hm this is kind of neat..
Would it be fair to expect that for a hash function with at least one collision and one cycle, around 50% of the elements(?) might exist as part of a strand, and the other 50% as part of a cycle?
The number of collisions apparently is = to the number of strands(?!), and for each strand there is another end, ie an input which is not possible to output given any input.. funnily enough these are probably the hardest to find, but pretty much guaranteed to exist =)
Like you said, very difficult to know how many cycles there is exactly =/