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Ask The Wizard #154

Millennium Sports presents a 6-point teaser bet for two teams at even odds. I'd appreciate an update on the teaser page to reflect these odds. Additionally, it would be beneficial to have a new table showing the percentage of individual bets needed to reach the break-even point. Based on my calculations, you’d need to win 75% of the two-team 6-point teaser bets to break even, which is quite challenging.

John from Herndon, VA

I just updated my Sport Betting Appendix 4 I suggest incorporating Millennium's teaser options and utilizing newer statistics as well. Here’s the house edge related to teasers, including the odds from Millennium, specifying whether the selection is a team or a total.

Two Team 6-Point Teasers

Pays Team Total
-120 12.85% 18.12%
-110 9.25% 14.74%
Ev 4.92% 10.68%

Two Team 6.5-Point Teasers

Pays Team Total
-110 5.85% 10.41%
-120 9.58% 13.97%
-130 12.74% 16.98%

To address your inquiry, to successfully navigate the 6-point teaser, your overall winning probability needs to exceed 50%. Hence, the chance of each individual pick covering the tease must be the square root of 0.5, which comes out to approximately 70.71%. For a 6.5-point teaser, the winning probability for each bet would need to be about 52.38%, or 0.5238.0.5=72.37% per pick.

What is the likelihood of obtaining each possible five-card hand dealt from a standard 52-card deck when the specific suit of a single, distinct card within a hand is regarded as generic? For instance, consider the hand consisting of A♠ A♣ A. A 2. In this hand the suit of the 2 is disregarded and would represent any of the four 2’s in the deck. Another example is A-J-8-6-5. In this hand the suit of all 5 cards is disregarded so that only one such combination can occur. Another example: 3♠ 3 7♣ 7♠ Q. In this hand the suit of the two 3’s and two 4’s is not disregarded because there is more than one in the hand but the suit of the Q is generic. In other words the suit of any card that is not duplicated in a hand is disregarded and that hand is considered to be one of the possible hands even though there would be many possibilities of the hand re-occuring if the suit of each card was not disregarded. Thus a straight or flush made up of five specific cards; say Q J♣ 10 9 8♠ or A♠ J♠ 8♠ 7♠ 3♠ could only occur once since any other combination of those same cards even though in a different suit would be a duplication. Therefore, using this criteria, what is the O/P of any single hand being dealt? In other words how many such five-card hands exist in a std 52 card deck? Thanks for your input.

Mike from Lavallette, NJ

I'm quite knowledgeable about this subject. There exist 134,459 distinct five-card combinations. My understanding derives from my initial video poker program, which examined all 2,598,960 possible hands over several days. However, by merely analyzing one of each of the 134,459 unique hand categories, weighted according to the total number of hands in that category, you can reduce the processing time by 95%. Occasionally, when a game requires specific suits, like in my recent analysis, I find it necessary to dust off my old program and revert to the lengthy method. Black Jack Bonus Poker Wizard, I have been reviewing your website as I prepare for my upcoming trip to Las Vegas since it's the ultimate gambling resource out there. Your analysis regarding when to stand with a 16 against a dealer's 10 caught my interest. As someone who enjoys math, I aim to maximize my chances, but I also recognize the marginal improvement. Like many players following basic strategy, I've always hit a 16 against a dealer's 10 when I'm holding a 2, 3, 4, or 5. I'm curious, now that this has been brought to your attention, have you modified your approach to secure that 'one unit every five years', or do you stick with hitting the 16 as before? Thank you for all your contributions!

I appreciate your kind feedback. When employing a basic strategy (instead of card counting), I generally choose to stand if I have a four or five in my hand. In a game where the dealer's cards are displayed, especially with other players around, I assess the table and utilize my best judgment. December 4, 2001 column In blackjack, when the dealer reveals both cards, a pair of 8s should not be split against a dealer showing a total of 10 or 11; instead, players should hit when the dealer shows a 10 and stand when the dealer shows an 11. Why does this scenario differ from conventional basic strategy, where players would split 8s against a dealer's 10 or ace?

anonymous

In typical blackjack scenarios, players should indeed split 8s when facing a dealer's 10 or ace. Yet, if the dealer inadvertently reveals both cards, displaying a total of 10 or 11, the player is advised to hit against a 10 but stand against an 11. This adjustment is made because when the dealer has a 10 or an ace showing, by the time it’s your turn, it’s clear he does not hold blackjack, having peeked at his hole card for verification. Hence, players can adopt a more aggressive playstyle. Conversely, if both of the dealer's cards are visible and total 10 or 11, the risk remains that the dealer could draw an ace or a ten, yielding a total of 21, suggesting a more cautious approach.

My boyfriend and I have a complex relationship. He’s broken up with me several times, only to return. The first time I suspect he was attracted to another girl. He went out to the movies with her and the following night reached out to reconcile. He then broke up with me for an entire month, only to ask for another chance after. He is very possessive, not allowing me to maintain friendships, claiming he cannot trust me. Ironically, when I express discomfort with girls calling him, he reacts with anger. What should I do, and do you believe he might be unfaithful with one of his female acquaintances? appendix 16 Based on your description, I find this possessive and indecisive individual intolerable. You should definitely move on from this relationship. There are plenty of better options available for you.

David from Fort Wayne, IN

I'm thrilled to see your return as you help to transform lives one mathematically challenged inquiry at a time. I have a mix of a relationship and a probability question: A colleague has spent his entire gambling life becoming frustrated with the player's actions at the third base position in blackjack, insisting they negatively impact his odds whenever they fail to adhere to basic strategy. He believes that 'bad' players are detrimental to his chances. I firmly believe that his odds remain unchanged regardless of who else is at the table. I've attempted to explain that he tends to remember the instances when their actions hurt him while overlooking the situations where they benefited him. Mathematically, his odds are identical whether he’s at a table filled with players who never hit, those who never stand, or those playing perfect basic strategy. How can I convince him of his misunderstanding? Should I even keep trying? If he acknowledges his error, he would have to confront the fact that he has unjustly criticized numerous players at blackjack tables when they weren't impacting anyone but themselves (and in certain cases, they were possibly aiding their own chances by adjusting their strategy). Don't you think that casinos would become more enjoyable if individuals truly grasped that my actions with my blackjack hand do not affect their odds in the long-term?

Your coworker appears to be a lost cause. As I’ve mentioned before, the more absurd a belief is, the more adamantly it is held. I would advise you to let this one go and accept that he prefers to cling to his delusions. Personally, I avoid giving unsolicited gambling advice as it’s rarely welcomed.

Mandy from Versailles

My boyfriend and I have been in a relationship for a year and eight months. He relocated about eight months ago, and we've endured a long-distance relationship since then. Regrettably, he has already cheated on me once while living here and again once he moved to Colorado. After discovering his infidelity, we broke up, yet he proceeded to engage sexually with another woman, and I forgave him for that. Now he asserts that he doesn’t want to make the same mistake again. Should I trust that, or is it inevitable that he will cheat again?

Naturally, he will claim he won't betray you again. Every dishonest partner will assure you of their fidelity. This reminds me of the saying, 'Fool me once, shame on you; fool me twice, shame on me.' Forgiving once may be a personal choice, but doing so again turns you into a fool. The next time he betrays you, which seems like a matter of time, stand firm and remove him from your life.

Aaron from Detroit, MI

In two different areas of your site, it’s stated that generally, it is more advantageous to wager on underdogs rather than favorites concerning the money line. Yet, as pointed out in your Sports Betting Appendix 3, the house edge is lower when betting on the favorite. Isn't this contradictory? Isn't it generally true that for any type of bet, one should seek out the lowest house edge?

You raise an excellent point. After some reflection, I've chosen to remove Sports Betting Appendix 3 from my site. It was contingent on the assumption that the fair line is precisely between the two money lines. For instance, during the last Super Bowl, the lines were usually Seattle +160 and Pittsburgh -180. My appendix was predicated on the unrealistic expectation that the fair money lines would average around +/- 170. In real scenarios, money lines are driven by the market. General betting trends on the money line typically favor the favorite, which creates added value on the underdog. Assuming historical data indicates a fair 4-point advantage for Pittsburgh, it suggests a winning probability of roughly 61%. This would translate to fair money lines of +156 for Seattle and -156 for Pittsburgh. To note, most casinos had the lines at +160/-180. Although Pittsburgh won this match, historically, I believe betting on the underdogs with the money line would yield better long-term results than wagering on favorites.

Jess from Albuquerque

My boyfriend and I discovered that I'm pregnant about two months ago. We’ve been together for three and a half years, and since the announcement, he has been spending nearly every night at his best friend's house until the early hours of the morning. He hardly speaks to me unless necessary, and often doesn’t share the same bed with me unless that happens to be the place where he falls asleep. It feels like he’s deliberately ignoring me. When I questioned him about infidelity, he denied it, but considering that his father and brother are known cheaters, I'm left wondering: do you think he might be cheating on me?

Certainly. However, that's just one part of the issue. This individual evidently is shirking responsibility for his actions. Is there someone of good character close to him who could have a crucial man-to-man discussion? Clearly, his father and brother are not suitable role models. I recommend that you give him a bit more time to improve, but it's wise to have an alternative plan in case he doesn't change. I would also suggest considering adoption as a legitimate option if things don’t work out.

Edward from Placentia

I would like to know about the house edge in blackjack after applying a 10% rebate on losses. Are the house edges the same for both 6-deck and 8-deck games?

It largely depends on how you play. If you adopt an aggressive betting style, you might get your advantage to nearly 10% by wagering half of your bankroll repeatedly until you multiply it significantly or go bust in the process. My advice is to keep your playtime brief and aim for a big win or a total loss, whichever happens first.

Crystal from Clio

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JJ from Seoul

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