The Gambling Machine

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.

 

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About Bowen Kerins
Bowen is a mathematics curriculum writer. He is a lead author of CME Project, a high school curriculum focused on mathematical habits of mind, and part of the author team of the Illustrative Mathematics curriculum series. Bowen leads professional development nationally, primarily on how math content can be taught with a focus on higher-level goals. Bowen is also a champion pinball player and once won $1,000 for knowing the number of degrees in a right angle.

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