Quote from: bill gator on June 10, 2018, 02:33:02 PM

~ the chances of winning the Powerball lottery are something like 1 in 300 million and it happens all of the time.

People win all the time because the chance to win is equal to the number of tickets sold. It's not rare that someone wins, it's rare that you win.

Back to Bitcoin: I can generate a random private key right now. The chance of me finding that key: 1 in 1461501637330902918203684832716283019655932542976 !
But the chance of me finding a key: 100%.

When comparing Bitcoin to the Powerball lottery, I think it's safe to say you're more likely to win that lottery without buying a ticket, than finding a collision on a private key.

Quote

I could type random keys on my keyboard

Humans are very bad at creating random keystrokes.

Quote

and potentially end up with an old Satoshi address at my disposal.

No you can't! It's easy to confuse a theoretical chance with a real chance.
Example: You can randomly generate my phone number, call me, and tell me my creditcard number. Although this sounds far fetched, it's still 1461501637330902918203 times more likely than finding a private key collision.

Quote

and increases exponentially when any of these attackers is using a method more effective than simple random generation or brute-force. Sophisticated hacks have a better chance than these figures would suggest.

That's why it's very important to generate your private keys at random. If your random isn't random, someone else can reproduce it.