What's the threshold for this though? If you choose the hash and I have to produce the preimage, that scenario means you could always pick a "strong" hash, but

What's the threshold for this though? If you choose the hash and I have to produce the preimage, that scenario means you could always pick a "strong" hash, but if e.g. 50% of hashes are "weak" hashes, then a completely randomly selected hash would have a 50% chance of being "weak" and therefore attackable. If I can break 50% of randomly-selected hashes, does that count? Or would it have to be more like producing a preimage for hashes generated by randomly-selected inputs (and therefore the "weak" hashes in this scenario would be unlikely to be produced).