Coffee shop coin promo, $18 or $6 gift card

Question

A coffee shop runs a promotion: flip one fair coin. Heads earns you an 18 gift card, tails earns you a 6 gift card. Either way you get something. On average, what is the gift card worth?

Accepted Answer

Expected value is the average payoff over many flips: each outcome times its chance, added up. The twist here is that there is no loss. Both outcomes are positive, so the average simply sits between them. A fair coin weights each side by one half. - Heads (probability one half): 18. - Tails (probability one half): 6. Blend them: EV = 	frac{1}{2}(18) + 	frac{1}{2}(6) = 9 + 3 = 12. Because both payoffs are positive and the coin is fair, the average is exactly the midpoint of 18 and 6, which is 12. A quick sanity check: the halfway point between two numbers is their sum divided by two, and (18…

Coffee shop coin promo, $18 or $6 gift card

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