Quote from: knightdk on May 06, 2016, 01:38:57 AM

The resulting hash of a multihash function (including multiple iterations) has the same collision resistance as the collision resistance of the weakest hash.

This is not exactly true, the collision resistance is weaker than the weakest.

Hashing many times protects from some preimage attacks. It's sometimes used to make the hashing slower on purpose (like in WPA, in order to make cracking slower and more expensive). Doing it twice for mining makes sense because it prevents some mining algorithm optimizations and also because ASICs for sha256 existed before bitcoin, but not ASICS for double sha256. So hashing twice may have been a way to prevent those ASICS from working.

Hashing more than once does increase the probability of collisions, however that increase is negligible. Consider the case of double sha256:
output = sha256(sha256(input))

If one of the two sha256 have a collision, then the double sha will have a collision too. So it's weaker: at least one of the two hashes is ~~required~~ sufficient for the double sha to collide. That probability of having one of two hashes collide is certainly higher than having only one hash collide.

However, consider that if double sha256 has a collision it is because at least one of the two iterations of sha256 did collide. So you see, it is still very unlikely because it still requires a collision in sha256. And as someone mentioned, a collision in sha256 is in itself more important news than having found Satoshi.

I consider it safe to assume that CSW didn't find a collision in sha256.