A systematic approach to explore viewpoints in thinking games
Posted by ardianto86 at 06:45 PM on January 11, 2007.
I gained this insight from game theory lecture. Let's take chess for example. How do we think systematically in order to cover the many arrays of possibilities? It's true that there are nearly infinite, and mind that i'm not talking about strategies, but rather, the viewpoint that we can take in order to develop a strategy. In other words, we assess how we usually think in a game such as chess. Basically, we can categorize it as follows :
1st order of thinking : "I know"
Meaning, we must 'know', we must be rationale! The application of adopting this 1st order of thinking is, if i do this, then that would follow. We assess each and every moves in this way.
2nd order of thinking : "I know what he knows"
To be a more competent chess player, not only do we assess things on our side, we should assess things in our opponent's point of view. We must also assess every of his moves and what might follow as a consequence.
3rd order of thinking : "I know what he (thinks) he knows about what I know"
This is often used to set a trap. It's logical to move a certain piece, because it would lead to A, which would be an advantage to us. Our opponent foresees this, he thinks he knows everything, and we should have guessed that he would block it. However, we're not going for A. Indeed when we move to A, we could gain B, which is more advantageous.
Another case is making he think that we're making a foolish move, he think he knows everything and there it is! He's going into a trap!
...
I dunno if we can extend this further to many more levels of thinking. Perhaps we could then devise a more advanced strategies by developing on these approaches =p