Optimal Play

_{This isn't intended to be harsh, but it may sound that way. You'll have to take it lightly, I've been thinking in terms of alien invaders and mad scientists all day.}

I got into a bit of an argument (Greek-style, rather than Bronx-style) with Patrick.

The gist is this: he believes that with perfect information (meaning "complete visibility", in relative vision terms), there is an optimum play pattern. Even if the player can't really figure out what it is.

There's three problems with this. One: it's wrong. Two: it's incomplete. Three: it's inapplicable.

Let me address the second one first. Assuming that, given perfect information, there is an optimum play pattern, you also assume that a player has perfect skill at playing. I haven't shown the other two to be wrong yet, but the second is painfully, obviously wrong. Sure, in chess it's not hard to play a piece exactly where you want it. But how about Duck Hunt?

Yeah, it's awfully clear exactly where you should be shooting. Does that mean you can hit the ducks? That depends on your skill and how fast the ducks are moving, doesn't it?

This is a core factor in many (probably most) games - the skill it takes is not just one of determining the best play path, but also playing it.

So, the idea of "ideal play" is incomplete, because an ideal path cannot be followed in any game where physical skill is required.

Now, the idea of "ideal play" is also flawed because it is wrong. There is not always an ideal play path, even assuming perfect information.

Rather, there might be, but we have not proven that there is, because many games with perfect information appear to have no ideal play path. Go (wei'qi, baduk), for example. This may simply be because the complexity of the game is too high to compute the information we are given, but the complexity doesn't need to be very high before this lack of an ideal path hits. Which means that, functionally, games of perfect information quite often have no discernable ideal path.

In addition to being wrong and incomplete, the idea of "ideal play" is also completely inapplicable:

A slight deviation from ideal play often radically changes the rest of the path. And, as mentioned, there is usually no way to (A) determine and (B) stick to an ideal path. Given you generally want your game to be as vivid and replayable as possible, most designers choose to maximize this drift rather than minimize it, where possible. In the past, this was impossible. These days, it is becoming more and more possible.

For example, what is the "ideal play" in Gran Turismo? There is no "optimal" optimal play. You might be able to compute "personal" optimal plays for any given individual, but even those will spread erratically.

If I'm better at cornering but worse at handling the shifter, my ideal car would be far different from someone who doesn't have a feel for corners but knows his engine intimately. Actually, knowing your engine intimately sounds rather painful, but each to his own.

The point is, even if me and MisterSecondPlayerMan have the exact same skills, we probably won't have the same optimal path after the first hour or two, because we will have bought different cars, made different tweaks, won and lost different races. This is despite all the cars' info being clearly available, either in the game or online: if we make slightly different choices, these choices compound into radically different playstyles.

And that's good! That means replayability! That means vivid, reactive gameplay! That means solid game balance! It's a dream!

Perfect or imperfect information has no effect on the calculation of optimal path. The amount of information available does, as does the difficulty of computing said information, but you can easily have a simple game with perfect information or an imperfect information game with huge tons of complex information. Checkers vs "Romance of the Three Kindoms Nth".

Optimal path calculation is just another half-assed shortcut to game balancing.