Well, what you are doing is a "generalized" binary search. Suppose you have a four-stor(e)y house. You can start from the second floor and proceed a la standard binary search. You're putting an implicit ordering on the parts of your house, essentially, and then doing a search.

And the bit about cutting the search space to a third (which is what I believe you meant, instead of cutting it /by/ a third) is something you can also do when searching a list, but IIRC halving is preferred because it has better worst-case time-complexity. You can always split a list into 1/3 + 2/3 instead of 1/2 + 1/2, but you risk having to search the 2/3 every time, etc.