Batman vs Joker(Prep Only)

I was thinking, Batman is really serious threat with prep, then I thought again, Joker is no joke when it comes to prep either(pun intended). So which would out do the other in prep. Takes place in Gotham.

Round One: Joker goes on the offensive prepping to make Bat's life a living hell in his own home. Batman preps for defense against this. Joker has 5 weeks to prep for this, Batman has 3.

Round Two: Batman is on the offensive prepping to take out Joker at Joker's Funland. Joker preps against it. Batman has 5 weeks to prep for this, Joker has 3.

Round Three: Both are out for each other in Gotham, other characters are a factor in this scenario only. They both have 6 months to prep, neither is looking to actually "kill" the other.

PS: When I say prep, I don't actually mean prep(while I do) as in like prep for a battle, more so like a game of chess, strategy and stuff like that. Also all three rounds IC.

Batman is just better than the Joker. Even if Joker gets a momentary lead with some crazy tactic, Batman will find a way to win in the end. That's just the way it is.

Batman all rounds.

I honestly think Joker is the smarter one, but on the whole it's stepped in Batman's favor. Rather favor an average, practical mind over a brilliant, addled one.