Spherical Chess 324

Capture your opponent's last queen to win. 4 variants (4 2-D perspectives of a spherical, 3-D game): white whole | black quartered (shown below) black whole | white quartered white halved N & S | black halved E & W black halved N & S | white halved E & W A draw is impossible. Each player begins the game with 8 queens. Once the last queen of either player has been captured, the game will end immediately. The pendulum-move rule applies which dictates double-moves alternating between the two players throughout the game except for the very first move which is only a single-move by white. All available 4-, 5-, 6-, 7- directional moving pieces can be half-promoted into pieces with 1 additional direction of movement at the cost of 3 moves. All available 4- & 6- directional moving pieces can be single-promoted into pieces with 2 additional directions of movement at the cost of 4 moves. All rooks (4-directional moving pieces) can be double-promoted into queens with 4 additional directions of movement at the cost of 6 moves. All pieces capable of movement can capture by replacement any enemy or neutral pieces. Portals connect opposite edges along all 8 geometrically-contiguous directions of linear movement possible within the square-spaced, flat 2-D gameboard. Consequently, 8 directions of movement are available from every square-space within the flat 2-D gameboard. Essentially, this is a spherical surface, 3-D chess variant that can be represented accurately and played well using as few or as many of the 4 available, congruent opening setups as desirable within the flat 2-D gameboard due to its exclusive usage of 2-D pieces. This means that an entire game played via any 1 given opening setup can be completed transposed, move-by-move, into entire games played via all of the other congruent opening setups. Notably, the naive appearance of geometrical asymmetry in 2-D between the two armies with any given opening setup is totally illusionary. When the fact that the 2-D gameboard has no real edges in any way (i.e., continuous space), despite its flat 2-D representation to the contrary, is taken into account, the positions and available moves for all of the 2-D pieces of the white army, relative to everything (friendly pieces, neutral pieces, enemy pieces and empty spaces), are mirror-image symmetrical to those of the black army. In reality, a 4-fold, perfect, holistic 3-D geometrical symmetry applicable to the surface of a sphere exists for this game despite the limitations due to its flat 2-D representations. This is the disadvantage to using flat 2-D representations of a spherical-surface, 3-D chess variant. The 2 most symmetrical, representative, opening setups (white whole - black quartered & black whole - white quartered) out of 4 available maintain perfect quadrilateral symmetry in 2-D by north-south, east-west, northwest-southeast and northeast-southwest axes. The playing surface consisting of a finite, 2-D plane with a square-spaced, flat 2-D gameboard of 20 x 20 spaces (400 spaces total) and a square shape overall (apparently) is perfectly mapped onto the surface of a finite 3-D sphere. [Note: The true shape overall of the square-spaced, flat 2-D gameboard is actually circular. This is not obvious. Instead, it appears to be square due to the commonplace elongation of the diagonal dimension and/or shortening of the orthogonal dimension which is the universal convention for representing them. This implicates why a perfect mapping onto the surface of a 3-D sphere, from a circle rather than a square, is ideally suitable and achievable.] Fortunately, the players are not required to deal with any complex, confusing 3-D curvature characteristic to a spherical playing surface. This is the advantage to using flat 2-D representations of a spherical-surface, 3-D chess variant.