Wicc
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A hoodie is, of course, simple and straightforward, but it doesn't make things any easier for those who lose after the first game.
Double elimination is much more reasonable.
By the way, 3rd place in double elimination isn't played for; it's awarded to the loser of the losers' final. And 4th place is awarded to the loser of the losers' semi-final.
The super final is played until one player from the losers' bracket wins two games, or until the winner's bracket player wins one game.