An higher order approach would be to look at probabilities for chains of letters. E. g. in English the chance for an 'u' should be higher than average after a 'q'.

That's the wrong way of approaching it. One shouldn't look at the frequency of chains of letters in the particular language - but to the frequency of chains of letters in the list of words that may possibly match. But then, I don't see when this algorithm gives you any better guesses than looking for the letter which occurs in the most words. If for instance the current guess has a 'Q', then almost any word in the list of possible matches will contain a 'U'.

Now, I'd be surprised to see an efficient hangman guessing algorithm to guess 'Q' before guessing 'U'.