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?

Accepted Answer

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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