Ask The Wizard #156

For those unfamiliar, a Super Bowl pool involves a grid that measures 10 by 10. Participants select squares at a fixed price, writing their names in each chosen space. After purchasing all 100 squares, random numbers from 0 to 9 are assigned to the rows and columns, much like a multiplication table, but shuffled. The last digits of each team's score then determine the winning squares. This shuffling exists because certain final digits appear more frequently than others. For instance, the person with the square for Seattle 0 and Pittsburgh 1 would have won since the final score was Seattle 10, Pittsburgh 21.

The table below illustrates how often each score combination occurred in NFL games between 1983 and 2005. It’s noteworthy that a rule allowing two-point conversions was introduced around 1998, which slightly equalized the distribution of these scores.

The upcoming table details the likelihood of different score combinations based on the previous table's data.

Even though there is an official home team in the Super Bowl, for our purposes, we can overlook this detail. Let’s also disregard specifics about either team and strictly focus on historical averages presented earlier. Additionally, we won't consider that Super Bowl games cannot end in a tie, which might lower the chances of a score like 4/4 being successful. Thus, we will calculate an average for when the last digits differ. So, for your Pittsburgh 7, Seattle 4 square, we calculate the average of Away 7, Home 4; and Away 4, Home 7, resulting in the following probability for your squares.

Pitts 7, Sea 4: (0.0346+0.0381)/2 = 0.0364
Pitts 7, Sea 0: (0.0385+0.0420)/2 = 0.0403
Pitts 4, Sea 4: 0.0192
Pitts 4, Sea 0: (0.0216+0.0245)/2 = 0.0231

Therefore, the overall probability of your winning one of those squares stands at 11.90%. Since you only covered 4% of the total squares, you've actually done quite well.

While you didn't directly request this, I've gathered some statistics about how frequently each last digit appears. The general frequency ranking from most to least common is 7043168952.

Lastly, here is the breakdown of the probability associated with each last digit.

For more on this topic, visit Mathematical and Statistical Tactics for Football Squares Strategy .

If a royal flush provided a payout equal to that of a straight flush, then a 9/6 Jacks or Better machine would yield a return of 98.03%.

1 in 635,241.

I often receive variations of this inquiry. The reality is, I have created countless simulations myself. I write these in C++ to tailor them to my specific needs. Most requests seem centered around testing betting systems. Regrettably, I don't possess a program that allows users to input the rules of a betting system for testing; if such a program existed, it would demonstrate that all betting systems are fundamentally ineffective, which is a point I’ve been emphasizing for years.

For the benefit of my readers, table 3 awards $500 for four of a kind, $100 for a full house, and $50 for a flush. The breakeven point on the Northern Indiana side bet payout table comes to $369,290.00.

In your scenario, the casino's take is 75%. This number reflects the proportion of the value of chips players end up with compared to the money the dealer collects. While historical averages exist, there's no direct correlation from house edge to hold. The hold is influenced by factors such as how long players handle their chips, which is unpredictable.

For those who are unaware, a hand of Omaha consists of nine cards. If a player were allowed to choose any nine cards, the probability would be (13* (48,5)-combin(13,2)*44)/combin(52,9) = 0.00605. However, if the player must use exactly two of their four hole cards, the probability changes to (13*combin(4,2)*combin(48,2)*combin(2,2)*combin(46,3)-combin(13,2)*combin(4,2)*combin(4,2)*combin(2,2)*combin(2,2)*44)/(combin(52,4)*combin(48,5)) = 0.00288. combin Keep in mind that these calculations account for the possibility of drawing two four of a kinds.

Recently, while my boyfriend was out, I found some really disturbing adult photos of him with past partners while I was using the computer. Although I should have respected his privacy, I felt compelled to share what I discovered and how uncomfortable it made me regarding him keeping those images. He casually mentioned that there were videos as well. I expressed my discomfort about these images of him with his exes, but he didn't perceive any issues with it, claiming they were merely souvenirs of the past (yet he also stated he never loved them—so what are they souvenirs of?). I've never allowed any other guy to take intimate photos of me, and now I feel incredibly used! I told him he could either keep the photos or get rid of mine; he refuses to do either. Since there's a noticeable age difference, he labels me as immature, but I don’t think my feelings are unreasonable—I feel violated, and honestly, I’m uncertain about our future. Can our relationship endure, and am I really overreacting? I genuinely apologized for looking at those folders.

I tend to side with him on this issue. He wouldn't judge you for keeping old love letters from previous boyfriends, would he? However, I understand your discomfort with being part of that collection. It might be reassuring if he agrees to your request, but I suspect he could easily forget about a backup somewhere. Therefore, I doubt your ultimatum will effectively resolve the situation. If you can't accept his laid-back approach, it's likely the relationship won’t survive.

For the Eastern U.S. and Canada, I strongly recommend Stanford Wong's resource. It will detail blackjack rules across nearly every casino in those regions.

For Las Vegas why not use my own blackjack survey Either option is feasible. Most slot manufacturers seem to prefer randomizing the prizes, meaning the outcome depends on both the box selected and the timing of that selection. From a mathematical perspective, it doesn’t alter the outcome whether they design it one way or the other. Current Blackjack News Help! I suspect my boyfriend of over a year might be cheating on me. Recently, he’s been receiving a lot of instant messages from his ex. They hadn’t communicated in ages, and he claimed it was for closure. Then one morning, he accidentally called me by her name, twice. I was understandably upset, but he insisted he must have been dreaming, so I forgave him. A week later, while doing his laundry, I discovered another girl’s underwear among his dirty clothes. He claimed it belonged to his sister, but she denied ever owning such a color and it was the wrong size. My suspicions grew stronger. One night after a fight over this, he tried to ease my concerns by saying, 'Yeah, I really wanted to get with her. It would be so easy, and you'd never find out.' Then he explained he hadn’t because he understood it would mean the end of our relationship. Now, a month later, he continues to act oddly. He used to always answer his phone, but now he sometimes disappears for hours without contacting me, claiming he left his phone in the car. I’ve known him for four years, and he typically brings his phone everywhere, answering it promptly. Additionally, he's gone 'out with his cousin' and returned home well after 1 AM, usually creeping in around 5 AM. He always has an excuse, but I can't shake the feeling that I'm being foolish to ignore the signs.

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