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?
My opinion on Random Search.
"There is only a PROBABILITY based on LUCK."
Since you put it back in the bag, PROBABILITY is the same and LUCK is the same in the system where Memory/Database is not recorded.
But here there are 2 types of PROBABILITY.
Independent probability and Dependent probability.
Independent Probability, after putting it back in the Bag, random selection result.
Dependent Probability, like shuffling the Bag, making the first selection from the left of the Bag, the next selection from the right or bottom. There are many variations of Dependent Probability effect triggered by the options.