In the German chess problem magazine feenschach, Heft 214 Band XXIV, July-August 2015 pp 178-180, I pose & solve the following puzzle: "Consider the 25 chess positions deriving from the 25 sequences of moves of the following form: 1. e4 e5 2. L~ L~. Show that at most six of these are wins for Black."
This is solved with a simple strategy-stealing argument, but I don't think this fragile approach can be generalized to the Holy Grail of showing that chess is not a win for Black. The population of 5x5 (or more generally nxn) positions examined here is kind of a best case, where there is maximal stealing possible. If one considers e.g. the population of 400 positions after Black's first move, then then we can show that at most 304/400 can be wins for Black. This is a much higher proportion, and shows the limitations of the approach.
27/12/2015: After the closing of this question for not being mathematical, I added the following to emphasize that it can very well be interpreted mathematically.
Thanks very much, Mr Calvert, for your support. I was a bit bemused that the question was suddenly closed for not being mathematical immediately after I posted an entirely mathematical response. The underlying article has simple lemmas and everything :-) The question of whether chess is a win for Black may be interpreted in terms of chess strategy, but my interest is only mathematical.
Claude Shannon wrote in his well-known 1950 paper (Philosophical Magazine, Ser.7, Vol. 41, No. 314 - March 1950. XXII. Programming a Computer for Playing Chess)
"It is interesting that a slight change in the rules of chess gives a game for which it is provable that White has at least a draw in the initial position. Suppose the rules the same as those of chess except that a player is not forced to move a piece at his turn to play, but may, if he chooses, 'pass'."
I was really looking for partial strategy-stealing solutions, in the spirit of Shannon, but in ordinary chess. So for White to lose a tempo takes at least two moves. Interestingly, parity concerns are particularly significant in the chess starting array.
In "More Games of No Chance" by MSRI Publications, Volume 42, 2002, Unsolved Problems in Combinatorial Games #29, p 465, Richard Guy also raised the question whether chess could be a Black win. However he misstated the result that I had emailed him, which has only now been published (feenschach, above).
As this discussion is closed, I'm happy to discuss this with anyone offline: there is an email contact given at the bottom of http://anselan.com/chess.html.