Trans-Taiga Road (2004)

Nerd snipe: given a compass and dropped in a random location what is the best strategy (based on direction assuming no clues from terrain) of finding a road. E.g. strategy might be 1000 steps south then 1000 east, repeat.

Nerd snipe 2. Same without a compass or any sense of direction. Assume you can accurately make a 90 degree turn and count steps

Honestly I’d just walk downhill. Most human settlements are on rivers, most roads take the lowest passes. At night, I’d just walk in the direction of the sky that’s glowing the most.

Melville (roughly) agrees -- from the first chapter of Moby-Dick:

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Once more. Say you are in the country; in some high land of lakes. Take almost any path you please, and ten to one it carries you down in a dale, and leaves you there by a pool in the stream. There is magic in it. Let the most absent-minded of men be plunged in his deepest reveries—stand that man on his legs, set his feet a-going, and he will infallibly lead you to water, if water there be in all that region. Should you ever be athirst in the great American desert, try this experiment, if your caravan happen to be supplied with a metaphysical professor. Yes, as every one knows, meditation and water are wedded for ever.

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You could still do that parallel to a road.

Go find water and then try to follow where it flows. Look at the scenery and try to determine whether you're in a valley or on a plateau or in the mountains.

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.

Specific to the U.S., assuming no terrain clues - go NW, SE, SW, or NE, as most roads in the U.S. go N, S, E or W - mitigates the possibility of parallel tracking.

The latter - pick a direction, walk in a straight line.

The idea is to minimise tbe chance.