So, evaluation function.

How do you do that?

Right?

So, again, we can't search all the minimax tree.

So what we do is we impose a search depth limit, which might be seven, right?

And we stop after reaching depth seven.

Or we might have some heuristic depth, saying, oh, we're around here.

Those are interesting games.

Let's search a little bit deeper there, stuff like that.

So we look at a couple of cutoff states that are at what we think of as the horizon.

And then we need to have numbers there.

And we can always formulate, and therefore we will, that as a function of states to values,

right?

Take all the states in the horizon, give everyone a value, that gives you a function.

And that's the evaluation function.

And if you think about it, that's almost the same as a heuristic.

Heuristic, sorry.

Right?

And it behaves the same as a heuristic.

We want to be this thing both accurate, because if they're accurate, ideally as accurate as

computing them with minimax, then we win.

There's always a way of computing the evaluation function accurately.

We just run full minimax.

But that's also not what we want.

We want to have these evaluation functions be fast.

And just like with heuristics, you can't have both.

And if you use either of the extremes, either completely inaccurate, you lose.

Or very expensive to compute, you also lose.

Because there's usually a time limit.

You can't wait for three million years until you move your next piece, because your opponent

will have either died or rusted away or whatever.

So you can't have both.

So you have to kind of find a balance between them, which is usually a bad compromise.

And today, typically, systems are on the side of being accurate.

If we have some information at all, then that's good enough.

And usually, we don't really have a good way of doing evaluation functions.

For chess, you can kind of count pieces or something like this.

Every pawn costs one.

Every rook, five, maybe five.

I think I have, oh yeah, here.

Pawns one, knights three.

Bishop three.

Rooks five.

Queen nine.

And the king.

What would you give that?

I would have said that before thinking as well, but the utility is plus 100 and minus

Right.

Exactly.