Tips & strategy
Always guess the middle of what is left. If you know the number is between one and fifty, guess twenty-five. Whatever the answer, you have eliminated half the possibilities in a single move, which no other guess can match.
Keep track of both bounds, not just the last clue. After a few guesses the range is squeezed from both ends, and players who only remember the most recent hint end up re-testing numbers they already ruled out.
Do not guess at random once the range is small. With four numbers left, the middle guess still beats a hopeful stab, because it guarantees you finish in two more turns rather than possibly four.
Notice how few guesses it actually takes. Halving repeatedly is astonishingly powerful: a range of a thousand needs only about ten guesses, and seeing that for yourself is the real lesson here.