A thread on probabilistic causation

I think I have a workable model of libertarian free will, though I haven't made much progress on a planned graphic illustration.  I stumbled across a thread at "The Garden of Forking Paths" that focuses on one of the critical issues facing libertarian theories of free will.

The list of contributors is intimidating with respect to the number of letters per contributor.

For what it's worth, Fritz Warfield's response to the original post resonates for me.

In part:

"It's then a matter of pure chance whether or not that subsequent event occurs. If it does, then, in a plain sense, nothing causes it."

What does "pure chance" mean so that the first claim in the quote is true? And what is the "plain sense" in the second sentence of the quote?