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Ask The Wizard #424

Your email account receives an average of one email every six minutes. The probability of receiving an Email at any given moment is always the same and not correlated with the time since the last Email was received. Once a minute, starting one minute from now, you roll a die until you roll a 1. What is the expected waiting time until the first thing to happen between receiving an Email or rolling a 1?

Ace2

The answer is 6(1-exp(-1/6))/(1-(5/6)exp(-1/6)) =~ 3.12666 minutes.

 

Here is my solution (PDF).

This question was asked and discussed in my forum at Wizard of Vegas.

A one-meter stick is cut in two random places. What is the expected area of the smallest of the three pieces created?

charliepatrick

1/9 meter

 

Here is my solution (PDF).

This question was asked and discussed in my forum at Wizard of Vegas.

On Aug 30, 2025, the University of Nevada played Penn State in football. Penn State was a +43.5 point favorite. There was no money line. What would you have made a fair line?

Aidan

The tricky part in setting a money line in a game like this is that there is so little data for games with such a huge point spread.

For situations like this, I like to use logistic regression. It would require a book to explain it, but the bottom line is based on years of college football data, the probability of the underdog winning can be estimated as e-0.11688s/(1+e-0.11688s), where s = point spread on the underdog.

In this case the probability of Nevada winning is 0.00615655. That equates to fair odds of 161 to 1.

The the way, the same formula for the probability of winning in the NFL is e-0.132772s/(1+e--0.132772s). Had this been an NFL game, I estimate the probability of the underdog winning is 0.003093. The main reason for the difference is less scoring in the NFL compared to college.