“There can be as much
value in the blink of an eye as in months of rational analysis.”
-Malcolm Gladwell
One of the trends I’ve noticed in games I’ve played a lot of
is that there tends to be a concept of “beauty” that is reflected in the way
the players think and talk about the games they play. What do they mean when
they say a particular position or aspect of a position is “beautiful”? I’m not
completely sure, even though I use this kind of language a lot as well. I have
some ideas, though. (That’s why I’m writing a blog post about it)
In games, it’s common to draw a distinction between
“tactics” and “strategy.” “Tactics” refers to calculated sequences of specific
moves, whereas “strategy” refers to larger patterns within the game. In essence
“strategy” is a approximation for “tactics” over the long-term; it is useful
when calculating enough moves in advance to make a decision becomes
intractable.
In many games, when I am in a situation where calculation is
too difficult, I find that I instinctively try to make my position as “beautiful”
as possible. I therefore associate beauty more with strategy than with tactics,
since it’s a thing I use when I don’t want to think tactically. That said, this
isn’t cut-and-dried by any means; I have seen plenty of tactical sequences referred
to as “beautiful.”
So what is beauty, then? All I’ve said so far is that I seek
it out when I’m too lazy to calculate. Well, here’s an example:
Several times in chess clubs I’ve heard people refer to specific
chess pieces as “sexy.” If you want to see an example of a sexy piece, the
black bishop in the upper right is a prime example. Look at that monster! Not
only is it putting pressure on the pawn on c3, it’s preventing the pawn from
moving, since if White pushed the pawn he would put in his rook in danger. In
order to fully deal with the threat, White would need to move his rook and then
push his pawn, which would take two moves, and even then the bishop would
remain very powerful.
It’s difficult to say exactly what makes a piece like that
bishop look quite so good to a chess-player. Of course, the bishop’s developed,
and it’s attacking a pawn, but it’s more than that; there’s something
peculiarly beautiful about the bishop that makes applying the descriptor “sexy”
to it seem not wholly inappropriate.
Experienced chess-players are likely to appreciate that
bishop more than inexperienced players; additionally, they’re likely to
appreciate it much more than computers will, despite the fact that computers
will beat them at chess every time.
Chess masters almost universally accept that there is
“beauty” in chess positions or aspects of it, but they have incredible amounts
of trouble teaching this concept to the computer programs they write to play
the game. Typical position evaluation algorithms depend on a move search many
moves deep (about 10 or 20 depending on the position) and then a crude
evaluation at the end. (That’s tactics, followed by strategy. Check it out) The
crude evaluation at the end tends to assign a value to each piece, such as
1/pawn, 3.5/bishop and knight, 5/rook, 9/queen, and then an extra quarter-point
per square of mobility available to the pieces. In the position I described,
the crude evaluation would assign to Black’s dark-squared bishop a value
inferior to her light-squared bishop, since it only defends 6 squares, whereas
the other defends 7! And yet it’s clear that the dark-squared bishop is not
only the better bishop, but the MVP of Black’s position.
Of course, this wouldn’t cause too many problems for the
computer, since it can just look so far ahead that it will see the tactical
benefits to Black’s sexy bishop. But it still feels like the computer has
nonetheless missed the “point,” somehow.
This gets brought home harder in games where there are more
moves available, so looking far ahead is harder, and patterns of “beauty” are
harder to predict algorithmically. In the game of Go, for example, there are
hundreds of moves available to each player at each move, and there is no
approximation for beauty like “mobility” that gives the computer some idea of
what pieces (or stones, in go) are really contributing. This makes computers
much worse at go than at chess. Take this problem:
One of these corner formations is strong and efficient, and of them is weak. Which is which? If you only know the rules of go, or if you know the rules and have played a few times but not enough to have learned which one is better (or to have been told), this problem is impossibly hard. The frustrating thing about being a beginner in these kinds of games is that you haven’t yet come to learn what makes a thing beautiful or not; experienced players will know at a glance that you have made a bad move when it would have taken you minutes (or sometimes, years) of calculation to tactically verify that your move was poor.
We can even see concepts like these in games like Starcraft,
where it is often necessary to instantly know which of two armies is going to
win a battle. Believe it or don’t, but I have heard people refer to Starcraft
units, games, and positions as “beautiful,” and I definitely think in those
terms a fair amount when I play the game.
Which army has the advantage? A Starcraft beginner will have difficulty guessing, but somebody who has played many games will know at a glance because she will have seen scenarios similar to this one many times before.
Beauty in games is a way for experienced players to describe
their intuition about a position. It comes up whenever experience allows
players to make snap judgments. But at the same time, it seems to me like it’s
more than that, more than a strategic shortcut. Game beauty seems to me to
deserve equal respect to “real” beauty, the kind we appreciate when we listen
to a good song or admire a piece of art. It’s sad, though, that unlike in
music, where beauty can be appreciated by everyone, appreciation of beauty in
games is restricted to those who play. (Excessively?)
Don’t be fooled by the chess. This entire blog post was
really just a long-winded, poorly-reasoned explanation for why playing a lot of
Starcraft makes me an artist.
An experienced
Starcraft player will recognize this as the widely feared “Six Pool” strategy.
For those who are curious, in the go example, the formation on the left is the strong one; a connection between two stones of two diagonal squares is weak. In the Starcraft example, the Zerg player (Red) has the advantage; zerglings are strong against stalkers and immortals, and there aren't enough stalkers to deal with the threat of the mutalisks.
-Adam
No comments:
Post a Comment