  We compare four different `game-spaces' in terms of their usefulness in
characterising multi-player tabletop games, with a particular interest in any
underlying change to a game's characteristics as the number of players changes.
In each case we take a 16-dimensional feature space, and reduce it to a
2-dimensional visualizable landscape.
  We find that a space obtained from optimization of parameters in Monte Carlo
Tree Search (MCTS) is the most directly interpretable to characterise our set
of games in terms of the relative importance of imperfect information,
adversarial opponents and reward sparsity. These results do not correlate with
a space defined using attributes of the game-tree.
  This dimensionality reduction does not show any general effect as the number
of players. We therefore consider the question using the original features to
classify the games into two sets; those for which the characteristics of the
game changes significantly as the number of players changes, and those for
which there is no such effect.
