there are two things we haven't considered so far. turn 1 minisquare bonuses on the outside faces (i estimate a 15% chance that player 1 will have at least 1 minisquare, without adding in the difficult-to-value extra chances caused by interlinking from adjacent points) and the number of non-neutral points (56 isn't a good number for 2-player games because player 1 can reduce player 2's initial deployment by taking only 1 point from him - 18 less 1 is 17, meaning a deployment of 5 troops compared with player 1's 6).
one solution is to start neutral a pair of white non-edge points on each face in a systematic manner. an example, using the A1w-D4z axis of rotational symmetry, is A3x, A2y, B1y, C1x, C2w, B3w and diametrically-opposing points. if we do this, then there are 14 initial points per player in 2-player and 11 in 4-player.
an alternative is to have 1 white non-edge point on each face allocated to one of 2 sets of start positions. an example, again using the A1w-D4z axis of symmetry, is A3x, B1y, C2w with their diametrically-opposing points for set 1 and A2y, C1x, B3x with their antipodes for set 2. if we do that, then player 1 starts with 20 initial points in 2-player and 14 in 4-player. games with 3 or more players are not affected by the start positions.
ian.
