Ask The Wizard #99

The design of the Wheel of Madness is biased towards lower prizes. It tends to land on them more frequently. Without specific weightings, a thorough examination is impossible. I've reached out to both casinos and the wheel's manufacturer for this data, but unfortunately, I've had no success.

I'm almost certain this question has been posed before, but it’s a good one worth reiterating. Here are some plays that fall into a gray area, indicated by having a card counting index of zero. This analysis is based on multi-deck play where the dealer stands on soft 17 and doubling after a split is permissible. The most favorable play is listed first followed by an alternative.

• 9 against 2 (hit/double)
• 12 against 4 (stand/hit)
• 12 against 6 (stand/hit)
• 16 against 10 (hit/stand)
• Soft 13 against 5 (double/hit)
• Soft 15 against 4 (double/hit)
• 3,3 against 2 (split/hit)

There is no specific number of hands that guarantees a 90% chance of achieving or exceeding that return. While the more you play, the closer your yield approaches 100.76%, statistically half the time it will yield above that and half the time below. A more pertinent question might be: how many hands must I play to confidently reach a 90% probability of getting to at least 100.66%?

The standard deviation for a full pay Deuces Wild is calculated at 5.08. For the standard deviation of the sample mean, it’s 5.08 divided by the square root of n, where n represents the number of hands played. Skipping ahead to the result, it's worth noting that you would need to play around 42,383,720 hands—a staggering amount! If your goal is simply to finish with a profit at 90% probability, then you would only require 733,790 hands. Even that is a considerable number, highlighting the volatility involved in short-term bankroll activities. For those interested, the general formula to assess your sample return being at least x with a probability of p in Excel is (normsinv(1-p)*5.08/(1.0076-x))^2. Applying this to my initial example should yield the expected results.

=(NORMSINV(1-0.9)*5.08/(1.0076-1.0066))^2

This formula can be adapted for any casino game by inserting the correct standard deviation for each specific game.

I believe that several casinos, such as Stations and Fiesta, offer full-pay Deuces Wild video poker, specifically in quarters. Green Valley Ranch also has them. Back when I relocated to Vegas three years ago, it was much easier to find.

Thanks for your kind feedback. You're not alone in your confusion regarding this issue. The trick lies in distinguishing between the house advantage and the hold. The house advantage refers to the average percentage that you will lose from each dollar wagered, while the hold is the proportion of money the casino garners in relation to the amount wagered. Because players tend to use the same chips over time during table games, the hold will usually appear much higher than the house edge. So, when it says that in baccarat the casino keeps 19.62% of the total amount put in the box, it implies that players receive the remaining 80.38%. Conversely, for nickel slots, the casino retains 7.89% while handing back 92.11% of what was wagered. This essentially boils down to comparing different criteria.

I appreciate your message. To clarify, the house edge remains unaffected by minimum or maximum bet limits. While a wider range between the two can heighten volatility, the longer you play, the results will trend towards the house edge. Some players mistakenly believe that increasing the maximum bet raises the house edge, but this isn't accurate.

Thank you! It must have taken quite some time to go through all the content on my site. The confusion arises when betting systems, which are ineffective, are mistaken for legitimate strategies that can provide an actual advantage. Two games that have demonstrated potential for profit, given the correct rules and strategies, are blackjack and video poker. I differentiate between a betting system—an ineffective method of chasing trends in games weighted in favor of the house—and a strategy, like card counting in blackjack, which has mathematical backing for its effectiveness. For video poker, players can achieve success by scouting for the best pay tables and following a consistent strategy regarding which cards to keep and which to discard.

Provided both players consent, the casino is unlikely to intervene. In some instances, this may not be practical because the other player might want to take additional cards. However, facing a dealer's 4 with a 10 should prompt the player not to take a fourth card, making your suggestion sensible. Even though it might be challenging, you could propose to purchase the player's hand and play it yourself if you can agree on a price. My calculations indicate the fair value of all hands. For example, if another player has a blackjack while the dealer shows an ace, most players might settle for even money. You could profit by offering that player a rate better than even money, yet less than 103.8% and then playing out the hand personally. However, be cautious not to extend this offer to a counter. blackjack appendix 9 Are there any official card-counting techniques available for Spanish 21? If not, do you think that the rules of Spanish 21 lend themselves well to counting strategies?

Is there a recommended strategy for determining the optimal amount for a Pair Plus bet in proportion to the Ante? For example, should the Pair Plus bet be doubled, tripled, or set at some other multiple of the ante to maximize potential returns?

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