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Ask The Wizard #256
I'be been having a good laugh about Paul the Octopus Regarding the 'predictions' being made, I tend to approach things with a more analytical mindset, focusing on statistical data for my wagers rather than relying on an Octopus. Nonetheless, I found the concept somewhat endearing and entertaining.
Do you have any insights on this topic? I found it captivating because the Octopus appears to have a preference for the German flag. Perhaps this is influenced by the other German flags present in its aquarium environment. It has also accurately predicted the outcomes of matches between Germany and Serbia as well as Spain. Are there any intriguing odds or personal experiences you might consider sharing in your upcoming column or article?
Paul has achieved 12 correct predictions and 2 incorrect ones. The odds of randomly selecting 12 correct answers out of 14 attempts are combin (14,12)×(1/2)14= 0.56%. The likelihood of hitting 12 or more correct answers from 14 tries is calculated as (1+14+combin(14,2)) × (1/2)14= 0.65%. He wasn't given the option to select a tie, and no games he assessed ended in a tie. I'm uncertain how his record would look if ties were possible, but I believe they would have been excluded.
This appears to be a case of sheer luck, potentially mixed with a bit of trickery. While it's entertaining, I don’t view it as credible news. Surprisingly, this story seems to have received more media attention than some conflicts occurring in Africa.
This topic was brought up and deliberated on the forum of my associated website. Wizard of Vegas .
In Pai Gow Poker, a player has received the following hand:Jh Qh Kh AhQs Ks Joker. How should the hand be set?
- Royal flush & A-K
- Two pair (KKQQJ) & AA
My pai gow poker appendix 1 is helpful for inquiries of this nature. To resolve the question, combine the low and high hand power ratings for all possible ways to play the hand. The table below illustrates the total power ratings (not banking) for both viable hand options. It indicates that while it’s hard to split the royal, doing so is the optimal choice.
Pai Gow Poker — Power Rating Table
| Low Hand | High Hand | Low Power Rating | High Power Rating | Total Power Rating | Expected Value |
|---|---|---|---|---|---|
| KQ | Royal flush | 0.452967 | 0.999507 | 1.452474 | 0.416162 |
| AA | KKQQJ | 0.989071 | 0.821870 | 1.810941 | 0.765667 |
This topic was brought up and deliberated on the forum of my associated website. Wizard of Vegas .
Statistics on life expectancy for individuals of different ages have been compiled and presented at the Social Security web site . However, I’m curious about the life expectancy for two specific individuals: a thirty-year-old male (myself) and my twenty-eight-year-old girlfriend. Based on the chart, I can expect to live another 46.89 years while she has a forecast of 53.22 years. But how do we project how long we both will live? What’s the process for calculating this?
First, it would be more suitable to utilize cohort life tables instead of the period life table you referenced. I attempted to locate cohort life tables online but faced difficulties. Nevertheless, we can still apply the provided table. Keep in mind it may slightly underestimate your life expectancy as it doesn’t account for potential improvements in life longevity.
To address your query, we had to construct a comprehensive matrix depicting the likelihood of each combination of year of death for both you and the thirty-year-old woman. I won't delve into the specifics, but the key takeaway is that one of you is anticipated to pass away in 41.8 years, while the other will likely pass in 57.3 years. Both estimates round down, meaning you don't get credit for partial years.
This topic was brought up and deliberated on the forum of my associated website. Wizard of Vegas .
I was hoping you could assist me with developing the probability distribution table for Jacks or Better. I understand that 52 choose 5 = combin(52,5) = 2,598,960, yet I have noticed that the video poker tables show a staggering 19,933,230,517,200 total combinations. I'm curious to know why this figure is so much larger than 52 choose 5, and how I might calculate them.
There are combin(52,5)=2,598,960 possible combinations when dealing the hand. The reason my video poker return tables indicate nearly 20 trillion combinations is that we must also factor in potential outcomes on the draw. Below is the breakdown of combinations based on the number of cards the player decides to discard.
Possible Combinations on the Draw in Video Poker
| Discards | Combinations |
| 0 | 1 |
| 1 | 47 |
| 2 | 1,081 |
| 3 | 16,215 |
| 4 | 178,365 |
| 5 | 1,533,939 |
The least common multiple among all those combinations is 5 × combin(47,5) = 7,669,695. No matter how many cards a player discards, the return combinations need to be balanced so that the grand total equals 7,669,695. For instance, if a player discards 3 cards, there are 16,215 possible draw combinations, and each combination should be adjusted by the ratio of 7,669,695/16,215 = 473.
Thus, the overall number of combinations in video poker amounts to 2,598,960 × 7,669,695 = 19,933,230,517,200. For further details on how to program video poker returns yourself, please refer to my page on Approach for Analyzing Video Poker .
This topic was brought up and deliberated on the forum of my associated website. Wizard of Vegas .
On average, how many spins would you need in a 38-number roulette before witnessing any number reappear?
Including the first spin, I find that the mean is approximately 8.408797, with a median of 8 and a mode of 7.
The odds of selecting two distinct numbers without any repetitions is 37/38 = 97.37%.
The likelihood of choosing three numbers without duplicating any is (37/38) × (36/38) = 92.24%.
The chances of four numbers being selected without repeating them stands at (37/38) × (36/38) × (35/38) = 84.96%.
Continuing this trend, the probability of not having repeats in 8 distinct numbers is (37/38) × (36/38) × (35/38) × ... × (31/38) = 45.35%.
Consequently, the chance of encountering a repeat among the first 8 numbers is 100% - 45.35% = 54.65%.
I believe many would underestimate the odds of encountering a repeat within 8 selected numbers. If you're keen on leveraging the naivety of your mathematically challenged friends, suggest a wager based on the premise that a repeat will occur within 8 selections. Therefore, you would be betting on 8 or fewer, while your friend bets on 9 or more. If they hesitate, you could propose the range of 7 and above, which offers a 55.59% likelihood of winning. Essentially, the betting side that encapsulates the median of 8 is likely to come out ahead.
This topic was brought up and deliberated on the forum of my associated website. Wizard of Vegas .