2017 Guts #31: Imbalance of league
Source:
February 21, 2017
combinatorics
Problem Statement
A baseball league has teams. To decide the schedule for the league, for each pair of teams, a coin is flipped. If it lands head, they will play a game this season, in which one team wins and one team loses. If it lands tails, they don't play a game that season. Define the imbalance of this schedule to be the minimum number of teams that will end up undefeated, i.e. lose games. Find the expected value of the imbalance in this league.