Ask The Wizard #281

The answer is 1-F^(t)_n+2/2ⁿ, where F^(t)_nThis refers to the n-th term found in a t-step variant of the Fibonacci sequence.

You might be curious about what exactly a Fibonacci sequence is. The initial number is always one. In a t-step sequence, every following number is derived from the sum of the preceding t numbers. For clarity, consider zeros preceding the first term.

Let’s examine a sequence with two steps. The first term is designated as 1. The second term results from adding the two prior terms. If we assume a zero before the one, the second term equals 0+1=1. The third term would then be 1+1=2, with the fourth being 1+2=3, and the fifth term calculated as 2+3=5.

The first twelve numbers from the two-step Fibonacci series are: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, and 144.

Let’s consider a specific example. What are the odds of flipping at least two tails in a row at least once over the course of ten flips?

Utilizing the two-step Fibonacci sequence is ideal since we are only looking for two tails. The 12th number in this sequence (which is two more than the total flips) equals 144. Hence, the solution is 1 minus F.⁽²⁾₁₀₊₂/2¹⁰= 1 - 144/2¹⁰= 1 - 144/1024 = 85.94%.

What are the chances we would get five tails in succession during 20 coin flips?

The first 22 numbers in the five-step Fibonacci series include: 1, 1, 2, 4, 8, 16, 31, 61, 120, 236, 464, 912, 1793, 3525, 6930, 13624, 26784, 52656, 103519, 203513, 400096, and 786568.

The answer is thus 1 - F⁽⁵⁾₂₀₊₂/2²⁰= 1 - 786,568/1,048,576 = 1 - 75.01% = 24.99%.

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Initially, you will need to provide a form of photographic identification, otherwise, the casino will withhold your winnings until you do. If you show your identification but opt not to supply a valid Social Security number or tax ID, 25% to 30% of your winnings may be withheld depending on whether the jackpot amount is over or under $5,000 and your residency status, be it in the United States or in a country that has a tax treaty.

As of 2011, such countries included Armenia, Australia, Austria, Azerbaijan, Bangladesh, Barbados, Belarus, Belgium, Bulgaria, Canada, China, Cyprus, Denmark, Egypt, Estonia, Finland, France, Georgia, Germany, Greece, Hungary, Iceland, India, Indonesia, Ireland, Israel, Italy, Jamaica, Japan, Kazakhstan, Kyrgyzstan, Latvia, Lithuania, Luxembourg, Mexico, Moldova, Morocco, New Zealand, Norway, Pakistan, Philippines, Poland, Portugal, Romania, Russia, Slovakia, Slovenia, South Africa, South Korea, Spain, Sri Lanka, Sweden, Switzerland, Tajikistan, Thailand, the Czech Republic, the Netherlands, Trinidad and Tobago, Tunisia, Turkey, Turkmenistan, Ukraine, the United Kingdom, Uzbekistan, and Venezuela.

I am trying to understand the precise rules here, but it’s proving to be quite challenging. Please refer to the IRS for accurate information. rules for issuing a W2G form for more information.

I want to express my gratitude to Marissa Chien, co-author of, and MathExtremist for their assistance regarding this inquiry. Tax Help for Gamblers Amir Lehavot, a player who made it to the final table of the 2013 World Series of Poker, is offering any winnings that exceed the base amount of $733,224 for ninth place for $29,248 per each 1% share. Do you think this is a reasonable offer?

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First, let's review the chip stacks.

If we assume all players have similar skills, we can gauge the probability of winning by looking at each player's share of the total chip stack. However, estimating this becomes increasingly complex with each place.


To help clarify the issue, I devised my Ask The Wizard #281 .

Once you've input all the relevant information, you’ll discover that Amir's expected winnings amount to $3,658,046. By subtracting the guaranteed minimum of $733,224 for ninth place, that leaves an expected non-guaranteed win of $2,924,822. Thus, each 1% share is valued at $29,248.22. This aligns well with the price mentioned in the article on cardplayer.com.

Lehavot ended up finishing third, securing $3,727,023 as his prize. If we deduct the guaranteed prize for ninth place ($733,224) and divide the remaining amount by 100, each 1% share would yield $29,938. The original investment for each share was $29,248, representing a profit of 2.36%.

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(t) n+2 It's wiser to test your system for free and discover its shortcomings rather than risking real money in a casino.

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All I can say is that the 'secret room' at the Venetian has cookies.

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