Consider a tournament between N teams, each team playing each of the other teams. Let’s call team i a k-winner if there is a group of k-many teams that were each beaten by team i. Other teams may have beaten team i, but there is at least a group of size k that was roundly beaten by i.
Question: For N= 100, what is the smallest k that 3.4 indicates the probability of having k-winners is less than 1?