My intuition says that they should almost always run at about the same time if you don't know anything about the distribution of guesses. Your algorithm has th

My intuition says that they should almost always run at about the same time if you don't know anything about the distribution of guesses. Your algorithm has the advantage that it will find an upper bound for the number much faster than the interviewer's algorithm. HOWEVER, having found that upper bound, your algorithm will probably be much farther away from the actual number than the interviewer's, so you have to do that much more narrowing down. What it comes down to is being lucky that you're close to the number in your initial guess, otherwise, you're still talking logarithmic time to either find an upper bound or (in your case) lower bound for the number.