Holy crap - seriously?
The thing is - it's SO incredibly easy to play Starcraft 2 lazily. Which is why most people don't improve. But if you force yourself to improve, maybe there's a mechanism? I actually posted such a thread here: http://www.quora.com/In-Starcraft-2-how-do-you-deal-with-game-theoretic-anticipation-chains-the-enemy-anticipating-that-you-anticipate-that-the-enemy-anticipate-that-you-might-do-X
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Here was my original question: In Starcraft 2, how do you deal with game-theoretic anticipation chains? (the enemy anticipating that you anticipate that the enemy anticipate that you might do X)
In other words, the gun and bridge problem illustrated at http://plato.stanford.edu/entries/game-theory/
It's an interesting problem (especially in repeated games, where you're playing against the same player). In repeated games, you ALWAYS have to ask "well, he used hydras last time - so is he going to use a different unit combo to be more unpredictable? or is he going to anticipate that I'll anticipate that, and use hydras again?"
But also in 1v1s where the enemy might not engage in anticipation chains. But there's a chance that he might be totally naive, but also a chance that he might be trying to trick you.
By anticipation chain, I mean this. You spy on the enemy's base, and you see certain units/structures. Except - that the units/structures are decoys designed to trick you into believing that he's producing Y, even when he's producing X.
So if you see structures for Y/small armies of Y, he might be producing Y (he could not be trying to play such mental games, or he might anticipate that you think that he's trying to trick you. Or he goes to even higher orders of thinking [although I don't think that's likely]). But he might be producing X too (he could play that mental game either to the 1st order or the 3rd order [or higher, but that's unlikely])
But it also illustrates within-game behavior too. If he suddenly wiped out a bunch of your units with Z - (he might anticipate that you might produce counters for Z). Or he might not. Or he might anticipate that you might anticipate the above parenthesized statement. The loop goes forever.
This sort of problem does have a game-theoretic solution, but statistically speaking, the game-theoretic solution isn't necessarily going to work because not all agents are rational.
Anyways, I'm sure this doesn't arise often in random 1v1s. But maybe it might arise in SC2 games between people in, say, MIT or Stanford?
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There was some paper on it some time ago, but it's gone now (http://expertvoices.nsdl.org/cornell-info204/2010/10/04/game-theory-in-starcraft-strategies/)
From all the SC2 games I've played and watched, there is very little anticipation and prepared counter. In other words, yes, your opponent might think you'll do X, but there is a small chance they'll actually prepare to counter X. (Unless it's something really really basic, like seeing a fast rash from your opponent and reacting by building more defenses.) Most of the time you can reliably predict that your opponents will do what they've always done.
I've run across a couple of questions about the value of dual n-back, and this is the best place I know of to find people who've worked with it.
If you've tried it, has it noticeably improved your working memory? Was it enough to be worth the time?