Each of the thirteen turns in Yahtzee begins by rolling five dice. You then have two more rolls when you reroll any subset of the dice you want. Once the three rolls are done you must score your roll in one of the categories.
1. Suppose that on the first roll you get 5, 5, 4, 3, 2. If you pick up one of the fives and try for a large straight, what is the probability you will succeed in the two rolls that remain?
2. Suppose that on the first roll you get 6, 5, 5, 3, 2. If you pick up one of the fives and try for a large straight, what is the probability you will succeed in the two rolls that remain?
3. If you can roll a die one or two times and you want to get the highest score then you should keep a 4,5,6 on the first roll and reroll a 1,2,3. If you can roll a die one two or three times (as in Yahtzee) then after the second roll you should keep a 4,5,6 on the first roll and reroll a 1,2,3. What should you do after the first roll?
4. If you roll a die three times. What is the probability yoou will get at least one six?
5. What is the probability you can get five sixes in three rolls at Yhatzee? Four sixes? Three sixes?
Bonus Question: Suppose you keep the number of the first roll that you get the most of. What is the probability you will get a yahtzee? Four of a kind? Three of a kind?