shapes vs formations

Bill Spight · **#21**

dohduhdah wrote:

Well, not just as a pure math problem. More as a kind of exploration of certain concepts that delineate
certain classes of patterns. This is not intended as a way to figure out how to play go in any optimal
fashion from the perspective of a human player, but more of a way to figure out all possible ways one
can play go from the perspective of a bot.
Try to imagine yourself as a bot that plays go, initially knowing only the rules of go and making
random moves.
After each game, you analyze what happened during the game and you try to memorize certain patterns
that occurred during the game. Bad patterns (you might want to recognize those so you know what
patterns to avoid) as well as good patterns.
The question is, how do you store these patterns in a kind of database efficiently, so you can quickly
look up a pattern in that database.

You might contact Frank de Groot. You might also try the computer go mailing list.

dohduhdah · **#22**

billywoods wrote:

dohduhdah wrote:

a collection of tens of thousands of patterns
as you can find them on the gochild tsumego website for instance

But, the stronger you get, the less those patterns crop up. In the same way, you can't learn tesuji from studying professional games, because no professional will allow themselves to get into a situation where a tesuji can be effectively used against them.

My real objection is: what do you propose this bot will do when its opponent plays something that's not in any predetermined pattern? Presumably it needs to do things like weigh up influence vs. territory, look for weaknesses, read, or something like that - something that it can't do using patterns alone if there are no familiar patterns to exploit.

Well, you start out with simple patterns and gradually you work your way up to more advanced patterns or patterns
at higher levels of abstraction. A concept like atari or snapback is fairly concrete and rather elementary, while
concepts like influence or weakness are more abstract and advanced.

If the bot encounters opponents that play something that's not in any predetermined pattern, the bot can just
play random moves and afterwards try to learn new patterns from the game until it comes up with patterns that
match up with those moves it hadn't encountered previously.

The idea of a learning bot is that you only program certain general methods for the way it can extract patterns
from the games it plays, and to supply it only with the rules and the ability to assess the status of groups
at the end of the game. So the programmer doesn't teach the bot anything as far as go skills are concerned
and the goal for the bot is to come up with such knowledge autonomously, simply by gradually accumulating
patterns and occasionally generalizing a pattern or something along those lines. But in order for this to work,
you need a kind of formalism in terms of which it can memorize and manipulate patterns, which I think of
as higher-level patterns.

Phelan · **#23**

Bill Spight wrote:

dohduhdah wrote:

Well, not just as a pure math problem. More as a kind of exploration of certain concepts that delineate
certain classes of patterns. This is not intended as a way to figure out how to play go in any optimal
fashion from the perspective of a human player, but more of a way to figure out all possible ways one
can play go from the perspective of a bot.
Try to imagine yourself as a bot that plays go, initially knowing only the rules of go and making
random moves.
After each game, you analyze what happened during the game and you try to memorize certain patterns
that occurred during the game. Bad patterns (you might want to recognize those so you know what
patterns to avoid) as well as good patterns.
The question is, how do you store these patterns in a kind of database efficiently, so you can quickly
look up a pattern in that database.

You might contact Frank de Groot. You might also try the computer go mailing list.

I'm not sure if you're being serious or not.

Edit: Well, not about the computer go mailing list. That's a good place to discuss this, as the developers probably discuss pattern storage there.

dohduhdah · **#24**

Chains seem to coincide with the concept of polyominos at Wolfram Alpha:

http://i.imgur.com/YTIPpFs.jpg

Yuc4h · **#25**

...which have no relevance whatsoever.

Bill Spight · **#26**

Yuc4h wrote:

...which have no relevance whatsoever.

You might be surprised.

HermanHiddema · **#27**

Also, more generally, chains are what is known in graph theory as connected components.

dohduhdah · **#28**

HermanHiddema wrote:

Also, more generally, chains are what is known in graph theory as connected components.

Do formations (i.e. a number of stones on the goban, none of which are touching each other) also have
an equivalent concept in graph theory?

Graph theory seems more about topological relationships. You can have a weight associated with an edge between
two vertices, but you can't really have a weight associated with a combination of vertices that are not connected
by an edge. In go, two stones can more or less be connected in one way when two stones are right next to each other.
But there are multiple ways for two stones not being connected. They can be at opposite sides of the goban
with a large distance between them, but they can also be relatively close to each other.

billywoods · **#29**

dohduhdah wrote:

Do formations (i.e. a number of stones on the goban, none of which are touching each other) also have
an equivalent concept in graph theory?

Sure, if the stones form an independent set. In general, you can call a stone 'isolated' if its connected component is just a single stone, and a 'formation' is a collection of isolated stones. I don't know to what extent this formalism helps...

dohduhdah wrote:

Graph theory seems more about topological relationships.

I agree. (It would be interesting to ask graph-theoretic questions about go, though I don't know whether we'd learn much.

)

dohduhdah · **#30**

Yuc4h wrote:

...which have no relevance whatsoever.

I think mathematics is relevant to go.

The abstract patterns of math are sometimes fairly similar to patterns in go:

http://i.imgur.com/AG2uCnv.jpg

This graphic is a way to depict the moebius function and one might wonder if there
are other ways to depict the moebius function in which all possible chains can
recursively be found (so given any possible finite chain, one would be able to
graph the moebius function in a finite number of recursive steps in such a way
that the chain pattern occurs in it).

http://www.wolframalpha.com/input/?i=moebius+function

The computer offers new possibilities to explore the patterns in go, for instance
a kind of time-lapse view of go by mixing up images in photoshop to visualize two
moments during a game (in the middle and at the end) simultaneously:

http://i.imgur.com/nOIGEPO.jpg

I'm interested in a mathematical approach to go, relating it to mathematical
concepts of combinations/permutations, symmetries, translations, reflections,
rotations, trees of game state progressions, etc.

shapes vs formations

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