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What are some good strategies for quickly removing limbs?
I will tell you some things about how I play Toribash,(don't forget this is on free play)I usually start with a jump (It takes about 5 turns to jump so I am thinking this will be pretty useless on multiplayer) then I grab and attempt to sever a limb,and fail,horribly so could somebody help?
1) Practice without jumping.
2) Practice some more.
3) Repeat step 2).
[19:39] <Birdflu> I'm just sad that I can't give myself one
[19:39] <Birdflu> I'd have a great time
Mainly, you need to aim for the bits in between the actual movement joints (hips ect.)

Or just hit the joint really hard.
For decaps aim for the neck rather than the head.
sometimes it requires force to knock off a limb of someone like in aikido, you have to do a certain speed and aim to dismember something from your opponent.
You should look up some tutorials in the Tutorial Section of the forum. Going to the Tutorial Index can help you a ton. I'll suggest you some tutorials, if you have any questions you could PM me anytime ;)

http://forum.toribash.com/showthread.php?t=6
http://forum.toribash.com/showthread.php?t=4
These 2 are probably the easiest tutorials out there. You don't even have to bother reading them.

If you're new to the game and want to know some stuff, click Here.
Depending on the engage distance, you can often get a dismemberment on your opener if you focus on a fast swipe with your hand. An effective kick will usually involve bending your knee and then extending it later, so they're not as viable for getting a break on your first turn.

When I was developing openers for classic and kickboxing and judo and stuff, it helped me a lot to use the game's speedometer ("/sm 1" in the console), to see how fast I was moving. 40-50 m/s is about ideal for dismemberment. Faster than that, and you run the risk of clipping through the target. Collisions don't register if there's only one frame of contact.
Radioactive torso's description should be, "You have cancer like wow."