Unbeaten Chess Streak

What this unbeaten-streak probability question tests

This is a medium-difficulty probability question that combines combinatorial counting with probabilistic reasoning. It asks you to reason about rare events in a symmetric setting—specifically, what it means for at least one player to remain undefeated across a round-robin tournament.

The problem rewards clear thinking about complementary events and mutual exclusivity. A typical approach involves identifying which player configurations allow an unbeaten record, understanding how many matches each player must win, and then either computing the probability directly or using inclusion-exclusion to avoid double-counting overlapping cases. The symmetric structure (equal win probability for each match) simplifies the calculation once you've set up the constraint correctly.

• Round-robin tournament structure and match counts
• Complementary probability and the union bound
• Symmetry arguments in independent events
• Inclusion-exclusion for mutually exclusive outcomes