On the Size of the Largest Distinct Extreme Score Set in Random Round-Robin Tournaments

Key Points

• The study aims to determine conditions under which the largest and lowest scores in a round-robin tournament are distinct.
• Modeling a round-robin tournament with equally strong players
• Analyzing scores represented as values in a countable subset of [0,1]
• Proving conditions for distinct extreme scores through mathematical limits
• As the number of players increases, the largest scores are likely to be distinct with high probability
• Similar results apply to the lowest scores due to symmetric properties of the model
• Condition with k(n) growing indefinitely is critical for the findings

Abstract