A die game where rolling a 1 wipes you out

Question

A carnival booth offers this game: pay \2, roll one fair six-sided die, and collect the face value in dollars, except a roll of 1 pays nothing at all (not even \1). What is your expected profit per play, and should you play?

Accepted Answer

First find the expected payout. The die pays 0 on a 1, and its face value on 2 through 6: E[	ext{payout}] = \frac{0 + 2 + 3 + 4 + 5 + 6}{6} = \frac{20}{6} \approx 3.33. Now subtract the \2 cost: E[	ext{profit}] = 3.33 - 2 = 1.33. The expected profit is about +\1.33 per play, so the game is favorable, you should play (and play often, since repeated favorable bets let the average dominate). Takeaway. Expected value of a game is expected payout minus cost. Changing a single outcome, here, knocking the "1" payout from \1 down to \0, shifts the mean by that amount over six, a quick way to repric…

A die game where rolling a 1 wipes you out

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