This is a common misconception. The actual real world effect is that you'll never ever run into a collision, because it is much more probably than any other catastrophic event will happen in your computer, or that bits will flip at random in your processors and so forth. Note that:
1) Economic transactions, signatures, files, are often verified using "incredibly long random numbers".
2) Rsync transfers files hashing blocks with hash functions and avoid transferring blocks with HMACs that match.
You'll never see a collision if not on-purpose in the case the hash function has a vulnerability that allows the attacker to craft a plaintext P2 so that HASH(P2) == HASH(P1), or at least allows an attacker to select two P1 and P2 so that HASH(P1) == HASH(P2).
If you don't trust crypto hash functions to be collision resistant in the explained use case, where even the above attacks are irrelevant since we are just using the distribution properties, you can't trust most modern computing at all.
1) Economic transactions, signatures, files, are often verified using "incredibly long random numbers".
2) Rsync transfers files hashing blocks with hash functions and avoid transferring blocks with HMACs that match.
You'll never see a collision if not on-purpose in the case the hash function has a vulnerability that allows the attacker to craft a plaintext P2 so that HASH(P2) == HASH(P1), or at least allows an attacker to select two P1 and P2 so that HASH(P1) == HASH(P2).
If you don't trust crypto hash functions to be collision resistant in the explained use case, where even the above attacks are irrelevant since we are just using the distribution properties, you can't trust most modern computing at all.