Ah! Thanks for the stimulation. That's an interesting problem that I had not thought of before. In fact a few related problems.

What's the minimum set of requested key presses that will uniquely identify a keyboard layout from a set of known types.

Given a budget of k key strokes what's the most informative subset that will reduce the ambiguity about layout.

Given the measurement from the requested key strokes find the posterior over the set of known keyboard layouts.

Given that the user is typing some free form text in his language how soon can one nail the layout when the user's language, the layout and the text are unknown. Will make a good practice exercise for hobbyist codebreaking.