Ask The Wizard #312

BookMaker indicated that for tracking political inaccuracies, the Washington Post, recognized for tallying false statements, would serve as the reference for determining the number of lies. According to their findings, Trump's average was 15 false claims daily throughout 2018. A pertinent follow-up question for assessing this bet is to estimate how long Trump engages in making public remarks each day. Considering tweets, interviews, and spontaneous remarks, a reasonable approximation might be around 20 minutes. Dividing gives us 15/20 = 0.75 false statements per minute, translating to one every 80 seconds.

Before the address commenced, media outlets projected it would last between six to eight minutes. Taking the average, let’s say it lasts about seven minutes. At a rate of 0.75 false claims per minute, this leads to an approximate total of 5.25 false claims. Therefore, I would have set the over/under at 5.5.

Moreover, if we accept 5.25 as the average number of false assertions, then the likelihood of three or fewer false statements occurring is approximately 23.17%, assuming the total follows a Poisson distribution, which seems like a sensible hypothesis.

In the end, the count of false statements recorded was six.

This topic has sparked extensive discussion within a lengthy thread on Trump over at Wizard of Vegas, with the specific focus on this subject beginning here .

Calculating the average is more straightforward, so we will tackle that first. Let's break it down step by step:

• On the very first spin, it is guaranteed that you will see a new number.
• For the second spin, the chances of it being a new number is 36 out of 37. If an event has a probability of p, the expected number of attempts needed for it to occur is 1/p. Therefore, the expected attempts to get the second unique number is 37/36, equaling 1.0278.
• Once two different numbers have been seen, the probability that the following spin will yield a new number becomes 35/37. Thus, the expected spins needed after seeing the second number to find the third is calculated as 37/35, yielding 1.0571.
• Continuing with this reasoning leads us to calculate that the total average number of spins needed to see every number comes to 1 + 37/36 + 37/35 + 37/34 + .. + 37/2 + 37/1, which sums up to approximately 155.458690.

Finding the median is significantly more complex. To derive an exact answer instead of relying on a random simulation, considerable matrix algebra is required. I've previously explored how to resolve similar questions in different Ask the Wizard inquiries, so I won't reiterate those steps. One instance of a related question involves achieving a pair of 6-6 three times consecutively, which we discussed earlier. Suffice it to say, the chance of encountering every number in 145 spins is 0.49161779, whereas in 146 spins, it rises to 0.501522154. Consequently, the median is identified as 146. Ask the Wizard #311 The forum discussion for this question can be found at

Imagine rolling 12 six-sided dice. After your first roll, you can keep any dice you choose and roll the remaining ones again. What is the probability of rolling a full set of 12-of-a-kind in these two rolls? Wizard of Vegas .

Which are the five largest casinos located in the United States?

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