expectiminimax with backtracking

I am creating an expectiminimax tree cutoff at a certain depth: MAX -> CHANCE -> MIN -> MAX ...

After creating the tree, I can perform a Depth First Search with alpha-beta pruning, but I was thinking that during the creation of expectiminimax tree, the moment at the depth cutoff, the current node becomes a terminal, we calculate the score and backtrack, using alpha - beta pruning, and whenever alpha becomes greater than beta, we can just return back to the parent, instead of considering any further moves ie not create more children nodes beyond that point.

Won't that method save more space and time as it will prevent further creation of the nodes? Is it the actual way of performing expectiminmax?

Or would it be better to first create a tree till a particular depth, and then perform DFS separately, starting from the root.

Moreover, I understand how to perform alpha-beta in minimax, but a bit confused how to do it for expectiminimax, when we consider chance nodes. Any help in that area would be nice too.

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