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Optimal Strategy for Connect 4

2swap.github.io

31–34 of 34 posts

Re: Optimal Strategy for Connect 4

#31
post #28

Earlier quoted context omitted.

isn't this very similar or a case of trading space for time or vice versa (e.g in algorithm analysis)

That is certainly an example of it, but I feel like what I'm talking about is more general. In algorithms you tend to be able to say concretely exactly how much space vs time you're trading off. But in a game like Connect 4 or chess it's a lot harder to say exactly how much you gain from, say, adding one more heuristic to your board analysis, or memorizing one more opening subtree. I don't know how to think about tha…

I’ll throw another example.

Do the work of indexing, or summarization or compression vs just do it retrieval on the raw records.

It could be embeddings, or presorts or indices.

But I think the parent poster is correct. There’s an inherent write vs read tradeoff as well as memory vs compute. Maybe with some generalization vs specialization.

Idk if im explaining properly. But you can always front load more effort on a narrower problem space and then utilize it on that space downstream.

I think with your llm example there is no code/data split. The llm is caching a solution to a narrow problem by writing the code.

Re: Optimal Strategy for Connect 4

#32

Sadly this doesnt have a simple way to know how to win besides the ForceEven approach and offering an Anki Deck. I wish there was some more intuition or guidance around winning that humans can memorize

He has 4 videos about human Connect 4 strategies on his YouTube channel[1], you should check them out.

[1] https://youtube.com/@twoswap

Re: Optimal Strategy for Connect 4

#33
post #26

I've been intrigued about the thing they call the "data product" for a long time: the fact that there's a sort of equivalence between precomputing position analysis and doing no runtime analysis vs knowing nothing and doing everything at runtime. It is a general property of a lot of algorithms that you can precompute various amounts of computation in order to reduce runtime complexity. It's also the difference betwee…

isn't this very similar or a case of trading space for time or vice versa (e.g in algorithm analysis)

There are many duality theories in mathematics where both of these perspectives are valid. Each instance is "Duh! What's going on here is just..." and the pragmatic move nimbly through each instance without concern. For others, the potential theory IS the object of interest. Is this apparent pattern a deep principle or just a mirage? When something is actually going on, one learns powerful new techniques by recognizing a precise pattern.

I've stumbled onto deeply disguised dualities in my career. (One could argue with a straight face there are only two, but this is not formalized.) It's more a psychological process than a technical one.

It's always possible to ignore that one is standing in a tree farm. Trees have such interesting bark.

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