> Given that 7 guesses covers 128 numbers

I might be confused, but don't 7 guesses actually cover 255 numbers? I think you have to count all nodes in the search tree, not only the leafs, because you can get the correct number before reaching a leaf node.

Or more generally k guesses cover 2^(k+1)-1 numbers, e.g. with one guess you get the answers correct/high/low, which can cover 3 numbers)

Maybe there is a mistake in my thinking, because this would mean you can cover 127 numbers with 6 guesses so you could not lose the original game.

Edit: My mistake is that you still have to explicitly guess even if you know the precise answer already, so you cannot cover 3 numbers with 1 guess. This means 7 guesses cover 127 numbers.