There are lots of fun ways to smooth out short-term variation in game randomness. This article shows a few used by various Tetris games, with one of them being your deck-of-cards approach: https://simon.lc/the-history-of-tetris-randomizers
One of my favourite techniques not listed there is weighting the probabilities by distance, so individual outcomes get more likely the longer you've not seen them (making the gamblers' fallacy real, I guess).
One of my favourite techniques not listed there is weighting the probabilities by distance, so individual outcomes get more likely the longer you've not seen them (making the gamblers' fallacy real, I guess).