Winning from deuce

At deuce, a player wins each point independently with probability p=0.6p=0.6; you must win two points in a row to take the game (otherwise it returns to deuce). What is the probability this player eventually wins the game? Give a decimal to four places.

Show hints (2)+
  1. Returning to deuce restarts an identical subgame.
  2. W=p2+2p(1−p)WW=p^2+2p(1-p)W.

Answer

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0.6923 (± 0.001)

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