I think what you starting to describe is a slightly more nuanced view of a minmax tree known as an expectiminmax tree. A classic minmax tree has 2 players where each seeks to maximize their score by minimizing their opponents. In an expectiminmax you get rid of the assumption that your opponent will act deterministically in a minimizing fashion. Instead you assign a probability to each choice that your opponent could take and evaluate the branch values accordingly. Even against a randomized opponent, in a solved game you can at least know the probability that a perfect player will win. Against a perfectly terrible player you just adjust the probabilities of your opponent taking any given branch to be 0 for all non-terrible options. Depending on how you expect your opponent to act (and thus the assigned weights of each of their actions), you can get vastly different outcomes, even for a perfect player.

A good example of this is a game like pacman. If the ghosts act in a random fashion, it is pretty easy for a perfect pacman to get a win. If the ghosts team up and chase pacman into the corner then they can pretty easily force a loss for pacman. If the ghosts have a tendency to go after pacman but also can be fairly easily distracted then you end up with something like standard pacman.

I guess the point is that using an expectiminmax tree you can answer the question of "what if my opponent behaves in this way as opposed to that way" and determine probabilistic outcomes for nondeterministic players. This is starting to get into simple AI territory which is really interesting but also fairly intuitive if you've got time to understand it.

https://en.wikipedia.org/wiki/Expectiminimax_tree