Player MAX and player MIN are playing a zero$-$sum game with a finite number of possible moves.

MAX calculates the minimax value of the root to be

$$

M$.$ You may assume that at every turn,

each player has at least $2$ possible actions. You may also assume that a different sequence

of moves will always lead to a different score $($i$.$e$.,$ no two terminal nodes have the same score$).$

Which of the following statements are true?

The following checkbox options contain math elements, so you may need to read them in your screen reader's $$reading$$ or $$browse$$ mode instead of $$forms$$ or $$focus$$ mode.

Choice $1$ of $2$:Assume MIN is playing sub$-$optimally at every turn, but MAX does not know this. The outcome of the game could be larger than

$$

M $($i$.$e$.$ at least as good a MAX$).$

Choice $2$ of $2$:Assume MIN is playing sub$-$optimally at every turn. If MAX plays according to the minimax strategy, the outcome of the game could be less than

$$

M$.$