As the tournament currently stands, including the play-in game between the 65th and 64th seeds, one game is played for every team that gets eliminated without winning a championship... so that is a total of 64 games.
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10
1 plays 2345
2 plays 345 because it has already played 1
3 plays 45 because it has already played 12
4 plays 5 because it has already played every body else
and 5 has played 1234and5
now every body has played each other and nobody has played twice
OR we could use the formula 5C2=5x4/2=10 where 5C2 means 5 choose 2.
Either 8 or 9 games. The 9th game is only necessary if the 8th game (the last team in the "winners" bracket against the last team in the "losers" bracket) is lost by the team with no previous losses. Since it is double elimination, a team must lose 2 games to be eliminated, and therefore the two teams will play one more time to decide the tournament winner.
10 games.
Using Team A, B, C, D and E. Each team would play 4 games.
A vs B, A vs C, A vs D, A vs E
B vs C, B vs D, B vs E
C vs D, C vs E
D vs E