Winning the pot isn't everything
Ed Miller wrote an interesting article on what he calls "Macro and Micro Poker".
He defines macro as a set of winning principles.
He defines micro as a process of optimization within the framework defined by the macro principles.
Then he goes about explain that it's more important to think in macro terms than in micro terms.
Well, duh?
Of course it is. The macro terms is what defines the micro process. In his definition the macro is the model that the micro is going to optimize. Should you know what the model is before you try to optimize that model? Well, I guess so.
These aren't two seperate approaches that are to be contrasted. They're one in the same. The way he defines it the macro is the overall model and the micro is the computational details of getting an exact solution to the model. I recently wrote a couple of posts in my mathandpoker blog on the contrast between general mathematical ideas and computational math. Although not exactly the same as Miller's Micro and Macro distinction, it's similar.
And it's got the same kind of "duh" to it. Of course formulating the overall mathematical model is more important than finding an exact solution.
Interestingly enough though a lot of people don't agree with Miller and I about that. A lot of people think it's better to formulate a model that's easy to solve because it's important to be able to have that exact solution. I happen to think it's more important to formulate a model which captures the essence of the situation than it is to be able to solve it.
This is starting to get more philisophical on the topic of math modeling than I intended for this blog. I'd started out this post intending to go in an entirely different direction. Maybe I'll pick up on that other direction some other day.
But this whole idea of macro versus micro or the approximate solution to a full model versus an exact solution to a baby model is really what strategic thinking is all about. The idea of strategic thinking is what I'm trying to organize my no limit book around, and it's really the fundemental part of everything I've ever written about poker.
How you think about things is much more important than what particular decision you might make given some particulars. As long as you're thinking about the right things, and thinking about them in the right ways, you'll get it right often enough to come out ahead.
Ed Miller wrote an interesting article on what he calls "Macro and Micro Poker".
He defines macro as a set of winning principles.
He defines micro as a process of optimization within the framework defined by the macro principles.
Then he goes about explain that it's more important to think in macro terms than in micro terms.
Well, duh?
Of course it is. The macro terms is what defines the micro process. In his definition the macro is the model that the micro is going to optimize. Should you know what the model is before you try to optimize that model? Well, I guess so.
These aren't two seperate approaches that are to be contrasted. They're one in the same. The way he defines it the macro is the overall model and the micro is the computational details of getting an exact solution to the model. I recently wrote a couple of posts in my mathandpoker blog on the contrast between general mathematical ideas and computational math. Although not exactly the same as Miller's Micro and Macro distinction, it's similar.
And it's got the same kind of "duh" to it. Of course formulating the overall mathematical model is more important than finding an exact solution.
Interestingly enough though a lot of people don't agree with Miller and I about that. A lot of people think it's better to formulate a model that's easy to solve because it's important to be able to have that exact solution. I happen to think it's more important to formulate a model which captures the essence of the situation than it is to be able to solve it.
This is starting to get more philisophical on the topic of math modeling than I intended for this blog. I'd started out this post intending to go in an entirely different direction. Maybe I'll pick up on that other direction some other day.
But this whole idea of macro versus micro or the approximate solution to a full model versus an exact solution to a baby model is really what strategic thinking is all about. The idea of strategic thinking is what I'm trying to organize my no limit book around, and it's really the fundemental part of everything I've ever written about poker.
How you think about things is much more important than what particular decision you might make given some particulars. As long as you're thinking about the right things, and thinking about them in the right ways, you'll get it right often enough to come out ahead.
posted by Gary Carson at 2:40 PM
1 Comments:
I agree with your general premise about modeling. It's better to have an accurate model with approximate solutions, than a baby model with exact solutions.
I have found toy models to be useful for thinking about the full model though. I've often found that my understanding of a situation (and thus my ability to construct a good model) improves dramatically after I've examined and solved some toy formulations.
Toy models also often provide bounds on the real problem which are useful, and you can sometimes demonstrate that they provide reasonable approximations to otherwise intractable full problems.
So I don't have a problem with simplified models at all.
The problem comes when people solve a toy problem (or more likely, come upon someone else's toy problem and solution) and then start assuming that all those simplifying assumptions are irrelevant or introduce only minor errors, without analysis of why that should be the case.
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