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# Game Theory and Chess

• #1

So I was browsing through 'The Great Courses' at subjects they're giving away with nice discounted prices. I was briefly interested in a mathematics course, maybe something with calculus (something to broaden my math, which I am not good at at all). I stumbled across a course on 'Game Theory,' about rational thinking and decision making between actors.

It's an economics term as well.

But it applies well to board games, especially Chess. The study of how two players compete against each other. I wonder if purchasing this course would broaden my Chess horizons. In addition it got me to thinking when trying to adapt my playing ability should I learn to "play the man," like Harvey Spector says in Suits (instead of pure calculations) and learn how to beat human opponents or would it be more wise to learn to play to beat strong calculations, like a strong computer?

• #2

The only relevant thing I can think of is that, in playing against a human, you want to create many different threats to increase the chance that they will miscalculate. The majority of game theory is designed to handle simple games of imperfect information but known values for each decision, whereas chess is exactly the opposite. The subfield that does focus on games like chess tends to rely on computers, since these games are highly combinatorial (i.e. too much to calculate by hand). So I'm not sure how any of this would reallymake your chess better.

In short, get whatever you're interested in.

• #3

Agreed. While computers use algorithms (probably developed from game theory) to assign values, these are not perfect, and anyway you can't use a computer in an actual game. So your decision has to be based on more qualitative things such as, like I said, generating multiple threats which overwhelm your opponent's ability to calculate, or setting yourself up in a position where you will have many options (the forerunner of threats).

• #4

Yes.  Give a player one way out and if their back's against the wall they're likely to find it even if they're not a very good player.

Give the same player many different reasonable tries at defense, only one of which works, and you're sure to win easily.

• #5

Here's what the originator of Game Theory had to say on this topic:

Chess is not a game. Chess is a well-defined form of computation. You may not be able to work out the answers, but in theory there must be a solution, a right procedure in any position. Now real games... are not like that at all. Real life is not like that. Real life consists of bluffing, of little tactics of deception, of asking yourself what is the other man going to think I mean to do. And that is what games are about in my theory.

--- John von Neumann

• #6

Game theory is hard to apply to chess as it assumes perfect play by both sides(see John von Neumann's theory of poker, where if your opponent acts like a fool his theory gets shot down).

Furthermore, when we see pieces crowding around our castled position, we rush to defend it and may not make the best move(which might be a6 or something surprising). Game theory fails to take this into account.

Another thing is that, if we were to choose between a familiar tactical motif like a fork that wins a pawn and a mass of random complications that might win two, we would choose the safe route, which is not what game theory wants you to do.

• #7

Playing the computer you'd have to be at your best with calculations.

But, and I've only scimmed Game Theory today, playing humans is nearly by definition different.

If I set up my laptop on Chess Titans level 10 vs another laptop of Chess Titans level 10 - it would be a battle of math.

Two people vs each other it isn't so similar. With two people you can bring in the ability to become artistic.

• #8

I think that if the really good mathematicians applied themselves, they could apply themselves to creating an operating system to approaching chess, much like Newton invented calculus to explain some of his theoretical ideas.

I bet it could be done. And it would probably be extremely helpful for those expert mathematicians that just happens to be a really good chess player. Those of us that cannot apply such a method would not be able to apply it, but the idea itself is interesting!

• #9

In game theory, the way sequential games are solved, which would include chess as it is a game of sequence rather than simultaneous play, you diagram a game tree which encompasses all your possible choices and all the possible choices for your opponent to respond to your choice and then all your possible responses to their choice and so on until you get to the end result which in chess would either be a win or a loss.  Then you use backward induction to find which choices you should make as your moves.  The game tree complexity of chess has been estimated at upwards of 10^120.  Because of this any use of game theory in the opening or midgame is unrealistic.  Game theory could, and perhaps even should, be used in simple endgame situations if for no other reason than to cause you to analyse the position a little more so you don't make an avoidable mistake that cost you the game.

As for game theory itself, I've taken a university level course in it and it is really not so terribly interesting as it seems on the surface.  It seemed to get a little dry over time.  If your interested in improving at math and maybe want to learn a little about game theory as well I would advise you to study microeconomics.  You could pick up a college level intermediate microeconomics textbook which will have some calculus based problems for you to do and most micro text have a few chapters on game theory so you could learn the basics of it without getting into the dryer aspects of it.  Plus economics rules!

• #10
Gdatum wrote:
waffllemaster wrote:

Yes.  Give a player one way out and if their back's against the wall they're likely to find it even if they're not a very good player.

Give the same player many different reasonable tries at defense, only one of which works, and you're sure to win easily.

ur speeches r irrelevent and nonsense.

Defense is a real problem for non-professional as everything in chess is geared toward attack( chess puzzles,openings /middle game/endings are taught as checkmate movement)...building a fortress too prevent an attack or tactics for draws are rare.

• #11

Game theory is actually applicable to chess. Chess players and chess engines alike think in manners that are similar to the game theory's extended form. In chess, it is famously referred to as "tree of variations".

However, the tricky part isn't with the tree or the game theory itself. The tricky part is with the evaluation function. How do you evaluate that the position is better or worse? If you use game theory for this, how do you evaluate whether this action is better for you? Or how do you know that Action A actually gives more benefits than Action B? Game theory teaches you the framework to logical decision-making, but you need to fill in the evaluation function yourself.

About "playing the person vs playing the board", it depends on whether you want to include the psychology element into your evaluation function. Either way, game theory is still applicable.

In chess, the role of game theory is obvious. By thinking "If I capture this, he captures that, and I check him there, and then..", the chess player is essentially applying the game theory. However, in real life situation, such as politics and economics, this way of thinking isn't always obvious. When businesses decide to lower their prices, they often don't consider how their rivals are going to react. In the end, they got stuck in price wars that they wish they hadn't started in the first place. This is where the game theory comes in. It shows people that they can apply structured thinking in their decision-making process.

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