Probability of Winning with Rerolls on Ties

Setup

• Three players: A (you), B, and C.
• A fair six-sided die is used.
• B and C have already rolled and both showed 4.
• You now roll once:
  1. If your roll > 4, you win immediately.
  2. If your roll = 4, all three players reroll simultaneously, repeating until there is a unique highest face. (If the highest face is tied by two or more players, everyone rerolls again.)
  3. If your roll < 4, you lose immediately.

Question: What is the probability that you ultimately win?