A friend chooses a 3-flip sequence of heads or tails, and gives me the option to choose my own (different) 3-flip sequence. We flip a fair coin as many times as necessary until one of our sequences comes up. If he picks H-H-H, which sequence should I pick, and what is my advantage on this bet? How do I calculate which sequence to pick based on his chosen sequence?

The following table shows the probability of player A winning according to all possible chosen patterns of player A and player B.

### Probability of Player A Winning

 Player A Player B HHH HHT HTH HTT THH THT TTH TTT HHH 1/2 2/5 2/5 1/8 5/12 3/10 1/2 HHT 1/2 2/3 2/3 1/4 5/8 1/2 7/10 HTH 3/5 1/3 1/2 1/2 1/2 3/8 7/12 HTT 3/5 1/3 1/2 1/2 1/2 3/4 7/8 THH 7/8 3/4 1/2 1/2 1/2 1/3 3/5 THT 7/12 3/8 1/2 1/2 1/2 1/3 3/5 TTH 7/10 1/2 5/8 1/4 2/3 2/3 1/2 TTT 1/2 3/10 5/12 1/8 2/5 2/5 1/2

A memory device to select the optimal pattern is his first and second picks should be your second and third respectively. Your first pick should be the opposite of your third. For example if your opponent chooses HTT your second and third picks should be HT. Your last pick is T so your first should be H, for an HHT pattern. Following this strategy your probability of winning will be 2/3 to 7/8, depending on what pattern your opponent picks.

In your March 20 column, you answer a question about turning your Hold’em hand over once all-in and action is complete. You mentioned your friend was sort of unsure, so I can tell you that in virtually every major card room in America, the rule is this: In a NL tournament, you MUST turn your hand over as soon as all betting action is complete (i.e., all remaining players are all in. This speeds up play as it allows the winning hand to be determined much more quickly. In a NL cash game, it is OPTIONAL to turn over your all-in hand... in fact doing so is the mark of a novice and some consider it rude to turn it over before the river. So there you have it. - Pete from NY

I would like to respond to the question last week about turning over the cards in an all-in situation. I believe I read that one of the main reasons they require the cards to be shown in a situation such as the one above is more specific to tournament play. Requiring to show the cards helps identify possible collusion and the act of dumping chips from one player to another to assist a certain player in getting a chip advantage.

Ed from Indianapolis

Thanks to both of you for the correction.

A friend and I were playing blackjack at Casinos East Chicago. He was playing \$50 per hand and I was progressive betting with a minimum of \$100 and a maximum of \$400 per hand. After about one hour, the pit boss came over, stopped the game and told us that the dealer had miscounted on an earlier hand and that my friend owed the house \$100. We asked for proof. I asked them to count the cards back onto the table. They told us they could not do it because the deck had been shuffled. We then asked for some type of proof. They refused to provide it and we asked for a manager. We both stopped playing and waited about 30 minutes while the Casino amassed a group of about 8 people, including security guards with guns. A person identifying himself as the Casino Manager told us that he had reviewed the film and that the dealer had miscounted and that my friend owed the house \$50. My friend was incredulous as: (i) the amount he was originally told (\$100) was wrong; and (ii) the Casino Manager told us that he had reviwed the film and that we would just have to rely on his word. I tried to interject and the Casino Manager told me that this was none of my business. I told him it was because the two of us were together and he was about to loose the business of two players, including me who had brought \$5,000 and was betting up to \$400 per hand. He told that he didn’t care and with Security with guns standing there again demanded \$50. I was stupified. I paid it on behalf of my friend, gave them my player’s card and told them I would never return.

Jeff from Chicago

I forwarded this story to Brian, who is a former gaming regulator and current operator. Here is what he wrote.

Mike:

This is just bad customer service. In fact, they’ve lost two patrons for life.

For \$50, I would have coached the dealer after coming off the game and never mention it to the patron. If we had a substantial mis-pay, I would allow the patron to view the tape; however, our casino is set up so that there is a monitor in my office where it can be played back conveniently.

Most casinos have a monitor in someone’s office, can burn a DVD for playback on a laptop or have a viewing room adjacent to the surveillance room. The casinos that don’t have such a setup won’t crack open the surveillance room for a patron.

If the patron’s held their ground and refused to pay back the money, the casino would have either had to drop it or notify the Illinois Gaming Control Board that they had a dispute. If the IGCB got involved, they would send an agent to review the tape and then make a ruling - most likely in favor of the casino because they wouldn’t bounce two guys simply to hustle them for \$50. The patrons could also file a complaint with the IGCB, but they would be wasting their time. The best course of action remaining to them would be to write a letter to the company headquarters focusing on how poorly the situation was handled, the integrity of gaming and that the money involved is irrelevant - take the high ground.

Brian

There are a number of inconsistencies with this. For starters, in the state of Indiana (aka the location of the East Chicago casino is) security is -not- allowed to have weapons on any type. The only people allowed to carry firearms in the state onto a casino gaming floor is the State and Local police (in uniform) that are on duty and the IGC (Indiana Gaming Comission). The "whities" or "white-shirts" that are security at any casino in Indiana cannot have any weapons when they are on the casino floor.

As it pertains to the money, it is a relatively minor amount that could have, and probably should have, just been let alone. Floor supervisors have leeway and can tell surveillance that they’re gonna let it go since the players in question will lose it most likely later on in the evening (if they hadn’t already by then). Also, there is no casino in Indiana that caters to players wanting to see the "Footage" of what happened. Surveillance goes over the incident, lets the casino manager see it if he requests it, and then the CM takes care of it as s/he sees fit. In general, \$100 is a minor amount (in case a dealer paid a \$50 bet, it was a \$100 error), however the casino itself actually -has- to take some kind of action to "get the money back" once surveillance has notified the CM about things like that. I’m not 100% sure why, but most likely the answer is once a CM gets involved there’s some sort of report that goes to IGC, in which case the casino has to make sure that we’re doing everything according to "code" or "standards" so to speak.

In general however, said floor supervisor did handle this wrong on several levels and would have been more correct to simply let the situation go into the events of "Oh well, I’ll talk to the dealer when he gets off the game, thank you for your careful watching". And afterwards either replaced the dealer with a different one or watched that particular table closer for more screw-ups.

Also, while I realize this is 2 years ago (wow - missed the date until after I was done with everything) - Figured I would give you my 2 cents as I am a floor supervisor and have been at a number of Indiana casinos.

Regards,
Prax

This is not a game theory question, but I figured since you answer dating questions you might handle this. I had a dream recently where I sat down at an open slot machine. I was getting my player’s card out of my pocket when a guy came up from behind me and put money in the machine. I told him it was my machine and hit the cash out button and gave him his ticket. He said he had his eye on the machine and since he had his money in first it was his machine. I turned to call a slot attendant and while I was doing that he put his money in again, pushed the button and hit a jackpot. In my dream we then had an argument over who gets the money, the person who clearly had the machine and intended to play it or the person who unsolicited put the money in the machine. I realize this is a bizarre situation but who do you think would win the argument?

Bill from Columbia, MD

My understanding is that the person who is pressing the buttons gets the money. I asked Brian, who helped with the last question, about this. Here is what he wrote, which I agree with.

In the scenario described, the person who put in the money and pressed the buttons would receive the jackpot.

What I find interesting about this question is the paradox that in all likelihood, the jackpot never would have occurred without this chance encounter.

As you know, the random number generator in the slot machine is continuously working even when the machine is not in play. So even though one patron feels cheated, their run-in ultimately led to pressing the spin button at that exact millisecond when the RNG was on the winning combination. So, if one patron had acquiesced, there is never a jackpot to fight over.

at the start of "deal or no deal" the odds of picking the 1,000,000 dollar case is 1 in 26. after eliminating all the cases exept 1, what are the odds that my case contains the million dollars. is it 50-50 or still 1 in 26 ?

Ken from Chester, NY

50-50

Are you printing those questions from those dumb bimbos who write in (some of them can actually spell in English) about their troubles with their boy friends strictly for comic relief? Enough already, I would much rather see you devote that space to real questions about casino gambling.

Jack from Troy

Your opinion is duly noted. The advice questions take me very little time to answer, while the gambling questions can sometimes take hours. I answer every worthy gambling question I get, so the advice questions are not taking from the gambling questions. However you are not the first to complain so I will segregate the questions starting now, so you will know when to stop reading.

I think a "good" relationship question is in order. My gf and I have been dating for a year and a half. We both graduate in the spring from college, I with my MS and her a BS. She is going to graduate school and wants me to follow her. Is moving in with her a good idea without a ring yet? I need to work a while before I can afford one, and a year of two apartments seems stupid. We get along perfect, but dropping that on her dad might be a bad idea.

Russ from Columbus, OH

If you can get her father to give his approval, even reluctantly, I would go ahead. Perhaps you can sell him on the idea if there are separate beds. So I would indicate you favor the idea but respect her decision if she opposes it for any reason.

dear Wizard, I have been dating my boyfriend for 6 months, we both came to our school not knowing one another, and we liked each other when we met. I didn’t know that he had a girlfriend, because he never told me, when I asked he said that he would leave her for me. He did and we have been together since except for a month into the relationship when he said that he needed time away to get over his ex. after that we have been very close, but i still feel like he may be secretly dating her or emailing her. even though he says he’s not and I am stupid for thinking so, what can I change?

Melanie from Victoria

There’s nothing to worry about until there’s something to worry about. Unless you have some compelling evidence he’s cheating you should give him the benefit of the doubt. For all he knows you could be cheating on him too. Eventually you will have to choose to trust him if there is any hope this will last.

hi. recently me and my boyfriend had an arguement and i walked out of his house. i rang one of my friends and said can i come meet you cause me and him have had arguement. she went into the toilets as she was at a loud bar and said hes not worth it dumphim, he cheated on you. i was gobsmacked. we had been together everyday and night except for a week after my gran died, he suddenly went round his friend jamies house saturday and sunday.on valentines had a pool game and left me at home on my own, and the dayafter said he would make it up to me but went out with his brother.i was crying when he left asking whyhe couldnt take me out, adn why he went back on his promise. he left me to sit at his all night til he came home out of his face drunk at 2 in the morning.he went out with is brother who is known for cheating and messing women about. apparently that night he saw one of my friends and he kissed two of her friend. there was no exchange of numbers or anything. the day after this hhad hapeened we were rowing alot and i moved out of his. now a month and a half later my friends tell me he cheated on me that night. my friend who saw it didn’t tell me herself and still hasn’t rung me or even text me. the friend who saw it did try and split het rx up with his new girlfriend because she wanted him back. they can say what he was wearing that night but he already said to me that he had seen them out. after i asked him we split up but got back together the next day. he said he will ring the girls and speak to them when i am there and even said if we see them out he will ask them with me why hey were lieing. i dont know who to believe. he has had so many chances to tell me and could have told me when we split up but still said he had never cheated on me.my friends who werent there that night keep telling me he is not worth it and i should end it but they have only heard the girl who supposedly saw its story. what do you think i am so confused. i believe him as he has not stopped telling me he didnt do it. aand even text a few of my friends asking why they lied and hey havent text back. Help

Carrie from London

This one I think sets a new record for my spell checker. I have read this several times and I still can’t make much sense of it. While this evidence of cheating is rather flimsy and hearsay, I’m big on listening to the advice of friends. Love can blind you but your friends can more clearly see what is going on. So if forced I would say go with your friends and dump him. I would recommend using the free time in your social schedule to take some remedial English classes.

is my boyfriend cheating?he goes out late at night for about two hours but comes home and tries to have sex with me.why is that?

Jametrice from Los Angeles

If he were cheating he probably won’t have the inclination or the stamina for you just two hours later. Plus if he were smart he would keep a longer buffer time afterward to help obfuscate an evidence trail. He probably got worked up whatever he was doing while he was out, perhaps at a club or watching pornography, and came home to release his energy.

i work nights on the weekends and when i come home to take care of our kids the next day my 3 year old son says things about another person he says she comes and plays with him sometimes askes where this person is at or says that he wants to go to her house or talk to her on the phone and there are no friends or relitives that have that name he keeps saying could my son have an imaganary friend or could my spouse be cheating on me

Renee from Springfield

Interesting question. To be honest I don’t know much about imaginary friends. My kids and younger brothers never had one. I would question your son further about the details of this mystery woman. What did she play with you? What did she talk about? What does she look like? If your son seems to be making stuff up as you go then it is probably an imaginary friend, if the answers are realistic and things a child would not come up with on his own then there was somebody else over. Even if there were another woman over that still doesn’t necessarily mean there was cheating. If after questioning your son you feel there was a real woman over then I would confront your husband about it. You can tell he is lying if he doesn’t look you straight in the eye and/or he fidgets when he answers. If it gets to the point where you think your husband is lying I would hide a video camera somewhere when you go to work, like the girl did in the movie ’The Sixth Sense’. I’d be interested to know what happens.

my boyfriend of two years is suddenly behaving suspicious,always complaining about having group work for school(hes in college)with all female group members,he even spends the entire night at her house doing school work or atleast thats what he says.he never has time for me if i ask him to visit me he says hes busy with sch. work or he has to meet a group member.the other night i called to ask him how he was and where he was he said he was in sunset i said what are you doing there and he did not reply,i kept asking in a calm tone and he would not answer me he kept brushing over the subject asking me where i am,i told him where i was and he still didnt answer my question,i asked one last time and he jus stayed on the phone in pure silence determined not to tell me what he was doing there.the he sends me a text telling me to leave him bcus he is stressed out.he is a wonderful guy just dont understand why his attitude his changing so much.he says he want to be with me,but hes getting so withdrawn,he use to call and text me all the time but he doesnt nemore.i love him,i can see myself marrying him in the future,but now i’m not so sure whats going on with him and its making me sad.

Joanne from Fort Lauderdale

My advice is to give him some space and time to sort out whatever he is going through. Tell him you are available to listen to whatever he is going through but he will have to make the next move, and stick to that. Hopefully after a time apart he will miss you and make things right.