As someone who often prints boardgames, this strikes me as a game that would be very easy to build a physical version of, just printing some tiles with random distributions printed on, and finding some tokens and a die to use. It would make a compact travel game. I do not think there would have to be a huge number of tiles. A few more than nine ought to be enough?
you would need different dice for each distribution but you could use a normal d20 and a lookup table for less needed equipment.. I think it could work!
I'm saying if you wanted to mimic the happy/meh/sad faces on the die in this game you would need multiple dice. But since all of the percentages are in 5% increments yes a D20 is all you would need. I suggest a lookup table for the players who are uncomfortable or uninterested in doing the percentage division in their head, and the sum of the two lower partitions. But you've got me thinking you could probably also have a run of custom-labeled D20s with increments of 5 instead of 1 to eliminate the LUT.