Street coin game, win $5 or lose $1

Question

A street vendor offers a game with one fair coin. Heads pays you 5. Tails costs you 1. On average, how much do you win per flip?

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Expected value is the average result if you played many times: multiply each outcome by its chance, then add. A fair coin splits evenly, so each side has weight one half. - Heads (probability one half): win 5. - Tails (probability one half): lose 1, written as negative one dollar. Put them together: EV = 	frac{1}{2}(5) + 	frac{1}{2}(-1) = 2.5 - 0.5 = 2. The win side averages out to 2.50 and the loss side trims off 0.50, leaving a net average gain of 2 per flip. This is a favorable game for you: the prize is large relative to the small penalty. Takeaway. A big win against a tiny loss on a fa…

Street coin game, win $5 or lose $1

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