...if you were playing Magnus Carlsen, and he blundered and lost a piece. You are now a piece up for nothing. Magnus offers you a draw. Do you accept?

If I ever get the chance to play against MC in an official tournament, my class of play would be so high that a piece would mean a win against anyone. OTOH, playing for a win against MC, watching him desperatly searching for chances, even if I don't win is an expirience worth savouring. 

No. What's the point? Unless a draw would guarantee me 1st place in the London Classic and a cheque for a cool €50,000...

Play the board, not the opponent.

Once you let Magnus get that far inside your head, you are already lost.

Yeah, cause I would lose anyway even with him a piece or more down.

 That's not the point woodshover. Assuming it's just some random game with no prize money etc. at stake you have nothing to lose and a lot to gain by playing on. Why would you accept a draw in a completely winning position? The prestige? People draw with great players in simuls all the time, can you name any of them?

I can - Steve Hayler - he once drew with Karpov in a simul (Karpov was giving the simul, not Steve)

In a heart beat.

One of my club teammates Charles Summers (rated about 2000) demolished Nigel Short in a simul last year.

But agree, this isn't the point. Of course you shouldn't accept the draw. Your position is winning and not difficult to win even against perfect play. I was just interested to see what others thought.

But here's a less clear-cut one. Magnus offers you a draw in a position where you are a pawn up, and although he doesn't have any 'compensation' in the classic sense, the position is quite complicated. Now what? I must admit that in this case I would at least consider accepting.

depends if its a tournament or not ? if so then another factor depends on if I have a chance at one of the top spots if I draw and if so yes and if its a caseul game HELL NO ! got nothin to lose anyway.

NM Reb once commented in a post that if a stronger player offers you a draw, you should become suspicious and look deeper into the position.   I think there is a lot of truth to his statement...

Yeah, I agree.

Play for the win.

i would decline the draw, but from then on be super careful so i could get the win without being murdered. And my advantage is I don't use the time they give me, so I would probably have a lot more time than him on my clock

I would slowly conceive a repeating beeping sound, push the snooze button and try to keep dreaming

This what-if question is a fantasy that many chess.com players have...and I can tell you even IF you were mysteriously paired with MC it's highly unlikely he'd blunder a piece for nothing, and even if he did - chances are you're still busted.

The worlds top players are scary good - you have no idea how good unless you've played them.

 Good answer.

Play a very strong engine or elite human giving you piece odds and see how easy the win is. A rook is fairly easy, but a piece doesn't seem like enough.

It would really depend on the position. I would definitely want to beat him if he made a full-piece blunder. I would try really hard to win, instead of taking the draw. I've got nothing to lose

 Except the game. :)