Fermatastheorem comments on Harry Potter and the Methods of Rationality discussion thread, part 28, chapter 99-101 - Less Wrong
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Well, for this applet the optimal strategy might depend heavily on how exactly its tameness is executed, which isn't very enlightening.
Edit: Derp, I tried out top-to-bottom and got it in 572. Definitely better than left-to-right or normals-first-ltr.
I used top-to-bottom, but dires first on each level, and that seemed to work consistently pretty well.