New answers tagged expansions
You could just not use all of the expansions at once. Instead, pick one or two expansions, maybe at random, every game. Now there is variability, and each game will be different, but you don't have a ton of extra tiles and rules in play in any given game. This is how collectible card games like Magic the Gathering, or deck building games like Dominion, ...
Another method we used in our games, which also cuts down on randomness is to give each player a "hand of tiles" — three was the optimal number for us — from which they can use one each time. Theoretically, that's increasing the number of options for play, but it actually tends to focus people one one "good" move which they pick before their turn.
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