The geometries have aligned and the new world is upon us, so henceforth the primordial generation shall roll hither…
(A HexaCube Game Mechanic)
Move 1 = 14.29% (1 square = 11.67%, 1 hex = 2.5%)
Move 2 = 14.29% (1 square = 11.67%, 1 hex = 2.5%)
Move 3 = 14.29% (1 square = 11.67%, 1 hex = 2.5%)
Blank = 14.29% (6 hexes = 14.29%)
Action x 1 = 14.29% (1 square = 11.67%, 1 hex = 2.5%)
Action x 2 = 14.29% (1 square = 11.67%, 1 hex = 2.5%)
Action x 3 = 14.29% (1 square = 11.67%, 1 hex = 2.5%)
Resource = 30.0% (any hex)
Income = 70.0% (any square)
(The above is a renumbered HexaCube d7.)
This is a mechanic is for a hypothetical hand building, race themed, board game. For some reason I am picturing a desert planet. In the game, Moves and Actions are equally good. Resources are highly valued in this game, much more than Income.
In addition to having 7 equal outcomes, this game die essentially makes 2 rolls at once. One is rolling among the 7 equal outcomes. The other is the square/hex roll, which determnes whether you get Income or Resources. For 6 of the outcomes, there is a 70/30 split on whether you get Income or Resources. The remaining outcome does not give you Moves or Actions, but always compensates you with a valuable Resource.
There is a lot of novelty here. You could approximate this system with two dedicated, less accurate dice, but the best solution is uniquely HexaCube.