Ask The Wizard #155

Thank you for your response. You should definitely consider surrendering more often if it means retaining the match play. My blackjack expertise appendix 9 is well-suited for inquiries like this. A match play is essentially valued at about half its face value. Therefore, if the expected value of the hand falls below -1/3, surrendering is advisable. Assuming the dealer hits on a soft 17, here are the scenarios.

• Player 6 vs. 10-A
• Player 12 vs. 9-A
• Player 13 vs. 8-A
• Player 14 vs. 8-A
• Player 15 vs. 7-A
• Player 16 vs. 7-A
• Player 17 vs. 8-A
• Player 8,8 vs. 9-A

The approach remains consistent even if the dealer stands on soft 17, with the exception of players not surrendering when they show a 6 against an ace.

I appreciate your kind words. The likelihood of being dealt pocket Aces in any given hand is 6 out of 1326, which means it happens roughly once every 221 hands. In my analysis of 10-player Texas Hold ’em (/games/texas-hold-em/10players.html), the odds of winning with a pair of Aces stands at 31.36%, assuming all participants remain in until the conclusion. However, that's a significant assumption. If I were to speculate, I would estimate the actual winning probability with Aces in a live game with ten players to be approximately 70%. Therefore, the odds of being dealt pocket Aces and subsequently losing would be 0.3*(1/221) = 0.1357%. This equates to an expected value of about 13.57 cents per hand at $100 each time. With ten players, this results in an average expenditure of $1.36 per hand for the poker room, which significantly impacts the rake. I tend to concur with your strategy of calling, as this keeps more participants involved in the hand, subsequently increasing the chances of losing.

You're welcome! In this situation, having four cards towards a flush with two displayed on the board after the flop, the likelihood of drawing precisely one of the necessary suit is calculated as 9 multiplied by 38 divided by combin (47,2) = 342/1081 = 31.64%.

In games such as Bonus Poker and Double Bonus, I believe they enhance payouts for specific four-of-a-kinds to give players a chance at bigger wins, albeit at the expense of smaller victories. It makes sense that four Aces would be the top premium four-of-a-kind since Aces rank as the highest card in traditional poker. As for why four 2’s yield better returns compared to four Kings, it’s likely due to the fact that players tend to hold lower cards less frequently, making it less common to hit four of them as opposed to four Kings. Therefore, although the chances remain equal for every card type, player behaviors result in a lower frequency of the low four-of-a-kinds, thereby allowing game developers to justify higher payouts for them.

I understand how it can be frustrating when I declare the house edge of a game under optimal strategy without detailing what that optimal strategy entails, as is the situation with Texas Hold'em Bonus. The reason for this is that I too do not know what the optimal strategy is. The number of potential combinations in most poker-based games is so vast that accurately defining the ideal strategy is a time-consuming and labor-intensive endeavor. Instead, I have programmed my computer to analyze each possible card combination and select the action with the highest expected value. The expected value quantifies what players can anticipate winning (positive) or losing (negative). This significantly streamlines my coding process. As such, there is no element of random simulation; my program projects the future by exploring all potential card combinations and adopting the strategy that leads to maximum profit or minimal loss.

Yes, I believe that kissing certainly qualifies as cheating. Still, at this point, it’s essential to understand that you don’t need to justify your decision to leave by gathering evidence against him. In my view, a breakup should be swift and straightforward. Dismiss any notions of maintaining a friendship; simply express that you’re unhappy and ready to move forward, while making it clear that future communication is off the table. Afterward, allow yourself some time to cool off. Remember, don’t let this experience sour your perspective on all men. There are numerous wonderful individuals out there who would treat you like royalty (to echo Peter Brady). Instead of blaming all men for your experience, focus on the choices you’ve made.

In my view, the dealer should adopt lenient rules in home games. It’s simply unfair to take advantage of your friends with overly stringent regulations. If you’re using two decks, I would suggest allowing players to double down on their initial two-card hand, double down after a split, and have the dealer stand on soft 17. Otherwise, stick to standard regulations. This approach would yield a house edge of 0.19%. However, keep in mind that player errors could provide you with a greater advantage.

You’re welcome! I enjoy helping people develop smarter gambling habits. This strikes me as a classic case of a self-fulfilling prophecy. It’s akin to how people often find themselves romantically involved with individuals who share the same first name repeatedly. Having a palindromic birthday is indeed a fun fact for those inclined towards mathematics, but it doesn’t hold any deeper significance. I personally take pride in having been born on 5/23 at 5:23 PM, not to mention that both figures are prime numbers. In any case, I wish you all the best with your new partner born on 7/7/78. [Editor's note: Wizard, please send me her email address; she sounds intriguing. -- M. Bluejay]