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Ask The Wizard #234
With 27 years of experience in the casino industry, I have held various positions ranging from dealer to casino manager. Currently, I am dealing and have noticed a frequent player who consistently visits our casino to play blackjack, winning $5,000 or more during at least 30 consecutive visits. From my managerial perspective, I understand that even the most skilled card counters can't secure wins every time. The idea of achieving such a winning streak seems unlikely without some form of manipulation. I have only dealt to this player once and didn't observe anything unusual during that time. He has a credit line of $35,000 and may start with losses, but ultimately, he always seems to come out ahead. His bets range from $200 to $5,000, and he doesn't appear to be using card counting. Is it plausible for someone to win this frequently without some form of deception?
For simplicity's sake, let's overlook the house edge. If this player sets his limits at winning $5,000 or losing $35,000, the odds of hitting the winning target stands at 7/8, which translates to a probability of reaching that point over 30 visits being (7/8)^30, equaling approximately 1.82%. This outcome could merely be a stroke of luck. I recommend allowing him to continue playing until you uncover the reasons behind his apparent success.30This situation reminds me of an excellent book I recently picked up, Casino-ology, authored by Bill Zender. The primary message of the book is that casino management tends to be overly paranoid regarding advantage play. The excessive caution is actually hindering gameplay and inconveniencing genuine patrons, a cost that exceeds the potential savings from catching a few advantage players.
Imagine you're engaged in a standard 80-spot Keno game that involves 20 draws, with the condition that the balls are drawn 'with replacement.' This means that after a ball is drawn, its number is noted and placed back in the hopper, allowing it to possibly be drawn again. If you mark a card with 4 spots, what is the likelihood of achieving 0, 1, 2, 3, and 4 unique hits?
This presents quite a challenging scenario. While it is straightforward to determine the probability of any of your selected four numbers being drawn, including potential repeats, the more complicated aspect is calculating the likelihood that a specific number of distinct picks will come out, given that some numbers may appear more than once. I provide a detailed answer and solution on my
Personally, I've found that betting on teams that have recently endured 5 consecutive losses can be fruitful, especially when betting against teams that have won 5 in a row. I contend that, unlike the game of dice or roulette, which operate without any memory, a professional sports team cannot continue winning or losing indefinitely. I selected the 5-game streak as it's when the likelihood of a turnaround seems to increase. I don’t consider factors like the location of the game or the starting pitcher, nor do I take injuries into account. Do you think my reasoning holds? MathProblems.info page, problem 205.
I believe your betting strategy has merit, but perhaps not for the reasons you've outlined. It's theoretically possible for a sports team to experience an endless losing streak. However, these bets are generally favorable because they often involve significant underdogs—who statistically present stronger betting opportunities than favorites. Moreover, casual bettors usually back the opposite side in these situations, creating additional value for your bets.
I'm curious about the development of California's gaming regulations, particularly concerning craps and roulette. Can you explain why California disallows the dice or the ball and wheel from directly determining the outcomes of these games? Additionally, do you know the origins of this law? What were lawmakers in California envisioning when they established this?
Unfortunately, I don't possess knowledge about the historical background or reasoning behind that particular law. It's possible it stemmed from a misguided compromise between puritanical views and gambling advocates. They might have had similar thoughts to Mississippi lawmakers, who allowed non-Indian gaming only on 'riverboats.' We all witnessed the repercussions of that poorly thought-out decision following Hurricane Katrina. For years, I've maintained that if you're going to permit gambling, it's best to be straightforward and allow it entirely.
If the odds are roughly 1 in 49,000, what are the chances of hitting exactly two within 6,000 attempts? My wife and I recently returned from the Red Rock, where I experienced this.
Given that the odds of a Royal in full pay deuces wild In reality, the probability of landing a royal flush stands at 1 in 45,282 per hand. The chances of hitting exactly two royals over 6,000 hands is
Accurate strategies and insights pertaining to various casino games such as blackjack, craps, roulette, and a wide array of others available. combin (6000,2)×(1/45282)2×(45281/45282)5998= 0.007688177, or 1 in 130.