People who have mastered a skill to the point of unconscious action rarely have the self-awareness to teach you how it works. For instance, to get a good idea of how human masters think about chess, it's too late to ask someone who's already very good. You need to take someone who is an amateur, or merely average, and observe them learning how to play at a much higher level. Then you will get some insight into their thought processes as they progress from average play to exceptional play. Learn how humans build mental models of a chess board and you might be able to build a chess program that doesn't require the analysis of millions of positions to play against a human.
Mokalus of Borg
PS - Chess programs are actually still improving, efficiency-wise.
PPS - Whether they are providing any psychological insight remains to be seen.