I gave only a quick read, and I'm completely unfamiliar with Scrabble... but: why not use a Markov chain? I would start looking at the two step case, using only the most probable letter. In this case you have to remember a 26x26 matrix, if this doesn't work you can extend it to the top-n letters.

Another question: are there other scenarios outside of playing Scrabble where something like this would be useful?

In the abstract? Probably. But in human domains I suspect you're unlikely to find something very amenable to this sort of approach without a lot of looking. I actually think he's better off just memorizing because the words are human words from human minds and just trusting to your own human mind is going to work better than a simple math approach.

The one thing I'd consider adding is memorizing the tuple (word, origin), because English's problem is that my first paragraph is simplified for English; we actually use many different distinct human patterns, and helping the brain partition the problem might be helpful.

hah, this is cool.