From a pure efficiency point of view, if you are bisecting like this it is best to divide in halves, which gives you 1 bit of information each time regardless o

From a pure efficiency point of view, if you are bisecting like this it is best to divide in halves, which gives you 1 bit of information each time regardless of the outcome. Of course, this assumes you can continue to apply the same method many times, which probably doesn't apply to this case, as you can only fool Light with a similar method a limited number of times (possibly once only). In that case you probably want to do it more fine-grained than 1/3 so that you get more bits of information once you get to the first (and therefore last) successful attempt.