Thank you. I just read posted links and now I understand it.
I didn't understand how is to possible not to generate same address.
Information, that it is actually possible, but highly unlikely, explains it all to me.
It's not impossible. But it's also extremely unlikely to happen.
The odds in colliding with a specific address is 1 in 2^160.
If there are a billion users and each have one million active addresses (1 quadrillion funded addresses in the blockchain) the odds in colliding with any address would be roughly 1 in 2^110 (1*10^33).
Vanitygen can produce 20 million keypairs per second. Lets say you build a super ASIC on 12nm (4 generations ahead of current tech) process that could create, validate, and steal one trillion keypairs per second (1 TK/s). That would be about 50,000x more powerful than faster GPU today. Lets also say you built a thousand of them and ran them continually with no downtime 24/7/365. In 1 year you could brute force 3*10^28 possible addresses.
If there are 1 quadrillion funded addresses you would still have a ~1% chance of colliding with a random funded address in the next 1,000 years.
Source:
https://bitcointalk.org/index.php?topic=104461.msg1143828#msg1143828