I disagree with the overall thesis here-- that somehow abstracting away all the randomness of minesweeper makes it less "mechanical." Oftentimes, 1 square's outcome is less likely or even much less likely then another. Even better, sometimes 2 outcomes will be equally plausible, but 1 of them might be expected to reveal more information or to reduce entropy more. After playing enough, most plays become ingrained in you and mechanical-- the problem solving element comes in comparing probabilities.
A small comment for clarification; my remark about making the game less mechanical is for the part of the game that automates the simple, purely deterministic, constaints. So there are two things: Automation of simple deterministic things, that makes the game less mechanical, plus "Request help" that makes the game less random. The two are separate.
I don't think this speaks to your central point, however :)
Oh, completely forgot about that part. When you have to guess, and both choices would be equally bad when guessing wrong, focus on which would bring the bigger benefit when guessing right. It almost has a "motivational poster deep wisdom" quality, heh.
