Cody

Problem 44502. Anyone for tennis? Your chances of winning a (standard) game

Imagine you are playing tennis, and for each point played your chance of winning is x % (input as a uint8). Given the ITF's scoring system for a "standard game" of tennis (excerpted below), please determine your likelihood of winning a game (output as a single).

Note that as x is taken to be the same for every point in this problem, it does not matter whether you are serving or not.

EXAMPLE

 x = uint8(40)
 chance = single(0.2642707692307693)

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" A standard game is scored as follows with the server’s score being called first:

  • No point - “Love”
  • First point - “15”
  • Second point - “30”
  • Third point - “40”
  • Fourth point - “Game”

except that if each player/team has won three points, the score is “Deuce”. After “Deuce”, the score is “Advantage” for the player/team who wins the next point. If that same player/team also wins the next point, that player/team wins the “Game”; if the opposing player/team wins the next point, the score is again “Deuce”. A player/team needs to win two consecutive points immediately after “Deuce” to win the “Game”. "

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See also Problem 44503. Anyone for tennis? Your chances of winning a tie-break game.

Solution Stats

75.0% Correct | 25.0% Incorrect
Last Solution submitted on May 04, 2019