He would have guessed and any timeline where he would have guessed wrongly would have been inconsistent, since he sure as hell would have remembered to include the relevant information then.
But this is essentially a less systematic variation of the trick he tried with factoring prime numbers. "I'll guess, and since guessing wrong would lead to paradox, it guarantees that I have guessed right" should have ended with another DON'T MESS WITH TIME note.
Besides, it costs him absolutely nothing to add a few more details to the letter. The only reason I can think of for not doing so is if he somehow evaded Flitwick's obvious question without arousing suspicion, (and so found himself needing not to know to replicate the feat).
The difference is that the factoring trick involved several thousand other timelines that had to be resolved while adding any information he lacked to the message involved one. Spontaneously generating timeline stabilizing random data that only requires resolving a low number of timelines to calculate being preferred over having to calculate thousands makes sense, being preferred over a stabilization that requires calculating at most one other timeline does not.
It's not really any different from any other trick that involves him observing the results of h...
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: