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Ask the Wizard #178

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:

  • 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

Book Author Copyright Player Banker
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 think you may be interested in this. I use Betfair here in the UK. I am sure you nice people in America are not allowed to use it for some reason, anyway if you are not familiar with it go to betfair.co.uk and have a look. It is a betting exchange, not a bookmakers. Anyway, my question is this. They are now offering roulette with NO ZERO, yes no zero. It is genuine really. Can you think of a good strategy one could use, and if so would you keep it to yourself? Best wishes, Jonathan. P.S. They offer other casino games with no house edge too.

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%.

I play at Bodog using Neteller. Do you know if they have any plans for deposit & withdraw if neteller & others quit accepting U.S. players? If you win, a check would be worthless if banks won’t accept it.

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.

I was playing pai-gow poker last week at a Las Vegas casino. The other player at the table got tired of losing to the dealer and decided to bank the next hand. Once that hand’s cards were dealt he immediately picked up his hand and started to set it. I told him that since I could potentially look at his cards it wasn’t a good idea to do that before I set my hand. I also added that he probably wasn’t even allowed to set his hand early. The dealer said that it was in fact allowed since it could only put him at a disadvantage. I didn’t look at his hand, but if I had I could have split my pair to strengthen the low hand and salvage a push. So I have two questions.

Is a banker required to wait to set his hand until after the other hands are set?

If he does not do so, is it poor etiquette to use the information to the player’s advantage? I would think that it is since doing so is essentially spying on the banker’s hand.

Brian from Crystal, MN

Here in Vegas they always seem to tuck the cards under your bet when you bank and don’t allow you to touch them until everybody else has finished setting their hands. If you try to look at them early the dealer will give you a sharp rebuke. However in your casino I wouldn’t hesitate to try to take a peek if the banking player is setting his hand early. Just try to be discreet. I would liken it to a dealer in blackjack flashing his hole card. That is great information to have and it is perfectly legal to use it.

In Oklahoma we play at the Indian casinos. I understand we are actually playing bingo. If this is true do they have same payback as Vegas machines with the random number generators?

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.

Five persons are in a room. What is the probability that at least 2 of them were born in the same birth month?

Amy

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.

What are the probabilities in five card stud using a deck with 5 suits instead of 4?

Jason from Egg Harbor Township

Combinations in Five Suit Poker

Hand Combinations Probability Formula
Five of a kind 13 0.000002 13
Straight flush 50 0.000006 5*10
Four of a kind 3900 0.000472 13*12*COMBIN(5,4)*5
Flush 6385 0.000773 5*(COMBIN(13,5)-10)
Full house 15600 0.001889 13*12*COMBIN(5,3)*COMBIN(5,2)
Straight 31200 0.003777 10*(5^5-5)
Three of a kind 214500 0.025969 13*COMBIN(12,2)*COMBIN(5,3)*5^2
Two pair 429000 0.051938 COMBIN(13,2)*11*COMBIN(5,2)^2*5
Pair 3575000 0.432815 13*COMBIN(12,3)*COMBIN(5,3)*5^3
Nothing 3984240 0.48236 (COMBIN(13,5)-10)*(5^5-5)
Total 8259888 1

Note that I reversed the order of the full house and flush.

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:

  • 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.

Okay, my bofriend and I have been together for about 6 years and I just moved far away from him to finish my schooling. He cheated on me with a promiscuous girl. But he told me that he didn’t mean for it to go that far and he was just trying to make out with her to get back at me for making out with another guy-- a couple years ago. I truly love him and want to get past this, but he ended up having unprotected sex with her, in an elevator. He seems sincere in his apologies and is extremely remorseful. Is this something I should try to get over and continue my life with him? Or am I wasting my time?

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.

My boyfriend admitted to cheating on me about 4 months ago, but we have been trying to rebuild our relationship. I’m having a hard time trusting him and I can’t tell if I’m being overly paranoid or if I truly have something to worry about. I don’t know how to talk to him about my concerns without him becoming defensive, but I need reassurance. What should I do?

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.