The minmax algorithm is a popular strategy used to design chess engines. Usually, since the state-space of chess is huge, we choose a fixed depth and evaluate the game tree down to that level, and pick the best sequence of moves so far.
Let's suppose we remove this limit, and we search for the whole tree. Would this techinque always win? If the answer is no, would it ever lose? (so, would it only win+draw, or also lose?)
A good answer would include theoretical underpinnings of why or why not this would work, both from the game-theoretic aspects of chess and from the proprieties of the minmax algorithm.