Ask The Wizard #206

You're welcome! Typically, those who count cards like to play solo, provided the circumstances are favorable. This preference stems from a variety of factors, such as being able to play more hands per hour, experiencing fewer interruptions, and avoiding the health risks associated with secondhand smoke from other players. I recall an incident on a cruise ship where I was caught counting cards, and the casino manager detailed all the suspicious behaviors I exhibited, which was a surprisingly lengthy list. One of those behaviors included playing at 3 AM when the casino was nearly deserted, and the other was playing without any companions. It seems that the management is more wary of card counters during late-night hours. Based on my experiences, I believe that trying to blend in during busy periods can provide a better advantage than taking advantage of quieter moments.

To help maintain your count, I suggest practicing with a deck of cards by flipping over two cards at a time while keeping track of your tally. Aim to go through the entire deck while keeping an accurate count in about 25 seconds.

To achieve this, you need to have one suit represented by two cards and each of the other three suits represented by one card each. There are four different suits that could be the one represented by two cards. For the suit that has two cards, there are:combin (13 choose 2) = 78 different combinations to select 2 ranks from the 13 ranks available. Each of the remaining three suits has 13 potential ranks as well. To find the total number of valid combinations, you multiply 4 by 78 by 13 by 13 by 13, giving you a total of 685,464 combinations. There are combin(52,5) = 2,598,960 ways to choose 5 cards from a total of 52. Therefore, the probability comes out to be 685,464 divided by 2,598,960, which equates to approximately 26.37%.

Let’s define the probability of this outcome as p. The chances of rolling a total of six are 5 out of 36, and the chances of rolling a total of seven are 6 out of 36. If this part is unclear, refer back to my explanation on: dice probability basics . We can define p as:

p = Probability of rolling a 6 on the initial roll + Probability of not rolling a 6 on the first roll * Probability of not rolling a 7 on the second roll * p.

This is because if neither player wins after the first two rolls, the game resets to the original scenario, and thus the likelihood of Player A winning remains unchanged.

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.

I would interpret that as more of a guideline rather than a strict mandate. That suggestion has likely been in place for many years, even before the advent of competing services for tracking mail. It's worth mentioning that only the postal service can deliver to a post office box; UPS and FedEx do not have that capability. For many, including myself, the closest post office is quite distant, and typically has long lines. For higher-value tickets, I would find the casino's street address and direct my mail there, specifically to the accounting department. As for lower-value tickets (those worth $200 or less), I would gamble on just using a stamp for first-class mail to the PO Box. Personally, I’ve sent in tickets three times, all of which had the registered mail stipulation, and I received checks within two weeks on each occasion. For two of those, I used UPS, and for one, I just affixed a first-class stamp.

These tables typically operate under the assumption that the dealer does not possess a blackjack. By the time a player has the opportunity to act, the dealer has already checked for a blackjack. Hence, making correct decisions around doubling and splitting should be informed by the conditional expected value, based on the assumption that the dealer does not have a blackjack. If this is overlooked, a player may become overly cautious about doubling or splitting against a ten or an ace. Summing up the product of probabilities and expected values will lead to an erroneous figure, given that a dealer blackjack is not accounted for as a potential loss.

To accurately ascertain the house edge for the entire game, you need to deduct the anticipated loss that occurs when the dealer has a blackjack. With six decks, the likelihood of a dealer having a blackjack can be calculated by taking the number of tens multiplied by the number of aces, divided by the total number of two-card combinations, which yields (6*16)*(6*4)/combin(312,2) = 0.047489. However, a player only faces a loss when they themselves do not hold a blackjack. The probability that a player has a blackjack, given that the dealer holds one, is (6*16-1)*(6*4-1)/combin(310,2) = 0.045621. Thus, the chance of a player losing to a dealer blackjack is calculated as 0.047489 * (1-0.045621) = 0.045323. You should subtract this figure from your earlier product above: 0.04518876 - 0.045323 = -0.00615144. Therefore, the house edge under the stipulated rules in the appendix is 0.62%.

Title 31 refers to regulations mandating that casinos document any single-day cash transactions exceeding $10,000 made by an individual. In such cases, a Cash Transaction Report (CTR) must be submitted. This requirement also applies to the cumulative total of multiple transactions if they exceed $10,000. If you cash out chips that amount to just under that figure on the same day, the casino may still make a note of the transaction for future reference in case you return later that day and exceed the limit.

My suggestion is to comply with their requests. The potential repercussions of appearing to avoid submitting a CTR far outweigh any concerns associated with the CTR itself. In fact, from my experience, there’s nothing inherently negative about a legitimate CTR; casinos frequently process them. Personally, I’ve filled out hundreds without any problems arising. It is, however, worth noting that attempting to evade the process raises red flags and can attract unwanted scrutiny. I know of a situation where an individual was denied his ability to cash out because he had too many prior transactions that were just below the $10,000 mark. This is simply my perspective, but for questions of this nature, "Brian," who is a current casino manager in Las Vegas and a former regulator, is better suited to address them with expertise.

In essence, Title 31 is legislation administered by the U.S. Department of the Treasury, aimed at combating money laundering. It necessitates that specific large cash transactions be reported to government authorities. These reports are made using FinCEN Form 103, referred to as “Currency Transaction Reports by Casinos”, with FinCEN standing for the Financial Crimes Enforcement Network. Casinos are required to report any currency transactions that exceed $10,000 within a single day. It’s important to note that the casino's definition of a “day” can differ from the traditional midnight to midnight timeframe - instead, they may choose a window such as 3 a.m. to 2:59 a.m.

All financial institutions adhere to Title 31. Casinos are classified as financial institutions due to the nature of their transactions, which are similar to what banks do (e.g., cash checks, conduct wire transfers, provide loans, and manage cash exchanges). Unlike conventional banks, however, casinos engage in many transactions with customers whose identities are unknown. When you open a checking account, you provide the necessary information for the bank to complete CTRs, but when cashing out chips, the casino must request this information from the patron. They are required to gather all necessary details to prepare a CTR before a patron surpasses the $10,000 limit. Given the substantial fines for failing to comply, casinos are diligent in ensuring they meet these regulations.

Casinos tend to be cautious about sharing too much information regarding Title 31 because they do not want to inadvertently violate the law. They cannot assist patrons in structuring their transactions in a manner that could circumvent Title 31 requirements. When inquiries are made, they typically prefer to direct customers to a pre-printed information card rather than engage in detailed discussions, fearing they might inadvertently provide incorrect or misleading guidance.

While it can be relatively simple to bypass Title 31 regulations for undocumented transactions (such as buying or redeeming chips), it’s worth considering why one would want to do so. If a casino suspects that you are consciously conducting transactions to evade the reporting requirements outlined in Title 31, they may file a Suspicious Activity Report by Casinos (SARC). Should the casino determine that you've exceeded the $10,000 limit without providing the necessary information, they will prevent you from gambling until you do.