Minimax question regarding alpha-beta pruning?

Question

Can someone explain to me why it is possible to eliminate the rest of the middle branch in this image for alpha-beta pruning? I am confused because it seems the only information you know is that Helen would pick at least a 2 at the top (considering if we iterate from left to right in DFS), and Stavros would absolutely not pick anything above 7. This leaves 5 possible numbers that the rest of the branch could take on that Helen could potentially end up picking, but can't because we've eliminated those possibilities via pruning.

Answer 1

Only:

1. B → B ⇸ B
2. C → C ⇸ C

are legal cuts.

Changing the order of root moves (swapping B and C) would allow the cut in your picture:

So... you're rightly confused!

For further experiments take a look at some online alpha-beta pruning simulator, e.g. http://homepage.ufp.pt/jtorres/ensino/ia/alfabeta.html

Answer 2

Alpha-beta pruning is based on the assumption that both players play perfectly and always make the best possible move. I don't know the rules of the game in your example so I can't answer you specifically on this case, but I think this link gives you a good exmplanation of how it works generally: https://www.geeksforgeeks.org/minimax-algorithm-in-game-theory-set-4-alpha-beta-pruning/.