Die Game
Let’s say we have the following two games, call them Game A and Game B. They both involve a fair, six-sided die.
In Game A, you roll the die once, and you get $1,000,000 times whatever the value of the die. For example, if you roll a 4, you would win $4,000,000.
In Game B, you roll the die a million times, each time getting $1 times the value of the die. For example, on the first roll, you get a 1, you win a total of $1, on the second roll, you get a 5, you win a total of $1 + $5 = $6, etc.
1) Which game would you rather play if you wanted to maximize your expected value, and why?
2) Which game has a lower risk? (Hint: let risk be defined as the standard deviation of your winnings)