Another point of discussion for which someone here might have expertise: random search.
I found that random searches sometimes gave me the same results several times. That means I'm scanning the same keys more than once!
Here again we have maths (statistics).
Imagine a big bag full of green beans and only one red bean (the private key we're looking for). If I pick a random bean blindly from the bag and throw it back if it is not the red one, every bean I pick will have the same incredibly low probability of being the red one. And for each pick, the chance of getting the red one will be the same as taking the one I threw back before... So I might end up scanning a lot more keys than the size of the range before I find the private key.
So even if I count the number of beans I test, I have no guarantee that after testing as many beans as there are in the bag, there will be no red bean. Maybe I was just unlucky and didn't pick it.
Any constructive thoughts/opinions on this?