One of my favorite problems asks the best strategy to get the highest number possible from a finite collection (say of 100 random numbers) whose values are told to you sequentially, and you must choose one of them at the moment you hear it. It has been posted here before, so I won't repeat it as a puzzle. It's a "stopping" puzzle and you choose when to stop in a way that maximizes your expected "score." (Not that maximizes your chances of choosing the highest number from the collection.) Here's another "stopping" puzzle that uses a standard deck of cards.

A shuffled deck is placed face down, in a stack. A dealer begins turning the top card face up and placing it in a discard pile. At a time of your choosing you say "stop." The dealer then turns over the next card, and if it's a red card, you win. Note you are free to say "stop" at any time. What is your strategy?

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## bonanova

One of my favorite problems asks the best strategy to get the highest number possible from a finite collection (say of 100 random numbers) whose values are told to you sequentially, and you must choose one of them at the moment you hear it. It has been posted here before, so I won't repeat it as a puzzle. It's a "stopping" puzzle and you choose when to stop in a way that maximizes your expected "score." (Not that maximizes your chances of choosing the highest number from the collection.) Here's another "stopping" puzzle that uses a standard deck of cards.

A shuffled deck is placed face down, in a stack. A dealer begins turning the top card face up and placing it in a discard pile. At a time of your choosing you say "stop." The dealer then turns over the next card, and if it's a red card, you win. Note you are free to say "stop" at any time. What is your strategy?

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