In a game of Farkle, you roll your first dice. You get a 2,2,2,4,5 and 6. You can either re-roll the dice or keep your points from this first roll.

a. You choose to re-roll your 4 and 6. What would you expect to be the value of points?

b. You choose to re-roll your 4,5, and 6. Now what is your expected value of points?

c. Should you re-roll the 4 or 6, re-roll the 4,5 and 6, or not re-roll at all and keep the points you got from your first roll of 2,2,2,4,5 and 6