Ask the Wizard: Baccarat - FAQ
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?
|Player Bet Count|
I show that if the true count exceeds 17,720 then the Player bet house edge is reduced to 1.06%, and becomes as good of a bet as the Banker. At true counts greater than 17,720, the Player is the better bet.
I can't help but say that you can just walk over to a blackjack table and have a much lower house edge with basic strategy.
What is the house edge for baccarat with 10% commission on a winning banker?
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 from Las Vegas, USA
What is the best game to use a match play coupon on?
If used in blackjack, the Match Play will usually only pay even money. This decreases the value of the Match Play itself by 2.3%, which is way too much. Of the true even money bets, the best game to use a match play on in the Player bet in baccarat. That has a probability of winning of 49.32% of bets resolved. For the don’t pass in craps, that probability is 49.30%.The value of a Match Play on the Player bet is 47.95% of face value, assuming you wouldn’t have bet otherwise.
What table game has the best odds for winning and is user friendly for a novice gambler? Thanks in advance.
— Dave from Port St. Lucie
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 from Manila, Philippines
Is there a progressive wagering system for baccarat? Is there a specific site for this?
— Emi from Manila, Philippines
I read your topic in Roulette on the Martingale method. I have tried this method a few times on the computer and I have been up $500. Then I went to the casino and lost over $1000. Because black came up 8 times in a row. But I’m just starting to learn baccarat. I was trying it on the computer and again I have been up $500, by betting on the banker. Starting at $20 then going to $40 then $80 and so on. I was up $500 even with paying the 5%on each hand. Do you think this method would work in a casino? I thought I would ask before I go and lose another $1000. Like I said black came up 8 times in a row. But do you think that the player hand would win 8 times in a row? Plus this game is good because a tie is a push, where in roulette 0, or 00, is a loss.
— Andrew from Maitland, Canada
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
In 500 hands of baccarat betting only on banker, what percent of the time will player win over 46% of the decisions. Thanks
pr(player wins > 230) =
pr(player wins-246.58 > 230-246.58) =
1-pr(player wins-246.58 <= 230-246.58) =
1-pr(player wins-246.58+0.5 <= 230-246.58+0.5) =
1-pr((player wins-246.58+0.5)/11.18) <= (230-246.58+0.5)/11.18) =
So the answer is 92.49%.
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
Are the on line casino baccarat games like a slot machine with the payout set at 98.8% or do they use a random chip? How would you be able to check that out? Wouldn’t it make a difference? Is there a casino you are sure uses a random chip? Thanks.
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 from Manila
Dear sir, I’ve read your FAQs with great interest. I’ve a question of my own. In the game of baccarat how many times on average can you expect a B/P winning streak of nine times in a row. Can you show the mathematics of it. Thank you.
Your site is amazing. Here’s my question. Does match play change basic strategy at all? My non-math-based instincts tell my that surrender becomes a bad idea, that is if you have to surrender your coupon.
Can you recommend a free baccarat game for the Mac?
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?
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%)
banker 19 (27.9%)
Tie 5 (7.4%)
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.
To answer this question we must first find the variance of a single bet on the banker. Here are the possible outcomes and their probabilities, as found in my baccarat section, based on the Microgaming single-deck rules.
So the variance on a single wager is .4596*(.95)2 + .4468*(-1)2 +.0936*02 - (-0.010117)2= 0.861468877.
The variance on 68 of these bets is simply 68 times the variance of one bet, or 68*0.861468877= 58.57988361. The standard deviation of the 68 bets is simply the square root of the variance, or 58.579883611/2 = 7.653749644.
The house edge on the banker bet in a single deck game is 1.01%. So over 68 bets you could expect to lose .67 units. You lost 25.95 units, which is 25.28 more than expectations. So your results were 25.28/7.653749644 = 3.30 standard deviations below expectations. You then use a normal distribution table to find the probability of this. Excel has a feature to do this calculation, simply put: =normsdist(-3.30) in any cell and the result is 0.000483424, or 1 in 2069. So this is the probability of losing as much as you did or more. I appreciate that you didn’t make any accusations about foul play. However, if you had, I don’t think this rises to the level to prove anything. It could easily be explained as simple bad luck.
Hi, wiz. Love your site, please keep it up. I have 2 questions would like to ask.
1) Does card counting only work with blackjack? Is it useless or simply not as effective for other card games like baccarat?
2) In your blackjack card counting section, you mentioned that the Ken Uston’s Plus/Minus strategy counts 3-7 as small cards. Doesn’t it seem more reasonable to count 2-6 as small, and 7-9 as natural?
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?
To answer your question, if forced to make just one even money type bet I would have chosen the banker bet in baccarat with a house edge of 1.06%.
Recently, I was watching an episode of the new a "high-roller" playing, I believe, blackjack. Apparently 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?
On a related note yours truly will be on The Casino sometime this season. The story is some college students try to parlay $1000 into $5000 as quickly as possible. They seek my advice on how to do achieve this goal.
Update: That episode never aired. Probably because of me.
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?
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+? P.S. Learning so much from your site, definitely the best I’ve found.
You say "No betting systems for me", but decision rules as to when to bet banker or player is definitely a betting system. But I’m still skeptical that you return a tidy profit over 1600 shoes.
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?
Dear Mr. Wizard, If you had $5,000 to bet and wanted to win only $200 what game would you play? Please assume European rules and choose only among roulette, black jack, or baccarat.
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.
I just read your answer about baccarat as played in 007 movies, and I would like to let you know that in South America with a point of 5 the player can choose taking a hit or not. As this option should be made prior the bank showing his card, only a fool would take a hit, since in this situation there are 4 cards that favors the player and 5 that hurts him. Best regards from your loyal fan
We see Bond dealing the cards but an unseen dealer is paying players. Bond is apparently betting the opposite of what the only other bettor at the table is doing. In the first hand the other character turns over a 2-card natural 8, Bond turns over a 2-card 5, and Bond wins the hand. This would imply that the other player bet on the banker hand, and thus Bond on the player hand. In the second hand the other bettor increases his bet from half a million to on million, at the goading of his wife. After receiving his first two cards he requests a third. Bond turns over his two cards, revealing a face card and a 5, and gives the other bettor a third card. The other bettor’s cards are not turned over yet but he seems pleased with his hand. Then a third character, who just walked up, comments to Bond, "The odds favor standing pat." However Bond takes a card anyway, which is a 4, for a total of 9. The other player storms off without turning over his cards.
This is consistent with what you said, except Bond is acting last, or as the banker. I tend to think the American makers of the movie didn’t understand European baccarat rules and incorrectly gave the banker the free will take card a card, as opposed to the player. It certainly wouldn’t be the first time a gambling scene was depicted incorrectly in the movies. I have seen numerous card counting scenes in the movies and television, and yet to find anything close to being realistic.
I agree that if given the choice the odds favor standing on 5 as the player. Assuming the banker rules are the same either way then if the player stands on a 5 the following is the house edge per bet, based on an 8-deck game.
Player Hits 5
So if the player consistently hits on 5 the house edge goes up by 0.29% on the player bet. The player will get a 5, while the dealer does not have a natural, 9.86% of the time, for a cost per 5 of 2.94%.
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
I was playing baccarat online at USACasino which uses a live dealer and Playtech software. Apparently Playtech has instituted a new rule that the dealer burns a card after each hand is dealt. This is not the way it is played in casinos. What bearing, if any, does this have on the odds of the game. I can’t believe the casino would institute a new rule that wasn’t in their favor.
— Phil from Yonkers
Love the site. Regarding Baccarat, what is the house edge if one bet’s 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
In baccarat, how much edge do 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 (included me) on player hand and lose both time. 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 from San Diego
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
- Banker wins: 45.8597%
- Player wins: 44.6274%
- Tie wins: 9.5156%
Here is how I calculate the expected return on each bet by counting ties.
- Banker: 0.458597*0.95 + 0.446274*-1 + 0.095156*0 = -0.010579
- Player: 0.458597*-1 + 0.446274*1 + 0.095156*0 = -0.012351
- Tie: 0.458597*-1 + 0.446274*-1 + 0.095156*8 = -0.143596
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.
|House Edge in Baccarat|
|Casino Operations Management||Jim Kilby & Jim Fox||1998||1.24%||1.06%|
|The Casino Gambler’s Guide||Allan N. Wilson||1965, 1970||1.23%||1.06%|
|Smart Casino Gambling||Olaf Vancura, Ph.D.||1996||1.24%||1.06%|
|The American Mensa Guide to Casino Gambling||Andrew Brisman||1999||1.24%||1.06%|
|Casino Gambling for Dummies||Kevin Blackwood||2006||1.24%||1.06%|
|Scarne’s New Complete Guide to Gambling||John Scarne||1961, 1974||1.34%||1.19%|
|The New American Guide to Gambling and Games||Edwin Silberstang||1972, 1979, 1987||1.36%||1.17%|
|Casino Gambling: Play Like a Pro in 10 Minutes or Less||Frank Scoblete||2003||1.36%||1.17%|
|Beating the Casinos at Their Own Game||Peter Svorboda||2001||1.36%||1.17%|
|The Complete Idiot’s Guide to Gambling Like a Pro||Stanford Wong & Susan Spector||1996||1.36%||1.17%|
Casino Math by Robert C. Hannum and Anthony N. Cabot lists the house edge both ways.
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
- Banker wins: 45.8597%
- Player wins: 44.6274%
- Tie wins: 9.5156%
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.
Some of the online casinos such as Bodog pay 9 to 1 for the tie bet in baccarat. What is the house edge for the tie bet with the 9 to 1 payout?
— Bryan from Mill Valley
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
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.
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
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
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
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.
Player wins: 282
Banker wins: 214
Player wins: 879
Banker wins: 831
— Arthur from Wayne, New Jersey
Skipping the ties, the probabilities for the banker and player are:
Banker: 45.68%/(45.68%+44.62%) = 50.68%.
Player: 44.62%/(45.68%+44.62%) = 49.32%.
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.
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
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
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 or $90 (depending on whether you win on the first or second bet), and a 24.32% chance of losing $300.
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
Why do casinos burn cards in blackjack and baccarat?
— Matt from Fort Myers, FL
I know the commandment to not make side bets. However, I have seen a side bet in blackjack that pays 11 to 1, if the player has a pair in his first two cards. Would it be possible using a count system to gain an advantage?
— Brian from Las Vegas
There is a no-commission baccarat game here that pays 1 to 2 on every banker win of seven, except if the player also has four points, it is paid 2 to 1. Do I get better odds if I play this game, or the no-commission baccarat that pays 1 to 2 on banker win on six?
— Raul from Manila, Philippines
I was wondering if there is a way to calculate on average how many trials it would take to lose ten units from any given point, betting on Player in baccarat.
— J.J. from Oceanside, CA
A 60 Minutes interview of Steve Wynn featured the following exchange:
Charlie Rose: You have never known, in your entire life, a gambler who comes here and wins big and walks away?
Steve Wynn: Never.
CR: You know nobody, hardly, who over the stretch of time, is ahead?
I find this hard to believe. What are your thoughts?
— Andrew from Fort Wayne, IN
In London, there is a royal match side bet in baccarat. It pays if the Banker or Player get a king and queen in the first two cards. Do you have any odds on it?
How high can a person off the street bet in the big high roller lounges?
This question was raised and discussed in the forum of my companion site Wizard of Vegas .
I was recently playing in a casino in London where they offer the "Egalite" total side bets in baccarat. These are bets that the banker and player tie at a specific total. Here are the payoffs:
This question was raised and discussed in the forum of my companion site Wizard of Vegas .
There is a well-known story about a freeze-out competition between a Japanese high roller, Kashiwagi, and Donald Trump, that took place 20 years ago. Kashiwagi was not allowed to play more than $200K per hand at baccarat. The game would be over when either the casino or the player was ahead by $12 millon. Assume that Kashiwagi always bet the maximum on Banker. What is the probability that Kashiwagi will win?
b = starting bankroll in units.
g = bankroll goal in units.
p = probability of winning any given bet, not counting ties.
q = probability of losing any given bet, not counting ties.
Here the player starts with $12 million, or 60 units of $200,000, and will play until reaches 120 units or goes bust. So in the case of the Player bet the equation values are:
b = 60
g = 120
p = 0.493175
q = 0.506825
So the answer is ((0.506825/0.493175)60-1)/(( 0.506825/0.493175)120-1) = 16.27%.
It is much more complicated on the Banker bet, because of the 5% commission. That would result in the distinct possibility of the player overshooting his goal. If we add a rule that if a winning bet would cause the player to achieve his goal, he could bet only what was needed to get to $12 million exactly, then I estimate his probability of success at 21.66%.
A simpler formula for the probability of doubling a bankroll is 1/[1+(q/p)b].
This question was raised and discussed in the forum of my companion site Wizard of Vegas .
I heard that blackjack pioneer Ed Thorp also had a card counting strategy for beating baccarat. What do you know about it?
— Tom from Hong Kong
But Edward Thorp and his computer are not done with Nevada yet. The classiest gambling game of all — just ask James Bond — is that enticing thing called baccarat, or chemin de fer. Its rules prevent a fast shuffle, and there is very little opportunity for hanky-panky. Thorp has now come up with a system to beat it, and the system seems to work. He has a baccarat team, and it is over $5,000 ahead. It has also been spotted and barred from play in two casinos. Could it be bye-bye to baccarat, too? —Sports Illustrated, January 13, 1964 issue
Thorp also addresses the vulnerability of baccarat to card counters in his book The Mathematics of Gambling . The link goes to a free online copy. Thorp concludes by saying:
Practical card counting strategies are at best marginal, and at best precarious, for they are easily eliminated by shuffling the deck with 26 cards remaining.
Interestingly, Thorp also says the tie bet pays 9 to 1. Perhaps that rule was more common in 1985, when the book was published. If memory serves me correctly, Binion’s paid 9 to 1 until the late 90’s.
My own analysis points to the same conclusion, although I studied the tie bet with an 8 to 1 win. I find the pair bets that some casinos now offer have the greatest vulnerability, but are still not a practical advantage play.
I asked Don Schlesinger about the apparent contradiction and Thorp’s baccarat team. Don said that he believed that Thorp did indeed have a team trying to exploit the tie bet. Either Thorp’s team found games with a cut deeper than 26 cards, or he had a change of opinion about it sometime between 1964, the date of the SI article, and 1985, when The Mathematics of Gambling was published.
I follow Macau casino stocks and they often quote the casino's theoretical win percentage at VIP Baccarat to be 2.85% of dollars wagered. This number is used by pretty much everyone to forecast earnings for the companies. I was wondering how they calculate this number, and whether this is accurate in your opinion.
That is likely a weighted average of all four types of bets on the table. Most of the money is bet on the Player and Banker, with a house edge of 1.24% and 1.06% respectively. However, the Tie and Pair bets carry much higher house edges of 14.36% and 10.36% respectively. Players apparently are betting a little on this to increase the overall win percentage to 2.85%.
The table below shows a hypothetical mix of bets that arrive at the overall Macau Win Percentage, ignoring the issue of Dead Chips .
|Macau Baccarat — Weighted House Edge|
|Bet||House Edge||Ratio of Bets||Expected House Edge|
Do you have any tips to remember the drawing rules for the Banker in baccarat?
- If the Banker's total is 3, and the Player draws anything except an 8, then Banker draws.
- If Banker's total is 4, then the Banker draws against a Player third card of 2 to 7.
- If Banker's total is 5, then the Banker draws against a Player third card of 4 to 7.
- If Banker's total is 6, then the Banker draws against a Player third card of 6 to 7.
I think I have a winning betting system. However, I need more than the 3,000 baccarat shoes that you have on your baccarat page to test it. Can you make more?
This question is discussed in my forum at Wizard of Vegas .