how many miles break in, before switching to synthetic motor oil ?

I have a motor with about 250 miles on it, and it has been sitting for 3 years. I wasn't thinking about the rings and I put synthetic oil in it, and after 25 miles, the oil is dark. I figure it's blow-by.

I'd rather run synthetic, but it looks like the rings aren't seated and I'll have to go back to regular oil. I will be mostly racing this motor.

Any experience here, would be greatly appreciated.