[madnak]

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But this isn't the question... The question is a simple 50/50 proposition: Does it MATTER whether or not you switch? The answer is undoubtedly, yes. And you have just admitted that illogical thought will almost always produce the incorrect answer of, "No. It doesn't matter". So clearly, one has a better chance through flipping a coin to arrive at the correct answer of "yes, it matters", than using illogical thought.

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Sure, people will typically arrive at the wrong answer here, but it's not because they're illogical. It's because one illogical reasoning process has more psychological appeal than the others. But you can easily use illogical reasoning to reach the incorrect conclusion on this question, too. "It matters because if you picked the right door you shouldn't switch."

The level of apparent absurdity increases as the question gets more abstract - that's because while all illogical processes are absurd, some concrete approaches "seem" to make sense. In reality, "it's going to come up black because I'm due" makes no more sense than "it's going to come up red because horseshoes are shaped like horse hooves." Remember, we're considering things logically - not psychologically.

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Clearly, if you don't think logically (or if your opponent thinks more logically than you do), you are better off not thinking at all and resorting to game theory. Otherwise, illogical thinking when it comes to guessing your opponent's hand, assures you'll have the worst of it. Certainly, you'll be worse off than if you used game theory.

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When playing a game against someone who plays better than you, particularly in a game where psychology is relevant, it is more likely that your opponent will exploit your mistakes than it is you will exploit your opponent's mistakes. Therefore, cleaving to the game-theoretical approach is better than attempting gambles to take advantage of your opponent. Every time you deviate from game theory, you make a game-theoretical mistake that your opponent can exploit. So if you know the GT approach, then you should apply it against good opponents. Against poor opponents, you can extract extra value by making plays that are not GT-correct, but that are more profitable against irrational behavior on the part of your opponent. Basically the idea is that you don't want to walk into a trap - you want to be the one setting traps.

This has little bearing on considerations of boolean logical propositions.