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Ask The Wizard #59

Dear Wizard, I want to express my appreciation for the exceptional quality of your service. Additionally, I’m curious about the possibilities of making a living through gambling, or perhaps using it as a way to increase one’s income, either on the internet or at physical casinos. I understand that for many, this might seem like a risky path, but for some individuals, it could yield satisfying results. Moreover, I would like to know how casinos set limits on betting amounts and how this might influence potential returns or performance during a gaming session. It appears that lower limits may benefit the casino more than the players because statistically, the longer you engage in gaming, the more likely you are to incur losses. It also seems more practical to start with lower bets and gradually increase stakes rather than beginning with large amounts. Another question I have is whether a player can shift the odds in their favor over time with a specific strategy in an online blackjack game.

Craig

I appreciate your kind feedback. I could talk extensively about your initial question. There are indeed methods to gamble successfully for a livelihood. In my view, the most viable options include card counting in blackjack, placing sports bets, and taking advantage of bonuses and promotions online. All three approaches necessitate a significant initial investment of around $100,000 just to maintain a basic standard of living. Most individuals start with smaller amounts and gradually increase their stakes. It's crucial for everyone to wager according to their financial capacity. Online betting limits tend to be accommodating for most players, as few are likely to wager more than $500 per hand. Although Boss Media has a single-player blackjack option that provides a slight advantage, it is minimal and not particularly worthwhile to engage with.

Could you shed some light on the numbers displayed on the right side of the slot machine screens? There are three figures shown there – what do they signify? How can I leverage this information to gain an edge?

Bo from Wetumpka, USA

These figures represent some sort of internal counter. As a player, they won't provide you with any advantage, so it's best to disregard them.

In Stanford Wong's publication, \"Optimal Strategy for Pai Gow Poker,\" he offers an in-depth analysis regarding the decision-making process when holding two pairs. Have you conducted a similar breakdown? If not, do you believe his conclusions lead to the best possible strategies?

Mike from New York, USA

Indeed, I've conducted a comparable analysis, which is available in my work. There are key distinctions between my approach and Wong's. His strategy is more intricate, taking into account the highest two singles, while my own focuses only on the highest single card. Moreover, Wong differentiates his strategies based on whether the player is the banker or not. Lastly, his guideline is tailored to the California variant of the game, without the typical 5% commission, differing from my methodology. I have great respect for Wong’s research and agree with much of his table. pai gow poker appendix 2 What is the likelihood of obtaining two identical straight flushes, in terms of both rank and suit, consecutively in Three Card Poker?

What are the chances of obtaining a royal flush in Texas hold-em on the river?

Ralph from Harpster

The probability of getting a straight flush on the first hand is 4*12/combin(52,3) = 48/22100 = 0.0022. The probability that the next hand will be exactly the same is 1/22100. So the answer is (48/22100)*(1/22100) = 48/488410000, on 1 in 10,175,208. This is a 1.37 more likely than hitting a 6/49 lottery, which has a probability of 1 in 13983816.

For those unfamiliar, the river refers to the fifth and final community card dealt in Texas hold-em. Players must construct the strongest possible poker hand using their own two cards in conjunction with the five community cards. Therefore, your inquiry is about the probability of a player completing a royal flush among seven cards, where the seventh card must also be part of that royal hand. Before taking into account the relevant cards, the probability of making a 5-card royal flush from 7 cards is calculated as 4 times the combination of 47 taken 2 at a time, divided by the combination of 52 taken 7 at a time, yielding 4324 over 133784560, or approximately 1 in 30940. The chance that the seventh card is part of the royal flush is 5 out of 7. Consequently, the final probability equates to 21620 over 936491920, or about 1 in 43316.

John from Trinity, Texas

What is the chance that, with 600 bingo cards, at least one card will achieve a coverall within 54 calls?

I have a fundamental question. Do casinos on major cruise ships generally offer slots and games like Caribbean Poker, Three Card Poker, and Let It Ride at less favorable odds than those found on land?

anonymous

The probability that any given card will have a coverall with 54 calls is combin(51,30)/combin(75,54) = 114456658306760/2103535234151140000 = 1 in 18738. The probability of 600 cards not winning are (1-1/18738)^600 = 96.79%. So the probability that at least one of the 600 players will hit is are 3.21%.

I cannot say for certain. The only cruise I ever experienced was a brief trip from Florida to the Bahamas that lasted around eight hours. This was prior to launching my website, so my focus on the house rules wasn't as intense. What I do remember is that the blackjack terms were quite unfavorable, and I ended up losing quite a bit! Other sources I’ve encountered support the idea that casino games on cruise ships tend to have tighter margins. After all, there aren't many alternatives for gaming aboard. However, since the games you mentioned already possess higher house edges, perhaps there is no necessity to modify the rules. I've also learned that Caribbean Stud Poker often features a more generous pay table in Europe and Africa, so it’s possible they utilize that version.

Paul from Novi, Michigan

Strategies and insights based on mathematical principles for various casino games including blackjack, craps, roulette, along with hundreds of others available for play.