If an algorithm lies at the root of biological life (state changes, Rocha - self organizing complexity, von Neumann) - then the outcome is planned, directed, not happenstance.
If master control genes are largely immutable causing eyeness to evolve simultaneously across phyla between vertebrates and invertebrates (Gehring) - then the outcome is planned, directed, not happenstance.
When an Intelligent Design proponent looks at these things, Occam's Razor is that an intelligent designer must have been involved.
When a creationist looks at these things, the response is "God did it!"
When a metaphysical naturalist looks at these things, the response is "Nature did it!"
The contention is basically between the ideology/theology of creationists and metaphysical naturalists (atheists, agnostics).
Strangely, the ID proponents don't specify who the designer is (God, aliens, collective consciousness) and are therefore the more neutral of the three - but are presumed to be creationist.
Quibbling over the definition of "happenstance" is a dodge, IMO. Happenstance in this context simply means "by means of a completely unplanned process" -- as you suggest.
I gather this is the part that PH just doesn't "get": IDers and some mathematicians and physicists are just looking at "what is," and realize that the likelihood of evolution being "unplanned" or random, accidental, just doesn't cut it; for it just doesn't explain at all what can actually be observed in nature.
Certainly there is a good deal of randomness in nature; but still, at the same time, the general direction of nature is not itself random. The genome, for instance, can hardly be explained as a purely random development.
Thanks for your astute observations, Alamo-Girl!
Oh please. ID proponents can hide their light under a bushel if they choose, for whatever political purpose they desire, but any assertion of a designer other than a supreme being just pushes the origins question back a notch. It's dishonest and should be shameful.
An algorithm (as we are using the term loosely in this case) may make use of random choices. There's much literature on the subject. One can plan to make a random choice and follow that choice.
This is simply not true. It is quiet easy to write an algorithm that has an indeterminate outcome.