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Ask The Wizard #12

As a newcomer to gambling in Las Vegas, I've been advised to try my luck at craps and Caribbean Stud. How much money should I bring to each game to ensure I can stay in for a while and potentially see some winnings?

Vinnie from Tulsa

If you gamble for an extended period, the most likely outcome is that you'll end up losing all your funds. It's crucial not to take more money to the table than you're willing to lose in that gaming session.

Second, Caribbean Stud Poker Craps has a house edge of 5.22%, so if your goal is to prolong your gaming experience, you might want to steer clear of that option. In contrast, the most favorable table games are craps and blackjack when played strategically.

This is my second inquiry for you, and now I'm curious about state lotteries. I'm sure you're familiar with the strategy some investors have used where they wait for the jackpot to reach a certain threshold, at which point they buy tickets for every possible number combination. This ensures they secure a portion of the winnings. If a ticket costs $1, what minimum jackpot amount would make this investment valid?

Ted

An important consideration is how many tickets are sold by other players. If there are multiple winners, the jackpot will need to be divided. Let’s define the total number of combinations as n, total tickets sold as t, the return rate for smaller prizes as r (for instance, in the Big Game, r=0.179612), and let j represent the jackpot. To determine break-even, the equation j*n/(n+t) + r*n - n = 0 must hold. This simplifies to j = (1-r)*(n+t).

In your strategy for blackjack, you surrender on a 16 against an ace, 10, or 9, but recommend splitting a pair of 8s against those cards. I've been advised that a pair of 8s totals 16 and should be surrendered instead. What's your take on this?

Jim from Naples, Florida

The advice you received to surrender a pair of 8s was misguided, particularly if we consider American rules. surrender To explain why splitting 8s against a 10 is preferable, take a look at my analysis. blackjack appendix 9b This analysis provides expected returns based on various scenarios for different plays. The findings indicate that splitting 8s against a 10 in a double-deck game yields an expected return of -0.4706, assuming the option to double down after splitting is available. Essentially, you could anticipate losing 47.06% of your initial bet on average. This is preferable to the 50% loss you’d incur by surrendering. If doubling down after a split isn’t an option, the return rate worsens to -0.4801. Thus, splitting 8s against a 9 or ace results in an even poorer return.

I've been contemplating this... Given that online casinos shuffle the deck after every hand, making card counting futile, I have observed that there are indeed some advantages.

A) You do not have to tip,
B) You can engage directly with the dealer without other competitors.
C) You have the opportunity to play more hands per hour, thanks to the absence of other players, compared to a conventional casino, and
D) You can place larger bets without drawing unnecessary attention.

Do these elements provide any sort of edge in online gaming? Have any studies been conducted regarding these factors? Personally, I've been quite successful online—better than my experiences in physical casinos. What are your thoughts? Any feedback would be greatly appreciated. Thank you!

Nathan

You've already highlighted several benefits of playing blackjack online as compared to in-person casinos. Unless you’re counting cards, the fact that they shuffle after every round is actually beneficial. In brick-and-mortar establishments, they tend to play until a certain point in the deck before reshuffling. This can disadvantage players, as it often results in more smaller cards dealt when the shuffle point comes in a deck that contains a lot of small cards versus larger ones. To put it simply, in traditional casinos, players will generally see more small cards than large cards over an extended period, which can be detrimental. Moreover, a significant advantage of online play is that you are not expected to tip. The quicker games, one-on-one format, and broader betting ranges do not substantially benefit or harm casual players. I believe your improved success in online establishments can be attributed to a mix of luck, favorable rules, and the absence of tipping obligations.

Would you agree that as a general principle, the longer you play, the greater your chances of losing, unless you're playing games that allow players to negate the dealer's advantage? Do you have a strategy to counteract this, such as starting with larger bets relative to your bankroll? If you succeed with these larger bets, then you could scale down your betting amounts to prolong your stay in the game.

Chris from Andover

Absolutely, in games with a negative expectation (which is the case for most), the longer you participate, the higher your chances are of losing. If you aim to enhance your odds of winning, even at the risk of a significant loss, the optimal approach is to increase your bets after a loss, attempting to recover earlier losses. Martingale This exemplifies a very aggressive version of that strategy.