What the Deuce? Djokovic V/s Federer

In a grueling Wimbledon final the scoreline is tied at \(2\) sets all. In the final set, Djokovic who is leading the set \(7-6\), is serving for game set and match. After six points, scores are level at \(40-40\) Deuce.

Having the serve, Djokovic has a \(0.75\) chance of winning a point against Federer while a tiring Federer has a \(0.25\) chance of winning a point against Djokovic.

What is the probability that Djokovic wins this game after Deuce is reached?

Details and assumptions

  • To win the game, Djokovic can win the first \(2\) points.
  • If he wins the first point and loses the second, its back to Deuce
  • If he loses the first point and wins the second, its back to Deuce.
  • If he loses the first \(2\) points he loses the game.
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