Ask the Wizard #153

You’re welcome. This is an interesting game. Assuming all wins except blackjack pay 1 to 2, and blackjacks pay 13 to 2 I get a player advantage of 0.7%, assuming six decks. Here is a basic strategy for that game.

You could complete the full house with an ace and a K, Q, or 9. There are 2 aces left and 3 each of K,Q, an 9. So there are 2*3*3=18 such combinations. The only other way would be a K, Q, or 9 pair. There are 3*combin(3,2)=9 such combination. The number of all combinations is 47*46/2 = 1081. So the probability is (18+9)/1081 = 2.50%.

You are just his sex buddy. If you are looking for more than that then my advice is don’t waste any more of your time with him. This also just goes to show what I always say, that it is almost impossible to be just friends after a breakup.

I can think of three reasons that a supervisor would swap decks after a big win. The first is that the decks were worn and due to be swapped anyway. The second is they are concerned the deck is flawed somehow. The third is they are "sweating the money" and incorrectly think swapping decks will change your luck. I would bet that the third explanation is the most likely.

There is an old saying that a man is not going to buy the cow if he can get the milk for free. Three years is enough to be kept in limbo by this guy. Tell him to stop contacting you unless it is with a wedding date.

Here is the probability of getting at least one number more than once according to the number of rolls:

First, the term ’pit boss’ is dated. The proper term for a supervisor assigned to several tables is a floorman. The person who oversees an entire pit is a pit manager. The person who oversees all the table games is the shift manager. Nobody in this chain of command may you give money to. The "suits" are supposed to look after the casino’s interests so a cash tip may seem like a bribe. However you may give money to the poker room supervisors. The reason for the poker room exception is the casino does not risk its own money in the poker room, therefore management is indifferent to who wins.

Let's call the players A, B, and C. The probability A has a pair of aces is combin(4,2)/combin(52,2) = 6/1326. The probability B has a pair of kings is combin(4,2)/combin(50,2) = 6/1225. The probability C has a pair of queens is combin(4,2)/combin(48,2) = 6/1128. However there are 3! = 1*2*3 = 6 ways you can arrange three pairs between three players. So, the answer is 6*(6/1326)*(6/1225)*(6/1128) = 0.000000707321.

You certainly have a valid complaint. However in my opinion online cheating is a much lesser sin than cheating in real life. I wouldn’t throw away three good years over this. My advice is to consider this strike one and keep an eye on his computer activities for a while. Other than that I’d give him a pass this time.