There are three possible outcomes of a game of chess: white wins, black wins, or the players draw.
Typically, we consider a win better than a draw, so when we say "white can force a draw" from a given position, usually we mean "white can force a draw or better (a win)". For the purposes of this question, consider the three possible results of a game as entirely separate possibilities. For example, in this question, a position is given where
- white cannot force a win nor a draw (remember, exactly a draw),
- black cannot force a win, nor a draw, nor a loss, but
- white can force a loss.
(This is interesting because "neither player can force a win nor [exactly] a draw".) Is something more extreme possible? Is there a position where
- white cannot force a win, nor a draw, nor a loss, and
- black cannot force a win, nor a draw, nor a loss?
For example, this would mean that if white attempts to force a white loss, then they cannot because black can force that either white wins or the players draw (but without actually being able to choose which).