Probability (orig. posted by rob77)

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Posted by Joel on October 13, 2002 at 14:42:14:

: A,B,C are evenly matched tennis players. Initially A and B play a set, and the winner then plays C. This continues, with the winner always playing the waiting player, until one of the players has won two sets in a row. That player is then declared the overall winner. What is the probability that A is the overall winner?

I guess it IS a trick question, and the trick is that although all are evenly matched, A and B, by being in the first round, have an advantage over C.
I don't know how to compute the probability but I believe it is a sum of the form 1/4 + 1/16 + 1/32 + 1/128 + 1/256 + 1/1024 + 1/2048 ... which seems to be approaching .375. (1/64 and 1/512 are intentionally omitted.
Here is my "attempt" at an upside-down tree diagram of the possible outcomes, which (if the board displays it as I am hoping) may show how I am getting to that.

`                                            AB                   AC                                    BC         **A**            CB                   --BA--            CA                      1/4                   --C--       BA                         -CB--      AB                       --B--          AC                        **A**    BC              1/16                            **A**           CB                     --B--    CA           1/32                                    --C--       BA                   --C--      AB                                         --B--       AC                   **A**   B      1/128                                              **A**        CB               --B--    AC  1/256`

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