[durron597]

Clearly if you get a 1-3 you should reroll and if you get a 4-6 you should keep. If the game was played with only one roll the $EV is 3.5. Thus the EV of this game is:

1/6 * (4) + 1/6 * (5) + 1/6 * (6) + 1/2 * (3.5) = $4.25