Dominion is a strategy game. It's at its best when there are lots of interesting decisions to make before (engine? money? or alt VP?) and during play (do I need to alter/switch strategies in response to my opponents' choices?).
I don't like playing random kingdoms (on Iso or IRL) where there is effectively no interesting strategic decision to be made, and the outcome is effectively determined entirely by shuffle luck. Honestly, randomly choosing Kingdoms usually leads to strategically uninteresting Kingdoms too often, for my taste. The speed at which some people expect the game to go on Iso (or how fast the animations should go on Goko) is one indicator of how often this happens.
But, we don't have to choose Kingdoms completely randomly! I like using old tournament decks and saving Kingdoms which were randomly drawn but turn out to be interesting and then switching them up a little another time. But, there is no arguing with the speed and efficiency of setting up a random Kingdom.
I would like a better way of quickly choosing interesting Kingdoms. I think the most promising way of doing this is a stratified random choice.
Here's the question for you: How would you choose strata to trade off the following two Kingdom-choosing criteria?:
1) maximize the chance of a strategically interesting Kingdom (e.g. multiple paths to Victory, non-obvious strategic synergy among cards, or interesting choices during play)
2) Play is varied Kingdom to Kingdom. (In other words, avoid the feeling that each Kingdom drawn from the strata "play the same" even if there are many choices to be made in the Kingdom itself.)
(Strata do not have to be mutually exclusive, here, but that would be benefit because it would be easier to divide the randomizers up into piles.)
For instance:
A) 2 Villages, 2 drawers, 1 trasher, 1 plus buy, 1 each of $2, $3, $4, and $5 cards.
or maybe:
B) 1 alt Victory, 1 alt Treasure, 1 plus buy, 1 $5 card, 6 random.