N players are entered in a singles tennis tournament.

probability/tennis.meeting New

New entry, edited from material collected for the archive and not yet in a released version.

Problem

N players are entered in a singles tennis tournament.  The loser of
each game is eliminated.  What is the probability that two particular
players will meet during the tournament?  Assume all players have equal
ability.

Show solution

[ Editor: posted, in verse, as an entry in a rec.puzzles poetry
contest. ]

If the players in a contest number N
And a player having lost won't play again.
And if they're equally proficient
Then the info is sufficient
To calculate the chance that A and B will dance.
When the sum of games they've played is N less one
Then the contest most assuredly is done.
And with very little trouble
That figure we can double
For each game is played by two.
For example, me and you.
Now divide this doubled quantity by N
For the contest does involve that many men.
And now we have arrived at something we can say
Is the likely sum of games that will be played by A.
This is value one
We'll need it to get done.
Now consider once again N less one.
Though we used it once before, we're not yet done.
for reciprocally speaking
It's the number we are seeking
To relate the chance per game
That A will draw B's name.
This is value two
And we're almost through
For now we have two values that we can multiply
The product is 2/N so we can close and say goodbye!

-- JB72DEN <jb72den@aol.com>