Machine Learning for Human Memorization

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?

hah, this is cool.