A few questions about "running it twice"

[lgkeeper]

This hand isn't from HSNL, but I figured higher stakes players would know the answers to these questions. The following hand came up in a live game last night and the conversation followed:

$1/$3 NL -
Me $450
Villain $400

I raise OTB to $11 with 69c
Villain (LAG) calls in SB
Flop is 652r
Villain checks
I bet out $16
Villain raises to $50
I re-raise to $125
Villain pushes
I call in a shot
(now, before you flame, we'd been playing together for 7 hours and I had a pretty good read on him throughout so I knew I was good for now)

He flips over 54s and asks if I want to run it twice.

So, here are my questions, b/c I've never been in a game where you've been able to do that.

- Am I correct in my understanding that if you do run it 2x, if you each win one time, you split the pot and if one guy wins both he wins the whole thing?

- Is there an advantage, mathematically, to either player?

- Should I have agreed?

Any help is appreciated. Turns out I said yes (pretty stupid since I don't completely understand the process). I won the first one and he won the second. Would have been an $800 my way....

Thanks.