Therefore, under the normal play convention, the first player automatically loses, and it is a second-player win.
[1] Simple examples of zero games include Nim with no piles[2] or a Hackenbush diagram with nothing drawn on it.
[3] The Sprague–Grundy theorem applies to impartial games (in which each move may be played by either player) and asserts that every such game has an equivalent Sprague–Grundy value, a "nimber", which indicates the number of pieces in an equivalent position in the game of nim.
[5] For example, normal Nim with two identical piles (of any size) is not the zero game, but has value 0, since it is a second-player winning situation whatever the first player plays.
It is not a fuzzy game because first player has no winning option.