Thanks for the informative site. I can effectively count cards at an online casino, playing head-to-head with the dealer. At a real casino, however, I usually get distracted and lose the count. If the cards are dealt face down, forget about it. The only time I’ve been to Vegas, I played a lot of late night/early morning blackjack, sometimes head-to-head. But that was in my pre-card counting days. My question is whether the card counting pros come out at night when table traffic is down, and if so, is the casino more wary of 4:00 AM players than daytime or evening players?

Freddy from Lansing

You’re welcome. Card counters usually prefer to play by themselves, all other things being equal. This is for various reasons, including more hands per hour, fewer distractions, and nobody to shorten their life expectancy via his/her second-hand smoke. Once when I was caught counting on a cruise ship, the casino manager was kind enough to list all the red flags I raised, and it was an embarrassingly long list. One was playing at 3 A.M., when the casino was almost empty, and another was playing alone. So, this casino manager at least felt counters were more of a risk late at night. Given that experience, I think blending in at busy times outweighs the better conditions at slow times.

About losing the count, I recommend getting a deck of cards and flipping them over two at a time, keeping the count as you go. Try to get through the deck, with an accurate count, within 25 seconds.

If you pick five cards at random from a standard 52-card deck, what is the probability that all four suits will be represented?

Carl Libis from Richmond

There would have to be one suit with two cards, and three with one card each. There are four possible suits for the one that is represented twice. For the suit represented twice, there are combin(13,2)=78 ways to choose 2 ranks out of the 13. For each of the other three suits, there are 13 possible ranks each. So, the total number of combinations is 4 × 78 × 13 × 13 × 13 = 685,464. There are combin(52,5)=2,598,960 ways to choose 5 cards out of 52. So the probability is 685,464/2,598,960 = 26.37%.

Players A and B throw a pair of dice. Player A wins if he throws a total of 6 before B throws a toal of 7, and B wins if he throws 7 before A throws 6. If A begins, show that A’s chances of winning are 30/61.

Sangeeta from Mumbai, India

Let the answer to this question be called p. The probability of rolling a total of six is 5/36, and the probability of rolling a total of seven is 6/36. If you don’t understand why, please see my section on dice probability basics. We can define p as:

p = Prob(6 on first roll) + Prob(no 6 on first roll)*Prob(no 7 on second roll)*p.

This is because, if neither player wins after the first two rolls, the game is back to the original state, and the probability of player A winning remains the same.

So, we have:

p = (5/36) + (31/36)×(30/36)×p
p = 5/36 + (930/1296)×p
p * (1-(930/1296)) = 5/36.
p * (366/1296) = 5/36
p = (5/36)×(1296/366) = 30/61.

Hi, I was recently in Vegas and made a bet on an NCAA tournament game that ended after I left town (I won the bet). While the back of the ticket says I need to mail it registered mail, is this actually a requirement to get my money or do they just want you to send it with delivery confirmation so you can’t claim the casino lost the ticket?

Joe

I would take that as more of a suggestion, than a requirement. They have probably said that for decades, since before the post office had competition tracking mail. Nobody except the post office, including UPS and FedEx, will deliver to a post office box. However, for many of us, including me, the nearest post office is several miles away, and usually has a long slow line. For high-valued tickets I would look up the street address of the casino and use that, attention to the accounting department. For low-valued tickets (\$200 or less) I would take my chances with a first class stamp, to the PO Box. Personally I have mailed in tickets three times, all of which had the registered mail rule. All three times I got a check within about two weeks. With two I used UPS, and one I used just a first-class stamp.

Thank you for your detailed site. In blackjack appendix #9 you state the expected value for the game and the expected value for each play. I would expect the expected value for the game would be the sum of Ei × Pi where Ei is the maximum expected value for the ith play (stand/hit/double/split) and Pi is the probability for the ith play. When I try this calculation I get a different result. For example, six decks, dealer hits on soft 17, and player may not double after split I get 0.04518876.

Frank from San Diego

Those tables assume the dealer does not have a blackjack. This is because by the time it is the player’s turn to act, the dealer has already peeked for blackjack. Making correct double and split decisions should be based on the conditional expected value, given the dealer does not have a blackjack. Otherwise, the player would be overly timid about doubling or splitting against a ten or ace. Adding up the dot product of probabilities and expected values will give an incorrect result, because there is no loss represented for a dealer blackjack.

To get the house edge of the overall game you should subtract the expected loss when the dealer has a blackjack. With six decks, the probability of a dealer blackjack is the number of tens, times number of aces, divided by the number of two-card combinations, which is (6×16)×(6×4)/combin(312,2) = 0.047489. However, the player will only lose when he does not have a blackjack. The probability of a player blackjack, given that the dealer already has one, is (6×16-1)×(6×4-1)/combin(310,2) = 0.045621. So, the probability of the player losing to a dealer blackjack is 0.047489 × (1-0.045621) = 0.045323. You should subtract this number from your dot product above: 0.04518876 - 0.045323 = -0.00615144. Thus, the house edge under the rules stated in the appendix is 0.62%.

Las Vegas casinos, namely Caesars and Bellagio, have recently been giving me a harder time when cashing out over a few thousand dollars in chips. This past trip when I cashed out \$8,000 at Caesers they asked for my Social Security number. When I naturally asked why, they said they couldn’t tell me exactly and all they could do was give me a card mentioning something vague about Title 31. Could you explain to me and your audience in greater detail what exactly is title 31 and, specifically, what will and will not get your flagged by the IRS. Thanks!

James from Los Angeles, CA

Title 31 is a regulation stating that the casino should make a record of cash transactions of over \$10,000 by a single player in a single day. In such cases, a CTR must be filled out, which stands for Cash Transaction Report. This includes making multiple transactions, adding up to over \$10,000. If you cash chips close to, but under, \$10,000, the cage will likely want to make a note of it, in case you come back later that day, and go over the \$10,000 daily limit.

My advice is to give them what they ask for. You have a lot more to fear by looking like you are avoiding CTRs than the CTRs themselves. In fact, I think there is nothing to fear from a legitimate CTR; the casinos generate lots of them. Personally, I have generated hundreds, to no known detriment. However, it raises lots of attention when you look like you are going out of your way to avoid them. I know one person who was rebuffed when he tried to cash in chips, because he had too many previous redemptions of just under \$10,000. So, that is my two cents. Better suited to answer this is "Brian," a current Las Vegas casino manager, and former regulator, whom I like to turn to for procedural questions like this.

In a nutshell, Title 31 is the U.S. Department of Treasury Code designed to prevent money laundering. It requires that certain large cash transactions be reported to the Government. These are filed on FinCEN Form 103 “Currency Transaction Reports by Casinos” (FinCEN is the Financial Crimes Enforcement Network). Casinos are required to report all currency transactions in excess of \$10K in a single day. The “day” doesn't follow the clock − a casino picks their day (e.g., 3 a.m. to 2:59 a.m.).

All Financial Institutions comply with Title 31. Casinos are considered financial institutions because of the types of transactions they perform, which are similar to those of a bank (e.g., check cashing, wires, loans, cash exchanges). Unlike traditional financial institutions, casinos conduct a great deal of transactions with unknown patrons. When you set up your checking account at the bank, you give them all of the necessary information needed to fill out CTRs. However, when cashing chips at the cage, the only way the casino can get this information is to ask. Casinos have to get all of the necessary information to fill out a CTR before the patron crosses the \$10,000 threshold. Since the fines for non-compliance are hefty, they make a diligent effort to comply.

Casinos are apprehensive to give patrons too much information on Title 31 for fear of inadvertently breaking the law. Casinos are specifically precluded from aiding patrons in structuring transactions in such a manner as to allow them to skirt the requirements. When you ask questions, they prefer to point to a preprinted informational card and don’t like to discuss the matter for fear of divulging inappropriate information.

Circumventing Title 31 is relatively easy for undocumented transactions (e.g., chip buys, chip redemptions, etc.), but why would you want to? If the casino has reason to believe that you are purposefully conducting your transactions in an effort to avoid the reporting requirements of Title 31, they'll fill out a Suspicious Activity Report by Casinos form (aka SARC). If a casino learns that you exceeded the \$10K threshold and they didn't get the required information, they will bar you from gaming until they get it. — Brian