The way you originally stated the problem was to pick a number between 1 and 100, so 0 wouldn't even be an option, and 1 is probably the pareto optimal strategy (proof left as an exercise for the reader, etc.).

But then you probably still have to account in your strategy for estimating the proportion of people who will reason to infinite degree and estimate 1, as well as the proportion who will reason to an infinite degree and misread the rules, and guess 0...