Is there any case where we can say Alpha-Beta pruning is inefficient. In other words, let's say we have a game where you have to reach 27 to win, and you and your opponent may only use 1,2,5 each time to add up. So is Alpha-Beta pruning efficient in here? Isn't it a little bit confusing to evaluate it that way, especially at the begining of our case where there are a lot of possibilities which we don't really care about?
I feel like I can explain this, but I can't! Help.
For this game, it might happen that it is possible to reduce it to some mathematical formula, and the tree search and alpha-beta pruning would be overkill.
But let's say it is not possible. You have a game with two or three outcomes: LOSS(-1), WIN(1) and possibly DRAW(0), and no meaningful evaluation of intermediate positions. Then you would need to search to the end of each variation, and so e.g. iterative deepening would be pointless.
However, alpha-beta pruning could be very efficient: If beta=-1 (meaning the opponent has found a win), you can just return -1 right away, without even searching a PV. If beta=0, the only time you would need to search all child nodes is when all (except possibly the last) moves lose.
The condition for alpha-beta to sufficiently efficient is, of course, that the complete tree is small enough to traverse in reasonable time.
EDIT: I forgot to mention that for your particular example, remembering evaluations would have much, much greater effect than alpha-beta pruning with regard to the number of nodes traversed (from 2688332 to 77).
