It's problematic because roleplaying is itself a mental exercise and the mind of the character is intimately related to the mind of the player, whereas the body of the character is disconnected from the body of the player.
The player doesn't physically swing battleaxes or jump over chasms on behalf of the character, but he does make all the decisions for him. Regardless of any kind of randomizing, the character can only have a bright idea if the player does it for him. Imaginary mental activity by the character is different from imaginary physical activity.
We can all pretend to be dumber than we really are, just by thinking "what's really smart?" and no doing it. What none of us can do is to pretend to be smarter than we really are because we don't know how.
Physical activity can be reduced to numbers and probabilities. I can jump this far, sometimes, but not that far, ever. I can hit this hard but not that hard. Physics is quantitative. You can imitate it with rules and dice rolls.
Mental activity can't be reduced to numbers and probabilities. Maybe one day it will be, but so far psychology and neurophysiology haven't caught up with physics. You can't imitate it with rules and dice rolls. It's somehow more than that.
What makes the game fun, at least for me, is the "more than that" part.
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