[matklad]

It is much better than this. You can _directly_ enumerate all the objects, without any probabilities involved. There's nothing about probabilities in the interface of a PRNG, it's just non-determinism!

You could _implement_ non-determinism via probabilistic sampling, but you could also implement the same interface as exhaustive search.

[pfdietz]

Well, yes. But the point is that random sampling lets you do it without thinking. Even better, it can sample over multiple spaces at the same time, and over spaces we haven't even yet formalized. "Civilization advances by extending the number of important operations which we can perform without thinking of them." (Whitehead)

An example is something like "pairwise testing" of arguments to a function. Just randomly generating values will hit all possible pairs of values to arguments, again with a logarithmic penalty.

[AlotOfReading]

The point is that you can exhaustively explore the space without logarithmic overhead. There's no benefits to doing it with random sampling and it doesn't even save thought.