A baseball league has 6 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 this season. Define the imbalance of this schedule to be the minimum number of teams that will end up undefeated, i.e., lose 0 games. Find the expected value of the imbalance in this league.
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