We Got A Problem #13: Deal or No Deal

This short game is played with ten playing cards: an ace, two, three, …, nine, and a joker.  I shuffle the cards and lay them face down.

Your decision: grab as many cards as you want, still face down. When you’re ready, flip them all over at once and win: $1 multiplied by the sum of the card values.

Except the joker. If you flip over the joker, you win nothing. Good day.

So, how many cards should you take to maximize your expected return? What would change if all nine non-joker cards were aces? Eight aces and a ten?

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.

One Response to We Got A Problem #13: Deal or No Deal

  1. Fun! I love the extensions as-is. How about changing the number of jokers though?

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