|The stupid question is the question not asked|
The crux of the problem is that there is a huge disjunct between patterns that we can recognize and act on, and patterns that we can describe in sufficient detail to train a computer to act on.
Bridging this gap is the main goal of AI research.
As so-called expert systems demonstrate, it is possible in many cases to straightforwardly break down complex decisions into many simple ones. And so a computer program with a good rule-set can do routine diagnostics quite effectively.
As chess-playing computers demonstrate, it is possible in many cases to give the computer very little general knowledge, but have them at each step work out from first principles how things will happen.
The problem is that Go has enough states to be infeasible to work much out from first principles. You are talking about how large the solution set is. Unfortunately the solution set is already far too large for us to calculate it statically once, or to calculate on the fly enough of the local decision tree to recognize what a human would see on general principles.
It isn't a question of just doing it intelligently. It is a question of being able to do it at all.
At a guess the problem shares a lot problems we deal with in voice recognition. The raw signal comes in a form that is essentially useless to the task at hand. The rules that people actually use are done at a level which they cannot even think about conciously. What can we do?
Well we can search for a transformation of the raw signal into alternate signals in which patterns are easier to state. For instance patterns in speech tend to involve features that are localized in both space and frequency. So we search for some way of describing that signal in terms of components that are themselves localized in both space and frequency. And we find that wavelets do that. Using wavelets, our signal is massively clearer. Still a mess, but oh well.
We then improved that by finding ways to make wavelet transforms dynamically choose the trade-off between localizing in space and time. We chose the one with the minimum entropy, meaning the shortest internal description. What did that do? Well it made the wavelet transform naturally break on the phoenemes of speech. And gave each one a recognizable "signature" we could work with. And now we had something to work with.
Something similar is true with games. Humans don't just sit down and learn a bunch of rules. Humans engage in the twin activities of learning how to recognize patterns, and learning how to react to them.
A good player of the board game of your choice does not merely know more rules about that board, they actually see a different board. For instance consider the task of memorizing a chessboard. If you take good chess players and poor chess players, and hand them a board with pieces randomly arranged, they perform about equally. If you take both and put down random positions from middle-games of real tournament games, the good chess players are substantially faster and more accurate at memorizing the board.
Why? Well when I heard about this, we didn't know for sure. But here is my best guess, that the good chess player has developed an internal model of pieces on a board that allows them to describe the board efficiently. (The efficiency of our internal descriptions is highly significant in memorization tasks. For instance native Welsh speakers can memorize more numbers if asked to do it in English than if they are asked in Welsh. That is because the same number said in Welsh has more syllables.) How efficiently? Well components are obvious because they are features you learn to analyze. Others because they are features which are characteristic of the opening.
Therefore I would guess that there will turn out to be a deep connection between having a computer that can play Go well, and the task of describing positions which arise in real Go games efficiently...