I think there is a draw back to the hyper-analytical approach so many people have:
It saps the enjoyment,
replaces their super-fast subconscious mind with their super-slow conscious mind and
sets them up for being on tilt:
"I'm playing the hands 'right' but losing. That should not be! How dare they beat when I'm playing better than them? I'll show them!"
Such a common complaint and such a shame to have that attitude because it produces so many sore losers.
I'd back a player having fun and playing the way he/she likes over someone following a legalistic strategy any day (experience and intelligence being equal: e.g. noob vs noob, pro vs pro).
They're less predictable and far harder to tilt.
Any reasonably intelligent person has a strong sub-conscious calculator that is superb at learning from experience and applying those lessons without any input from our conscious minds. (Just watch a skilled musician: They are not 'thinking' about what key to press/string to strike. Their trained subconscious mind is doing it all.)
An experienced player shouldn't really need to go through lots of probability calculations in his head. His sub-conscious will do them automatically and a thousand times faster.
It's like Luke putting aside the targetting computer. Psychologically, it's a much stronger position to be in.
Similarly for ego's (a player's belief that they are 'better' than their opponents): they have the same effect; put them at a psychological disadvantage.
These things are true in all aspects of life and no less so in poker.
Other people's thoughts on this would be interesting to me