Chuck-A-Luck is a carny game in which 3 dice are tossed. You pick a number from 1 to 6. If one of the dice shows your number you gain the value of your bet; if two of the dice show your number you gain twice the value of your bet and if three of your number show, you gain three times the value of your bet. Otherwise you lose the amount you bet.
What is your expected loss for each game?
Matches Gain
Probability
Expected Gain
0 -1 (5/6)^3 -125/216
1 1 3(1/6)(5/6)^2 25/72
2 2 3(1/6)^2(5/6) 5/72
3 3 (1/6)^3 1/216
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-17/216
So you expect to lose -0.0787 of every dollar spent.
(For a carnival game this isn't too bad. For a casino game this is bad.)
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Posted by Jer
on 2020-10-22 12:54:47 |
Alternate tabulation for solution
