Now, since it seems complicated to solve this game in this form,
one way we can address it is to change from this matrix form
into the familiar tree form.
We'll move this over here,
and we'll draw it as a game tree.
Max will be the even player, and min will be the odd player,
and for the moment, let's look at the game
of what would happen if max had to go first
rather than having them move simultaneously.
So, max would make a move either 1 or 2.
And then min--so max is even and min is O--
would also make the move, 1 or 2, 1 or 2.
And then the outcome in terms of E would be 2 here
-3 here, -3 here and 4 here.
And now what does min do? Well, try to minimize.
So, we choose 2 here, so this node would be -3.
We'd choose 1 here, so this node would be -3,
and then E tries to maximize.
It doesn't matter what he chooses,
and we get a -3 up here.
So, that's giving E the disadvantage of having to reveal
his or her strategy first.
What if we did it the other way around?
Let's take a look at that.
What if O had to go first and reveal a strategy of 1 or 2
and then E as the maximizing player goes second
and does a 1 or 2?
And then we have these 4 terminal states here,
and I want you to fill in the values of the 4 terminal states
taken from the table and the intermediate states
or the higher up states in the tree as well.