat game), and it has worked great. Is it flawed? ñ Brantley of Waycross, Georgia All betting systems are flawed. Progressive systems, like yours, usually do win but with occasional large losses. Over the long run you will niether do better nor worse than the flat bettor or user of any other system. Nov. 4, 2000 I was playing Baccarat at OasisCasino.com, they claim that 6 decks are shuffled for each game, however there is no indication of the end of the shoe, hence you can play endlessly without knowing where the shoe starts and where it ends. My question is. How many hands are in a 6-deck shoe? Also, how many hands should I play until I start recording the plays (hands) as a new game? -Gil Zerda, Fullerton , California First, it is very possible that they are shuffling after every hand. Even if they do penetrate into the shoe I doubt they play through the entire thing. Because every round can have 4 to 6 cards the total number of rounds in a shoe would be 52 to 78. Unless you are a master card counter at baccarat I wouldn't bother tracking when they shuffle. Oct. 15, 2000 Dear Mr. Wizard thank you for your very informative website.My question is about Baccarat. What are the good cards for the Player and what are the good cards for the Bank. Kindly give them in their order of strenght. thank you and more power to you. - Herman Garcia of Manila, Philippines Peter Griffin devotes a chapter to the subject of card counting in baccarat in his book The Theory of Blackjack. Here he shows that the best cards (to be left in the deck) for the player are, in order: 4, 3, 2, ace, 10, 9, 8, 7, 5, 6. The best cards (to be left in the deck) for the banker are the opposite of this order. In the book he explains the impact of removal to three significant digits of each card for each bet and explains a card counting strategy based on this information. Be warned, however, that situations where there is an expected gain on one side or the other happens very infrequently. Aug. 13, 2000 Dear Mike, In baccarat game, the odds for Banker, Player and Tie are 45.843%, 44.615% and 9.543% as mentioned. Can you please clarify on how you arrive at 1.064% and 1.228%, please? - Steven from Miri, Malaysia The expected player return per unit wagered on the banker is .45843×.95 + .44615×-1 = -.01064. The player's loss is the casinos gain. Thus, the house edge is -1×-.01064 = .01064 = 1.064%. Likewise, the expected return on the player bet is .45843×-1 + .44615×1 = -.01228; thus, the house edge on the player bet is 1.228%. July 18, 2000 I have a thick, and I mean thick, friend who is intoxicated with having won a fair amount betting player only in baccarat. He plays $10 units and does the dumb play that 9 straight banks won't happen. He escalates to a risk of $3,980 by going 10 10 30 60 120 250 500 1000 2000. How can I find solid mathematical evidence to try to convince him to stop? - Charger This is a close variation of the Martingale betting system in which the player doubles after every loss. Usually the Martingale player will win but occasionally he will have more consecutive losses than he can handle and suffer a major loss. Assuming your friend is betting on the player, the probability that any given bet will begin a streak of 9 losses in a row is (2153464/(2153464+2212744))9 =~ .001727, or 1 in 579, assuming ties are ignored. There is more information available about the folly of the Martingale in my section on betting systems. However, the more ridiculous a belief is the more tenaciously it tends to be held. It usually takes a big loss to convince a believer in any particular betting systems to stop. July 2, 2000 Recently, at a casino I occasionally visit, they had a "teaser" for Baccarat that reduced the commission to 4% during certain periods of the day. I know this would have some effect on the 1.06% house edge on a banker bet, but is it enough to create a +EV for the banker bet? How much would it drop the house edge with a 4% commission on banker bets? - Michael Phillips of Sand Springs, Oklahoma
First of all, thanks for providing reliable gambling info. You are one of only about 4 or 5 sites on the net doing so. In your opinion, is it possible that a mathematically sound method (card counting etc.) could ever be devised to give a positive expectation in baccarat? There has recently been some speculation (and wild claims) on the bj21 'other games' forum. - Gavin Parnell of Bury, St Edmunds, England Every respectable gaming analyst that I know of who has studied baccarat has come to the conclusion that only with a very wide betting spread (like 100 to 1) could the player gain even a very small edge by card counting. The potential advantage of card counting is much better in blackjack and involves less risk. I went to bj21.com to see the discussion you mentioned and not surprisingly the person making these claims was secretive about his system and had only his own limited experience as evidence. April 2, 2000 I was playing baccarat online and out of 75 hands the banker won 52 and the player 23. This is a difference of 29, what is the probability of that happening? - Jon Moariarty of Danville, New Hamshire, USA
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Ask the Wizard: Baccarat