How can I protect and monetize an algorithm?

As an agent my comments do not constitute the practice of law, but another good guideline is the Bilski "machine or transformation test," in which it can be shown that the invention is the algorithm tied to a computing machine specifically configured to store and execute the steps of the algorithm, you've got a good case (machine,) or if you can describe and characterize data in a "before" state, then describe the structure of the data in an "after" state after the algorithm has done its work, and then show that the difference between these states (transformation) represents a useful improvement (utility.)
The converse of this guideline, similar to Mr. Lau's remarks is that any computing process which you can complete entirely in your head is very likely NOT patent eligible. In re Bilski, the rejection of that algorithm reads: "...the invention is not implemented on a specific apparatus and merely manipulates [an] abstract idea and solves a purely mathematical problem without any limitation to a practical application, therefore, the invention is not directed to the technological arts."
So, include some of the elements that the Bilski rejection is lacking, and you may have something you can own and protect.