Runtime of various versions of binary search
Instead of cutting the interval in half, it's cut in to a piece 1/3 of the length and it's cut in to a piece 2/3 of the length. If you are lucky enough that the item you're searching for is in the left half, then you've done a better job than regular binary search. If you're unlucky and it ends up in the right half, then you do slightly worse than regular binary search.

What happens if the algorithm has "bad luck" twice in a row. The interval gets cut to 2/3rds and then to 2/3rds again, meaning it gets cut to 4/9ths which means it is now slightly shorter than 1/2. This means that in the worst case (bad luck every time) this version of binary search will take only 2x more steps than regular binary search.

On the other hand, if the algorithm is lucky the interval is cut to 1/3rd. If we look at regular binary search, after two steps the algorithm has been cut in half two times, meaning it has been cut to 1/4th - slightly shorter than a 1/3rd. So in the best case, the algorithm takes at least half as many steps as regular binary search.