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(2 edits)

I believe the best possible score is 60 but it's a 1/4 to get it instead of 54 even if you wait the eons to get perfect RNG to put the stations down on, since you need the planet that comes in to move one of the scores from 54 to 60. Conveniently, if you achieve this, all of your scores will be exactly 60 ^^


Let us characterize the score for each color as the sum of the scores obtained on planets of that color.  There are 18 planets, 5 of which will be bordered by 16 stations, 5 by 14, 7 by 12, and 1, the top central planet on which we can have no stations, by 6.

The formula 16A_n+14B_n+12C_n+6D_n gives us the score for the nth color, where A_n,B_n,etc correspond to the number of planets with the appropriate number of stations (16 for A, 14 for B, etc) in that color.

Fiddling with a matrix of the relevant equations, we can arrive at:

2 Class-A and 2 Class-B planets for two colors,
1 Class-A and 1 Class-B and 2 Class-C and the 1 Class-D for one color
5 Class-C for the final color

or an equivalent configuration with each color scoring 60.  In order for any color to score higher, points would have to be removed from one of the other colors, meaning that the score of the lowest scoring color can't be above 60, so 60 is the maximum high score.  However, it requires the planets to be in only a handful of possible positions out of ~69 billion (4^18). Good luck if you decide to go for it, I haven't calculated the actual exact odds yet but I bet the expected number of turns required to achieve it is very high.