Of course it's always easier to just use the bottle opener on the bar (yes there is a vise on my bar top, which is actually an old work bench made in the 50's by the home's original owners).
This is really more of a party trick... But there are plenty of other things you can do with a sheet of paper. This is a good demonstration of the strength of paper with just a few folds.
I'm certainly not the first one to do it. I saw someone do it over 20 years ago and I am sure plenty have done it since.
(also... Yes I have a flask that holds a half gallon. I found it at Goodwill)
Step 1: Fold the Paper in Half
Step 2: Important
Step 3: First Try
You can see that in the paper vs. steel contest the paper holds its own.
Step 4: Success!
These are stills from the video. You can see the bottle cap flying off.
I suppose I should add another step and say drink... But I assume you have figured that out.