You can write a story about a chessmaster without ever showing your reader the sequence of moves in a chess game.
As a reader, I hate hate hate this strategy, and I always know when it's being used. This sort of copout is an instant fail in my books, no matter how highly reviewed it is. The Master of Go is fine because the author is fictionalizing a real match, which he actually reported on live. The Player of Games is not, because Banks has not worked out Azad in any real detail.
present the character as coming up with those strategies/information in real time without warning
So, weak superintelligence. That might work - does seem pretty much to cover Eliezer's approach for Harry & Quirrel in MoR.
As a reader, I hate hate hate this strategy
I don't know about "hate" but it always feels empty and hollow, every time I read about a fictional supergenius, and that is where MoR came from.
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: