# Chuck-a-luck is an old game, played mostly in carnivals and county fairs. To play chuck-a-luck you p

Discussion in 'Calculator Requests' started by math_celebrity, Feb 22, 2018.

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Chuck-a-luck is an old game, played mostly in carnivals and county fairs. To play chuck-a-luck you place a bet, say \$1, on one of the numbers 1 through 6. Say that you bet on the number 4. You then roll three dice (presumably honest). If you roll three 4’s, you win \$3.00; If you roll just two 4’s, you win \$2; if you roll just one 4, you win \$1 (and, in all of these cases you get your original \$1 back). If you roll no 4’s, you lose your \$1. Compute the expected payoff for chuck-a-luck.

Expected payoff for each event = Event Probability * Event Payoff

Expected payoff for 3 matches:
3(1/6 * 1/6 * 1/6) = 3/216 = 1/72

Expected payoff for 2 matches:
2(1/6 * 1/6 * 5/6) = 10/216 = 5/108

Expected payoff for 1 match:
1(1/6 * 5/6 * 5/6) = 25/216

Expected payoff for 0 matches:
-1(5/6 * 5/6 * 5/6) = 125/216