2011-11-06, 09:17 PM
Mathematical Hope for the value returned for this game is 0.5 of the initial bet:
(5/6)^3 chance to get zero - ~58%
3 * 1/6 * (5/6)^2 chance to get what you bet - ~35%
3 * (1/6)^2 * 5/6 chance to get double your bet ~7%
(1/6)^3 chance to get triple your bet ~0.5%
It adds to exactly 100% and multiplying it by the returns will give you 0.5 =D
It means that on average you will walk off with half of what you invested.
The statement that "Since each face has a one in six chance of coming up, when three dice are tossed there are therefore 3 in 6 chances that the number I bet on will appear..." is already wrong. The chance that at least one face will be the one you chose is (1 - (5/6)^3) = ~42%.
(5/6)^3 chance to get zero - ~58%
3 * 1/6 * (5/6)^2 chance to get what you bet - ~35%
3 * (1/6)^2 * 5/6 chance to get double your bet ~7%
(1/6)^3 chance to get triple your bet ~0.5%
It adds to exactly 100% and multiplying it by the returns will give you 0.5 =D
It means that on average you will walk off with half of what you invested.
The statement that "Since each face has a one in six chance of coming up, when three dice are tossed there are therefore 3 in 6 chances that the number I bet on will appear..." is already wrong. The chance that at least one face will be the one you chose is (1 - (5/6)^3) = ~42%.