Ask the Wizard #178
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:
- 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.
Jonathan from Preston, England
I tried to sign up for an account there to check this out but they block U.S. players. I’m told the minimum bet is £2 and the maximum is £50. Even in a zero house edge game like no-zero roulette there is still no betting system that will get above, or below, that 0% figure. No matter what you do the more you do of it the closer the actual house win will get to 0%.
Ron from Tulsa
I’ve received lots of foreign checks from Internet casinos. They never came on casino letterhead. Often I didn’t immediately know whom the check was from because they looked more like generic money orders. So if it comes to this I think Bodog would use a generic looking check or money order that your bank wouldn’t be able to easily trace back to the sender. Besides, I don’t think Neteller is going anywhere.
Is a banker required to wait to set his hand until after the other hands are set?
If he does not do so, is it poor etiquette to use the information to the player’s advantage? I would think that it is since doing so is essentially spying on the banker’s hand.
Brian from Crystal, MN
Here in Vegas they always seem to tuck the cards under your bet when you bank and don’t allow you to touch them until everybody else has finished setting their hands. If you try to look at them early the dealer will give you a sharp rebuke. However in your casino I wouldn’t hesitate to try to take a peek if the banking player is setting his hand early. Just try to be discreet. I would liken it to a dealer in blackjack flashing his hole card. That is great information to have and it is perfectly legal to use it.
Sharon from Oklahoma
Yes, that is true. In some states like Oklahoma traditional “class 3” slots are illegal. A way to get around that law is to have a machine pick bingo cards and balls at random. Certain patterns will be mapped to certain wins and the outcome will be displayed to the player like a slot machine win. If done properly, and often they aren’t, the games play just like those in Vegas. If I recall correctly I saw some popular Williams slots like Reel ‘em In when I was at a casino in Tulsa, with just a little bingo card in the corner of the screen. Otherwise they looked the same to me. I don’t know what return they set their slots to in Oklahoma so I can’t help you with that question.
To keep things simple let’s assume that each person has a 1/12 probability of being born in each month. The probability that all five people are born in different months is (11/12)*(10/12)*(9/12)*(8/12) = 0.381944. So the probability of a common month is 1 - 0.381944 = 0.618056.
Jason from Egg Harbor Township
Combinations in Five Suit Poker
|Five of a kind||13||0.000002||13|
|Four of a kind||3900||0.000472||13*12*COMBIN(5,4)*5|
|Three of a kind||214500||0.025969||13*COMBIN(12,2)*COMBIN(5,3)*5^2|
Note that I reversed the order of the full house and flush.
Darryl from Longueuil, QC
As I quoted in an earlier question the probabilities in 8-deck baccarat are:
- 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.
Abby from LaVista, NE
Sex in an elevator? How come these things never happened to me while I was single. It took me about six months of dating just to get to second base. As I have said numerous times before, forgiveness for cheating the first time is optional but never a second time. Since you say he seems sincere and remorseful I’d get past this if he otherwise has no major faults.
Neeki from San Jose
I wouldn’t bring it up. It will at best accomplish nothing and at worst cause a big argument. Over time you will start to get past this. This also just goes to show that if you do cheat, stop it, but don’t confess.