Ultimately after several attempts at trying to like chess, I find its determinism bit boring. Games with random elements have gameplay elements like evaluation of risk and rewards, so I gravitated towards them(like Scrabble).
Tactics still dominate, but strategy leads to tactics.
You're often left making decisions on the basis of, well, maybe if I do this I'll be able to poke my rook through later, but maybe they'll win counterattacking the file I'm leaving.
The order of the back-rank pieces is randomized (but identical for both players).
You also might want to give "Liar's Dice" a look - some of the variants are similarly great for bigger groups, and still rely heavily on strategy.