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Ask The Wizard #90
I truly appreciate the content on your website. Earlier today, I was going through your reviews of online casinos and I noticed you frequently faced losses on your deposits, which felt quite disheartening. Upon seeing your call for donations, I now understand your situation better!
Since I began my online gambling journey four years ago, I've managed to earn approximately $20,000, with about half of that total coming from winnings at Golden Palace. What I share in my reviews reflects only my latest experiences, and like many, I occasionally go through losing streaks that last a month or two. Nonetheless, I recently won $786 at Casino.Net and $2317 at Casino Kingdom. I don’t solicit donations to support a gambling habit, but rather they allow me to maintain this site for free for everyone. Typically, I receive donations via PayPal, which I then use to make purchases on eBay.
Placing bets on all 38 numbers in roulette would make it exceedingly difficult to win over time, as betting $1 on each number results in a loss of $2 with each spin of the wheel (assuming a 0 and a 00 on the wheel, without any beneficial rules for even money bets). Is there a rational argument to propose that there’s an ideal range of numbers to bet on based on statistical analysis?
I evaluate the worth of a bet by its expected payout rather than the odds of winning. Betting on all 38 numbers guarantees a house advantage of 2/38 = 5.26%, identical to betting on a single number or any combination thereof. While covering all 38 options yields a 0% likelihood of achieving a net gain, the downside entails losing just 5.26% of your total wagers. If you're compelled to place a bet and aim to reduce variance, betting on all 38 numbers is your best bet. For example, if you have promotional chips to utilize and wish to ensure you get your expected value from them, that’s how you should proceed. Thus, to address your question, no range is more optimal than another—every range has the same expected value.
At the Seneca/Niagara Casino in Niagara Falls, NY, I’ve been denied access to their official rules for pai gow poker. I believe it’s important to understand the house rules before engaging in play. Is it mandatory for them to provide that information?
Likely not. On one occasion at the Tropicana in Atlantic City, their pai gow poker rules stated that the house way could be obtained upon request. When I inquired, they claimed they had run out of publicly available copies and could not show me a house version because it lacked the necessary Gambler’s Anonymous disclaimer. I firmly believe players should have the right to know the game’s rules, but sadly, it seems gaming authorities do not share this view.
I’m curious about the impact on the house advantage if one could see the hands of all seven players. Could this potentially lead to a situation where the house advantage becomes negative?
In his book 'Mastering the Game of Let it Ride,' Stanley Ko discusses this very subject. He states that the primary benefit of viewing other players' cards arises when you possess a borderline hand of four cards towards an outside straight without any high cards. Simply seeing a single card shouldn’t encourage you to 'let it ride,' but if the card you view is unhelpful, it might sway you to take that route. Ko doesn’t imply that this can create a negative house edge, and I have doubts it significantly reduces the house edge at all.
What are the chances that in a game where four players each receive 13 cards from a 52-card deck, all four players end up with a straight from Ace to two? The suits of the cards do not matter.
The answer is (413/COMBIN(52,13))* (313/COMBIN(39,13))* (213/COMBIN(26,13)) = 1 in 61,204,166,001.
In most blackjack counting systems, the index number of 16 against a dealer's 10 is considered zero. Thus, if the deck were perfectly neutral, you would ideally stand since you should do so when the count equals or surpasses the index number. However, basic strategy charts suggest hitting, which seems to contradict the previous point.
That's a solid query. My educated assumption is that if the index numbers weren’t rounded, they would likely be above 0 but below one half. Therefore, they are rounded down to zero. Elevating the index number to 1 would cause greater rounding errors, leading players in slightly favorable decks to hit when they should stand.