Intersting! I know that in the contiguous USA, you will never be more than 20 miles from a road no matter where you are, but have no idea how far one can drive from a town.
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(Assuming nothing kills you in nature)
Edit: Wait, no. You could be extremely unlucky and be walking parallel to the closest road, lol.
Nerd snipe 2. Same without a compass or any sense of direction. Assume you can accurately make a 90 degree turn and count steps
Compasses are pretty useless without a map or a terrestrial view of some sort, as all you can do with them is shoot a bearing relative to magnetic north, or if your compass includes a declination adjustment a bearing to true north, provided you know the declination beforehand. It's often printed on topographical maps for this reason.
If you're on top of something then you can use the compass to get somewhere you can do dead reckoning. Usually there's little landmarks every 10 or 20 feet that you can stay on a bearing to. But if you can't see any topography from where you're at you'll have to infer it somehow. So another strategy might be to head uphill if you can ascertain there will be some kind of view there.
A lot of what you'd do depends on the terrain you find yourself in.