I'm trying to learn to play without anchoring my picking hand on the body of the guitar, but I seem to lose a ton of accuracy and sometimes feel like I just don't know where my hand is.
Tell me, is learning to play without anchoring my hand a worthwhile pursuit?
I think it's all a personal thing, if you wanna play anchored and that suits you best, go ahead.
But if your are unhappy about anchoring, then the only thing to do is keep practising.

Personally, when I'm strumming, I play un-anchored, otherwise I normally anchor.

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Just use whatever you feel comfortable with man. There is absolutely no hindrance when using Anchoring...its a myth. Just look at John Petrucci...enuff said.
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Personally, when I'm strumming, I play un-anchored, otherwise I normally anchor.

Same. I find that I just can't pick comfortably without anchoring.

But, with practice, I suppose you could get used to it, TS.
Mate just anchor your hand if that's what you feel comfortable doing, just don't do it if you're like me and you sweat battery acid and have chrome pickup rings, becomes quite obvious after a little while >_>
For me it's the other way around, I can't play when anchoring. My guitar teacher would tell me to practise it, but I never got it down. I guess it's more preference and both ways can be good, as long as it feels comfortable.
Nothing wrong with anchoring, I remeber seeing a list of people who anchor, and it was pretty huge and impressive. Just do what you are comfortable with.
Recently I've started anchoring when I play technical stuff and it helps out a lot. And as a guy above said, there are lots of pros who do it and are incredible players. Takayoshi Ohmura for instance.
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Most guitarists anchor including Petrucci, Gilbert and Yngwie. It doesn't matter if they hook their pinky around the pickup ring or not, most of the time you'll find they anchor somewhere.

One of the hardest picking techniques is to float pick, that is, no anchoring on the guitar whatsoever. It will allow your picking hand to glide across the strings without hindrance but requires significant control from your upper arm, which is still anchoring, just away from the guitar.

If you want to break the habit of anchoring I suggest you lift your palm away from the bridge and curl up your fingers when you pick. Alternatively you can learn to pick with your arm while keeping you wrist stiff which will increase your speed and speed transition, but unless you wanna pick with your arm it's just a waste of time.