I read a blog post recently about the limit of speed-solving records getting to a point that rely on easy scrambles to beat. One of the most obvious head starts would be to get a scramble that already has the first phase done.
For this question, assume we are using the CFOP method and the solver is color-neutral. What are the chances of a random scramble having the cross already solved on one side?
Just an anecdote: I have done thousands of solves and have never had this happen, at least not on the white side. I'm curious what the odds are.