What is better probability to find a key? To search 66-puzzle only or search 66-67-68-69-puzzles simultaneously?
puzzle-67 is twice as difficult as puzzle-66.
puzzle-68 is twice as difficult as puzzle-67.
and so on.
The best chance to find a key is when you focus on the easiest available puzzle, that is puzzle-66 now.
But after you find a key you may have difficulties claiming it, it even can be stolen as soon as you try to move it. Maybe there is a work-around but that isn't 100% secure either.