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And the answer is, in the game of pig the opponent
is trying to defeat "me," so they want the worst for "me."
The dice has no intentionality.
Everything is equal in terms of outcome for the dice,
so that works out to average.
So now we have a way of describing the world.
When we start out, it's "me" and I have options I can take--
roll or hold--and I go in one direction and I get to a point
where it's the dice's turn to roll, and that can have six outcomes.
Rather than trying to choose the best, we'll just average over all of them.
Let's say there's one here, and now it's my opponents turn to move
and my opponent makes a choice, and let's say ends up here.
And I look at all these paths through that keep on going
until they get to the end of the game.
And then if I say, if I always choose the best,
and if my opponent always chooses the worst for "me,"
and if the dice average out, then I can describe all the paths
to the end, and I can describe the value of those paths.