MathDB

In the game of Yahtzee , players have to achieve various combinations of values with

5

dice. In a round, a player can roll the dice three times. At the second and third rolls, he can choose which dice to re-roll and which to keep. What is the probability that a player achieves at least four

6

’s in a round, given that he plays with the optimal strategy to maximise this probability?
Writing the answer as

p/q

where

p

and

q

are coprime, you should submit the sum of all prime factors of

p

, counted with multiplicity. So for example if you obtained

\frac{p}{q} = \frac{3^4 \cdot 11}{ 2^5 \cdot 5}

then the submitted answer should be

4 \cdot 3 + 11 = 23

Problem Statement