When will quantity turn into quality?

Final position of the one and only Botvinnik – Fischer game (1962). Click on the image to enlarge.

Analyzed the position with the 64 bit Rybka 3, and even after the depth of 39 moves it still can’t see that this is a draw. I wonder how many moves would reveal this draw for a chess program. It is really hard to estimate. The program tries every variation without repeating a position 3 times – because that means draw by the laws – and without any exchange, because that would also lead to draw in this situation, if white keeps his pieces on the proper squares.

But black’s pieces are also immobile: the rook can leave the 3rd row in some cases only, e.g. when it gives a check to the white king, but has to return immediately after that. Also the black king can’t move too far from the f6 pawn, because it would move to f7 followed by a Ra7.

Even an endgame tablebase would not help, because we can’t have an exchange, and there is no tablebase for 7 pieces. The computational time doubles after every step, and the 50th move is so far away.