  We introduce a generalization of "Solo Chess", a single-player variant of the
game that can be played on chess.com. The standard version of the game is
played on a regular 8 x 8 chessboard by a single player, with only white
pieces, using the following rules: every move must capture a piece, no piece
may capture more than 2 times, and if there is a King on the board, it must be
the final piece. The goal is to clear the board, i.e, make a sequence of
captures after which only one piece is left.
  We generalize this game to unbounded boards with $n$ pieces, each of which
have a given number of captures that they are permitted to make. We show that
Generalized Solo Chess is NP-complete, even when it is played by only rooks
that have at most two captures remaining. It also turns out to be NP-complete
even when every piece is a queen with exactly two captures remaining in the
initial configuration. In contrast, we show that solvable instances of
Generalized Solo Chess can be completely characterized when the game is: a)
played by rooks on a one-dimensional board, and b) played by pawns with two
captures left on a 2D board.
  Inspired by Generalized Solo Chess, we also introduce the Graph Capture Game,
which involves clearing a graph of tokens via captures along edges. This game
subsumes Generalized Solo Chess played by knights. We show that the Graph
Capture Game is NP-complete for undirected graphs and DAGs.
