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There have been programs that attempted to work out every possible move and counter-move to the end of the game...

Not that I know of - the number of possible configurations of a chessboard is something like 10¹²⁰, which is far more than can be managed in the available space or time, so the program has to prune the search tree somehow - that's where the "rules of thumb" come in. "Deep Blue", for reference, was capable of evaluating about 200,000,000 positions per second - do the math, and you'll see that the total search space is waaaayyyy out of reach. In such a case, the real trick is in the search algorithm - how "clever" the computer is about finding the best possible moves in a limited time and with limited resources, since it can't examine them all.

If, on the other hand, you want serious complexity, the number of possible moves in Go is said to be 10⁷⁵⁰, which is part of the reason that Go-playing computers, by and large, suck compared to humans - in such a game, the human facility for pattern-matching just blows the brute force of the computer right out of the game.

True. I believe Deep Thought could see upwards of seven moves ahead, not counting rules-of-thumb. Depending on the state of the game, this could count as seeing to the end. Particularly if you play by the unwritten human rules, where loss of a major piece or loss of position can lead to resignation.

I would argue that humans have a lot of hardwired rules-of-thumb. These account of optical illusions and other perceptual tricks, as well as our propensity to make decisions based on perceptual probabilities rather than mathematically sound probabilities. This list could go on and on.