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Both get one hour prep and all their regular supplies
Battle is in creepy abandoned building
Win by kill

Daredevil kills him...

With prep, Joker wins majority if he's allowed Harley's help as part of his prep

Joker is pretty good at prep. I mean, he's able to match wits with Batman. And half the time, he's not even really trying to "beat" Batman, just troll him. *shrug*

World War Daredevil kills him effortlessly, though.

Joker kills him. Go here for his respect site.

jokerfeats.blogspot.com

Joker wins if he doesn't set traps and play games.