A 12 before two 7s

Two players roll a pair of dice repeatedly. A wins if a sum of 12 appears first; B wins if two consecutive 7s appear first. What is P(A wins)? (to 3 decimals)

Show hints (2)+
  1. Add a state for "a 7 just occurred".
  2. A 7 followed by a 7 makes B win.

Answer

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0.5385 (± 0.005)

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