Among first-class masters the capture of the adverse king is the ultimate but not the first object of the game and by best play on both sides a draw ought to be the legitimate result. – W. Steinitz, The Modern Chess Instructor
Thus did Steinitz enunciate his principle theoretical intuition, one still unprovable even using the computer. Chess is intrinsically difficult, it requires search to all terminal positions to validate the utility of any single move.
Computational complexity theory tells you there is no clean answer for games like Chess, Checkers, and Go. If you believe in the perspective of complexity theory, it tells you that all you can do is sit there and do the bookkeeping and exhaust the exponential possibilities. – Erik Demaine, interview
What indeed are we doing between the moment we sit down at the chess board and the moment the game resolves itself to a calculable endgame? We are exercising what are sometimes called heuristic techniques which Wikipedia defines as “any approach to problem solving, learning, or discovery that employs a practical methodology not guaranteed to be optimal or perfect, but sufficient for the immediate goals.”
Various chess masters (notably Steinitz and Nimzovitch) have believed themselves to be enunciating fundamental scientific principles of the game, but most, if not all of their thought has been directed to expanding and refining our store of heuristics. Bronstein and most problemists delight in the irony of the positions which defy the approved heuristics.
This variation, given by Tchigorin, shows that masters of the last century were capable of accurately calculating deep combinations. – Imre König, Chess from Morphy to Botwinnik
Heuristics in chess are effectively prods to calculate certain variations, the concepts of the struggle for the center, the advantage of two bishops, overprotection, pruning the search tree, but none answer the fundamental question, what’s my next move?
A teenaged expert recently expressed to me in a voice close to tears his frustration with opening study. “There are no openings,” I offered, “calculate from the first move.”