The Gambling Machine
March 11, 2013 Leave a comment
The NY Times “Numberplay” blog recently posted an interesting question called “The Gambling Machine”. The problem was based on a problem found in the NCTM 2011 slides from “Mathematics of Game Shows”, from the PCMI 2007 materials, and originally from the (thankfully cancelled) game show National Bingo Night.
The Numberplay article asks about the expected return of proper play in the game, and whether or not a player can get $40 return from the game. A reasonable guess is for the player to guess higher when the first number is half or less, and guess lower when the first number is more than half, but this is not the best possible strategy.
The article provides some analysis and solutions, and I’ve provided my solution as this PDF.