I wrote here about my solution to this week's Riddler. I wanted to expand a bit on the method, and present some simulation results.

# Monthly Archives: March 2016

# 538 Riddler: Simulating the Boarding Process

I wrote here about my solution to this week's Riddler puzzle. I think that explanation is sufficiently convincing, but I also decided to simulate the problem to see if the results match my solution.

# 538 Riddler: Will Someone Be Sitting In Your Seat On The Plane?

In this Riddler we are taking flight:

There’s an airplane with 100 seats, and there are 100 ticketed passengers each with an assigned seat. They line up to board in some random order. However, the first person to board is the worst person alive, and just sits in a random seat, without even looking at his boarding pass. Each subsequent passenger sits in his or her own assigned seat if it’s empty, but sits in a random open seat if the assigned seat is occupied. What is the probability that you, the hundredth passenger to board, finds your seat unoccupied?

# 538 Riddler: Should You Pay $250 To Play This Casino Game?

This week's Riddler presents us with an interesting casino game:

Suppose a casino invents a new game that you must pay $250 to play. The game works like this: The casino draws random numbers between 0 and 1, from a uniform distribution. It adds them together until their sum is greater than 1, at which time it stops drawing new numbers. You get a payout of $100 each time a new number is drawn.

For example, suppose the casino draws 0.4 and then 0.7. Since the sum is greater than 1, it will stop after these two draws, and you receive $200. If instead it draws 0.2, 0.3, 0.3, and then 0.6, it will stop after the fourth draw and you will receive $400. Given the $250 entrance fee, should you play the game?

Specifically,

what is the expected valueof your winnings?