Difficult probability with a Die

Dirac and Pauli are playing a game with an ordinary six-sided die. Dirac’s target numbers are
1, 2, 3, and Pauli’s target numbers are 4, 5, 6. They take turns in rolling the die, with Dirac going first. If the one whose turn it is rolls a target number which he has not previously rolled, he gets to roll again; if he rolls a target number which he has previously rolled, or a number which is not one of his target numbers, his turn ends. The first player to have rolled all three of his target numbers (not necessarily all in the one turn) wins. What is the probability that Dirac wins?