Top two seeds meeting in a 128-player final

Question

A knockout tennis event has 128 players with distinct strengths placed into a uniformly random bracket, and the stronger player always wins each match. What is the probability that the two strongest players meet in the final?

Short answer

$64/127$ . The best player always wins, so the second-best reaches the final exactly when they start in the opposite half of the draw. Of the 127 other slots, 64 lie in that half.

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Lessons behind this question

Sample Spaces, Events, and the Probability Axioms
Conditional Probability, Total Probability, and Bayes' Rule

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