Advantage: Crazy Brain
The Joker is insane and this may seem like a detriment to most people but he himself revels in it. His mind is so shattered and twisted that it is almost unrecognizable, providing him with a few helpful little defenses. First and foremost only the most powerful telepaths are capable of discerning anything from the jumbled mess of his mind and efforts to cure him with psychic powers last only moments before he bounces back to crazy like a rubber band. It also makes his actions nigh-impossible to predict, giving him a deadly advantage over certain detectives.
Advantage: Goons
The Joker has quite a lot of goons around him when he's not in Arkham and if he finds himself without then he knows exactly where to find them. A lot are insane and drawn to his brand of crazy, willing to do his bidding. The others are just your average goon who needs employment and finds that the Joker pays well. They're all loyal to him and will even fight the Batman if he wants them to. You just can't buy that kind of loyalty (you can, it costs quite a bit).
Advantage: Hard to Kill
Like Steven Seagal, the Joker is hard to kill. He's been shot, stabbed, electrocuted, blown up and drowned and yet he always seems to come back. There's little to explain just how or why this happens, he isn't any more durable than a normal human being. Being shot hurts him just as much as it would hurt anyone else and his bones snap as readily as a normal man's (just ask Batman), but no matter how mangled he is at the end of the day he always finds his way back to being just as spritely as he was before. After a nuclear war, the only survivors will be cockroaches and the Joker.
Advantage: Hideouts
The Joker has a hard time getting a hotel room given his tendencies towards mass murder. Because of this, he has established all manner of hideouts throughout Gotham City (and even abroad). Most of them are little holes in the wall or abandoned warehouses, but he does own the occasional disused amusement park for when he really feels theatrical. These hideouts also contain a lot of stolen loot which allows the Joker to fund his escapades.
Advantage: Immune
Smilex is delicious and the Joker partakes quite a bit of his chemical creation. He also took a dive into a vat of crazy chemicals. Because of this, he has a resistance to most kind of chemical-based poisons. He can survive his own poison easily enough and others do little to hamper him. It is also handy to be able to shrug off some of what riot squads like to throw at him when they're storming his headquarters during a police siege.
Advantage: Joker's Stuff
The Joker is quite clever and his genius for engineering allows him to manufacture all manner of gadgets. He's not about to build a Death Star or anything of the like, but he can put together death traps and even clever little weapons when he needs them. Generally he sticks to his acid flower, his joy buzzer and his revolver but he has all manner of things that he can whip up or has in storage for when he needs them. Never anything large or jaw-dropping, just clever little tricks that could really spoil someone's day.
Advantage: Joker Venom
The Joker's favorite (but not only) method of murder is a deadly poison created by his cousin (whom he murdered to keep the secret) that causes his victims to die laughing, made from a 'healthy mix of hydrogen cyanide and Strychnodide.' When exposed to it (and it can be distributed in all manner of ways), the victim begins to laugh uncontrollably until their muscles contract and they literally break their own back in fits of laughter. The laughter also becomes so overpowering that the victim cannot breathe, eventually asphyxiating in a horrible way. The victims die with the same coloration and grin that the Joker sports. The Joker is capable of making his poison from even basic household cleaning materials and years of exposure has left him immune to it.
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