Share this

Ask the Wizard #162

Hi. I'm curious about the house edge in a game which, I believe, is played only here in Portugal. The game is called Banca Francesa (in a literal translation, French Bank) and is played with three dice. Players can bet in "Big" (sum of 3 dice is 14, 15 or 16), "Small" (5, 6 or 7) or "Aces" (sum is 3 or one spot in each dice) - the dealer will be re-rolling the dice until one of these results shows up. Big and Small both pay even money while the Aces pay 61 to 1. Thank you for your time.

Carlos from Lisbon

From my Sic Bo appendix we see the probability of a total of 5 or 16 is 6/216, a 6 or 15 is 10/216, a 7 or 14 is 15/216, and a 3 is 1/216. So on any one throw the probability of "big" winning is 31/216, "small" is 31/216, and "aces" is 1/216. The number of ways any of these could win is 2*31+1=63. So given that one of these events did occur, the probability that it was big is 31/63, small is 31/63, and aces is 1/63. The house edge on all three bets is 1.59%.

As a dealer, I hear a lot of "Fuzzy Math" from players and always come to your site when I have a question about the odds of a game. I only offer advice when asked because in my view, it’s their hard earned money and they can play however they see fit. My question is, when you sit at a table and hear someone say something mathematically incorrect, do you cringe but keep silent, or do you correct them?

Mike from Vegas

I cringe and keep silent. It is my policy to not offer unsolicited advice. Why pick an argument? Also, I’m not trying to convert everybody to proper strategy. The casinos need some bad gamblers to subsidize the good ones.

First off, thanks for maintaining this site! I find it helpful, and also being a fellow actuary, I can appreciate the amount of detail that you put forth here, and how you can explain the math behind these games in layman (i.e. - non-actuarial) terms. Anyway, I have an etiquette question regarding Pai Gow Poker. I often play this game while in Vegas with friends, and several of them will pull back their bet and sit out a hand when a fellow player decides to be banker. I personally don’t do this, being of the mindset that, (a) if I lose, I’d rather my money go to another player instead of the house, or (b) if I win, if the banking player wagering the money, and they’re willing to lose it, so it’s not difference to them if I get the winning or the house does. I’m curious as to what your opinion is on this practice. Thanks again for maintaining this site! Keep up the great work!

Andy from Chicago, IL

Thanks for the kind words. I always like to hear from real actuaries out there. My opinion is that it is very bad etiquette to pull back a bet when another player is banking unless the player banking doesn’t mind. Sometimes there is collusion between players to not bank against each other, to reduce losses and volatility. Absent that, refusing to play against a player banker denies the banker the favorable odds the dealer usually enjoys. That just isn’t cool to happily give your money to the casino but not a fellow player. It would be like refusing to give somebody your luggage cart at the airport when you were done with it, even if offered the 25-cent refund.

In multiple-deck blackjack, I don’t count cards, and I understand that insurance is generally a bad bet. Sometimes, with six or seven hands playing, I check on what cards are exposed for that deal and place an insurance bet if there are two or fewer 10-pointers visible. How foolish is this?

Jim from Atlanta

In a six-deck game you should have to see 24 non-tens, and no tens, for insurance to be a breakeven bet. The probability of that happening is extremely low. So unless you are counting, I would never take insurance in a shoe game. However, in a double deck game if you can see eight non-tens, and the ratio of non-tens to tens in the rest of the visible cards is at least 2 to 1 then insurance would be at least an even bet. For example: 8 non-tens and 0 tens, 10 non-tens and 1 ten, 12 non-tens and 2 tens. In true single deck (blackjack pays 3 to 2) you only need to see four non-tens and then have the same 2 to 1 ratio in the rest of the visible cards.

In your March 27, 2006 column someone asked about who would win the money if someone put money into your machine and hit the spin button and won. You replied "According to my understanding of the law, the person who pressed the spin button wins the money. Whoever is sitting in front of the machine, and why, or even who put the money in, or even whose money it is, does not matter." Are you telling me someone can just run through a casino hitting other peoples spin buttons and any winnings are theirs to keep?

Nicole S. from Brooklyn

I asked three casino executives about this hypothetical situation. They all said that you can’t win a bet if you don’t make a bet. In the case where betting somebody else’s money is consensual then they will pay the person pressing the buttons. However in the case where it is not consensual they will not pay the person who pressed the button. A more difficult question is whether they will pay the person who did put money in the machine. That seems to be taken on a case by case basis. Considerations include whether the player was vigilant in guarding his machine, how much the player was playing for, and if he is a known good customer. Basically a player should follow the McDonald’s rule of "keep an eye on your fries." However even if the player was remiss in guarding his machine the casino may not want to anger a good customer. It also helps to be playing a high denomination game.

My ex and I have been dating for 5 months. We broke up 2 days before valentines. Mind you he was on the verge of losing his job. Got back to getter two weeks later. Everything seemed fine, no fights. No he’s in the middle of a little legal trouble. We got into an argument on the phone. I hung up. Had some time to think and went over to his house to talk. H broke up with my and said I don’t want a girlfriend that’s what he said last time but we ended going out a gain. I’m very confused. Is it I or is it just when stress kicks in he takes it out on me.

Jen from Vancouver, Canada

I’m not big on yo-yo relationships like this. Legal and job troubles are no excuse to act like a jerk. You already reconciled twice. If you’re happy now then I would continue with the status quo. However, the next time you break up, truly end it.

Hi, I met this great guy through the internet 3 years ago so it’s been a long distance relationship everything went well until he decided that one day he needed space ’coz he is not sure if he is ready to settle down. Just the beginning of this year I found out that he has been seeing someone from work and has not told me anything about it. Guess you are wondering how did I find this out? Well, I found out from someone and also I saw emails between the two of them which made my stomach turn. I kept asking him if he is honest with our relationship and he replies "YES and that he LOVES me and there is nothing for me to worry about ’coz there is no one in the picture but me." The hard part is that I fell in love with him for who he is but now seeing the other side of him I don’t know if I want to be with him in the future if he is "cheating" behind my back. What should I do? Should I just move on or stay in this relationship even though I may see him different everytime we meet or if we meet don’t even know if I want him to be touching me? I need your advice please...

Angel from Edmonton

On the singles market of course people tend to put out their best side at first. The purpose of dating should be to get to know the real person, including the bad side, before starting a life together. You have discovered that this guy is a cheater and a liar. This is an easy one to call, I’d move on immediately. Trust in what your brain is telling you to do. The next time, don’t be so quick to fall in love until you know the guy better.

is my boyfriend cheating on me? i have 2 friends that talk to him a lot more than me. when i tell him to call he almost never does. people also tell me that he’s on drugs and is cheating on me. no one wants us together so i’m afraid to trust them. does it look like he is cheating on me?

Mia from Minneapolis

Why is he talking to your friends more than you? If he isn’t calling then it doesn’t sound like he is truly a boyfriend to begin with. I would ask yourself whether the people who say he is cheating and taking drugs have a reason to lie. If not, I would take what they say seriously. However, does it really matter? It sounds like he has already let you go but doesn’t have the courage to break up to your face.

my boyfriend of 2 years keeps talking to his ex girlfriend (she hurt him really bad) on the phone. I found out he is text messaging a girl from the same town we live in. He said he doing nothing wrong and for me to stop worrying about everything. He has never gave me a reason to doubt his action but I don’t know if I’m being paranoid.

Kabra from Odessa

This alone doesn’t sound like enough evidence to doubt him. There’s nothing to worry about until there is something to worry about. I’d give him the benefit of the doubt and stop worrying.

I was with my boyfriend for a year and a half when I found out that he would have to move to america as part of his job as he is in the military. We were madly inlove and as I was in the 1st year of uni & couldnt move with him we decided to try a long distance relationshio. That was almost two years ago and until days ago I thought we were both happy. I visit him in all term breaks but in the stretch before xmas a mate informed me that he was listed on a singles site. I didnt mention to him that I knew about the site but I did tell him that I couldnt understand why attached guys would go on there. I then got another email from a friend sayin they saw him on another website which he had paid at least $30 per month to become a "gold member". When I confronted him he said that it was his way of dealing with our long distance relationship & he swore blind he had never contacted or met any of the girls on there. After setting some strict conditions & askin to see his recent emails I took him back. However there was one email that I wasnt happy with. It was to a girl & it asked for a photo of herself. He said that it was harmless and just a friend but it was too shady so I emailed her & she told me that my boyfriend had tried it on with her at the pool where they live, petting was involved before she stopped him saying she had a boyfriend. When I asked my boyfriend about it again he denied it & it wasnt until I told him about the email she sent that he admitted to it. I have broken off the relationship but i love him soo much & I want him back but I know that I cant trust him anymore. Please can you advise me on the right thing to do! And if there is potential solutions that we could try to try and build bridges. Or do you think that he might have cheated more times-as everytime Iv looked Iv found something. Is this just a coincidence that I managed to find it all or do you think that there are many more dark secrets? Please Help!!!!

Sophie from London

Long distance relationships are tough. For every one lie you catch him in there are likely several you don’t. However, I would keep in mind that it is tough for a young single man to stay true to a long distance relationship for a long time. I think this will continue as long as you two are apart. In this situation I would be generous with the forgiveness. Unless one of you is able to move soon I suggest agreeing to an open relationship where dating others is allowed, both ways. He sounds like he is still in love and is just looking for something temporary. Hopefully you’ll survive the test of time.

I have been with my boyfriend for almost 4 years. We’ve had a child, but given her away for adoption. While pregnant he would instant message an ex frequently, with very sexual messages. He said that it was nothing. Now, 2 years later, I found hes saying very sexually explict things to another girl. (I found pictures on his cell phone with her from when i was pregnant)I work in the day, he works at night, so i have no clue what goes on during the day. What are your thought? Any advice would be greatly appreciated.

Confused from Chicago

I consider sharing sexual banter electronically with other girls a low, almost harmless, degree of cheating. It could easily be a man at the other side pretending to be a girl (no, I don’t do that myself). So if this is the worst thing he has ever done I’d give him a pass.

My boyfriend of 8mo swears he has not cheated on me. But every time I ask him if he has he says no and looks away, or squints his eyes. And i just get this qut feeling he has, although I cant prove it.Is it just me or could he have really cheated on me.

Ameli from Deerwood

It is a good sign somebody is lying if he can’t look you in the eye. You can never totally rule out cheating unless it would somehow be physically impossible. However, unless you have some much harder evidence I’d give him the benefit of the doubt and stop nagging him.

Me and my boyfriend have been together for 4 1/2 years and we just had a son whom is now 7 months old. when i call my boyfriends cell phone he never picks up, or ill keep calling him and he’ll turn off his phone. and when i tell him why wont he answer my calls he says that his phone died or that he didnt hear his phone or that he was bussy. Sometimes my boyfriend dissapears from me and his family and wont come in contact with us. He doesnt spen as much time as he did with me and his son like before. Hes always braking promises and all he can say is a plain and simple sorry but ends up doing it again. He also leaves me hanging but always tells me that he loves me and that he wants to be with me but at the same time lies too much? I want to know whats going on. is he with someone else or what??

Fairy from North Hollywood

Actions speak louder than words. There could be lots of reasons for his behavior, including just being too young to be a father. Regardless of the reasons there is no excuse for neglecting his responsibilities to you and his son. I would strip him of his boyfriend status and don’t take him back until you get a marriage proposal.

I suspect my b/f of 8 years is cheating what are some of the signs I should look for?

M.T. from Fort Lauderdale

You can tell he is cheating if he is happy.