I took the problem to mean "Based on the current set, give yourself the best move you can make at this time." To which, what I mentioned was true. With the information you know, you are making the best possible move for the available ranges. (Looks back at problem description...) Ah. see I was assuming an unknown number of guesses after you. In which case, the "split the biggest" would give you a best case scenario.
Actually, if you go first, you're screwed anyway unless there are only 2 people playing. I can't picture a scenario where the first player has a good chance to win, other than a 2 player game.
Anyway, I was thinking of it as not knowing how many people were possibly going next.