Suppose you are playing a dice game and you have three options to find a score....

Suppose you are playing a dice game and you have three options to find a score. The options are:

A. Rolling an 11-sided die and using the outcome as your score.*

B. Rolling two 4-sided dice, adding 1 to their sum, and using that number as your score.

C. Rolling two 4-sided dice, doubling the result of the first die and adding it to the result of the second, subtracting 1 from this result, and using this number as your score.

Assume that each die is fair.

1) Calculate the expected value of your score for each of the dice rolling options.

2) Calculate the variance of your score for each of the dice rolling options.

3) You want to pick the best option that will win the game. Using the previous problems as justification, which option should you pick if:

a. Higher scores are always better?

b. Scores closer to 6 are better?

c. (Extra Credit) Scores that are multiples of 3 are bad?

*Note: While there is no such thing (that I know of) as a fair 11-sided die, you can easily simulate it by rolling a 12-sided dice (which definitely exists) and re-rolling any 12 until you get a number between 1 and 11 (inclusive).

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Expert Solution

orchestra answered 1 year ago

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