Ok I have a problem here and I'm finding it quite difficult. The question involves a tournament bracket of a video game competition and of course for a game to be played, a TV must be available. So for example if we have 32 people, then we will need 16 TV's for all 16 matches to be playedAT THE SAME TIME.

However as the tournament progresses, people are knocked out and the number of playable matches at the same time decreases from 16 to 1 (initially 16 matches can be played at once but in the grand finals only 1 match can be played because theres only 2 people remaining in the tournament).

The question is, given adouble eliminationtournament, what is the Average Number of Playable Matches at any one time if the number of players in the tournament is N?

For a single elimination bracket its not too difficult to calculate but calculating a double elimination bracket is proving much more difficult. Any help?

A double elimination Bracket looks like this.