3
$\begingroup$

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?

  • 0
    I haven't seen any effective methods to attack this question. To try to get some intuition as to what may be happening, I did a tree diagram, but i) the diagram becomes unwieldy within just 2 moves and ii) I realize it will never end, as there are scenarios where the players keep on rolling non-targets, though the probabilities of these scenarios decreases with each move. The first player to roll a target number disadvantages themselves since it becomes harder for them to roll a target number from then on, so Dirac's chances are probability less than 50%, but that may just be plain wrong.2011-08-03
  • 1
    Yes, that's wrong, since the other player will eventually have to go through the same "disadvantage" in order to win.2011-08-03

2 Answers 2