Dumbledore is an r-strategist.
He tells Harry to carry around a random object purely on the theory that "it is wiser to do than not", and he tells Blaise that it's important to have multiple plots going at once. His basic strategy is to try as many things as possible, in the hopes that a few of them will work.
Furthermore, he's in pretty much the ideal situation for r-strategy: a highly chaotic environment, and few to no direct rivals or real peers.
I like this analogy.
Dumbledore's cost per plot is also very low: he has a large supply of minions whose time would otherwise be wasted playing Unicorn Attack, and he has no credibility to lose when his plots fail.
He also tries to force his rivals to be play the same way, since they don't have his advantages. If Voldemort is scheming to get at the Philosopher's Stone by year's end, he has to simultaneously target the third-floor corridor, Harry's father's rock, the Hogwarts vault at Gringotts, and who knows what other decoy locations. Similarly, Dumbledore engineered a three-way tie in Battle Magic to try to force Quirrell to pursue three different plots (Quirrell being a rival for the students' hearts and minds).
Update: Discussion has moved on to a new thread.
After 61 chapters of Harry Potter and the Methods of Rationality and 5 discussion threads with over 500 comments each, HPMOR discussion has graduated from the main page and moved into the Less Wrong discussion section (which seems like a more appropriate location). You can post all of your insights, speculation, and, well, discussion about Eliezer Yudkowsky's Harry Potter fanfic here.
Previous threads are available under the harry_potter tag on the main page (or: one, two, three, four, five); this and future threads will be found under the discussion section tag (since there is a separate tag system for the discussion section). See also the author page for (almost) all things HPMOR, and AdeleneDawner's Author's Notes archive for one thing that the author page is missing.
As a reminder, it's useful to indicate at the start of your comment which chapter you are commenting on. Time passes but your comment stays the same.
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically: