...there is something at work in chess that is not just about calculation.
I have trouble believing that you honestly believe this.
Surely our ability to build complete five, six and now seven peice tablebases is compelling evidence to the contrary.
Is there something fundamentally different between the game with seven peices verus with eight that makes luck a factor in the latter and not the former? Does this somehow mysteriously change when we acheive a complete eight peice tablebase? If not, at what point between nine and 32 does it change?
If there is no chance, probability, luck, then why do computers lose to each other? In tests, Houdini is supposed to be the best engine. But in a match, the score was 19-14 for Houdini over Rybka. We can't predict with 100% certainty the outcome of the next game.
Whether you describe that as luck or chance or probability, you are describing the same phenomenon. The best way to minimise such chance is to play a long match. But that doesn't eliminate the element of chance, it merely takes it into account.
Certainly not because of luck -- in fact, computers are the perfect illustration of this because of their entirely deterministic appropach to calculation in chess.
Like human play, it may not be exhaustive, and it may not be perfect, but when one computer gains and advantage over another it is definitely not because one was lucky and the other unlucky.
Computers don't make blunders in calculation, but their vision is also limited. Let's say that computer A has calculated a tactical line 20 ply deep and figured that the line wins a pawn. However, it also leads to an endgame that is drawn. This was not foreseen by either computer, it just happens to be a drawn endgame. In this sense, computer B was lucky.