Just wanted to say, there are several solo abstract strategy games (or "logic puzzles" or whatever) that have the potential for unsolveable states. At the moment this is actually very appealing to me, and I think you should just embrace it. Some examples - Boxoff, Queen's Quadrille, Scorpion Solitaire. This can almost be a stand in for strategic depth, as opposed to like sudoku, which may be extremely difficult compared to some games, but will never approach chess, because there is a skill ceiling and a findable solution every time.