# How to interpret the output of alpha-beta pruning in terms of which position to play next in a game

I'm trying to understand question 4 of this paper.

This is a tree pruned with alpha-beta pruning:

I understand technically how this pruning worked (i.e. calculating mix/max/alpha/beta values). My question is, how do you interpret the output of this tree? Which way should the max player go?

Watching this YouTube video, the best path for max is suggested to be: take the max of the first layer (below the starting below), then the minimum of the next layer and then the max.

In that case:

• The games starts with a point of 7
• Max chooses from 6, ≤5 or 7, so will choose the max of 7.
• Then max wants min to choose the min of 7, ≥8, ≥9, so 7.
• Then max will choose the max leaf node (which is 7, already implied from step above).

So I think this might be the best path, start at node 7, then choose 7 from the next layer, then choose 7 from the next layer. Can someone confirm this please?

Conversely, what is the worst first move for the max player? I think it is to first play the $$\leq 5$$ node (node B) and then I guess they only have one choice after that.