First to roll a six

MediumProbability~4m

You and an opponent take turns rolling a single fair die, and you roll first. The first person to roll a six wins immediately. What is the probability that you (the first roller) win? Give a decimal to four places.

Show hints (2)+
  1. After both players miss, it's the same game again - set up p=16+2536pp = \tfrac16 + \tfrac{25}{36}p.
  2. Solve the one-line equation; the answer exceeds 12\tfrac12.

Answer

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0.5455 (± 0.001)

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