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Bet your coffee

Act 1

A loyalty card for a coffee shop is shown. For every ten coffees bought, a free coffee is offered. As an alternative, you can put your card in a bowl and each day there is a chance to win a free coffee each day for a year. When should we keep our free coffee card? When should we bet it?

Act 3

There are different scenarios to consider, using the concept of expected value. It is best to keep the card if there are more than 365 cards in the bowl. It is best to bet the card if there are fewer than 365 cards in the bowl.

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