All modern implementations of Tetris implement a "7 bag" random generation system; whereby the game puts all 7 possible pieces into a bag, draws them in a random order until the bag is empty, then repeats. This guarantees that you'll see all pieces at least once before you'll see one duplicate (at the edges between the bags, ~14% chance per bag to get a duplicate). In that sense, the idea that all Tetris games must eventually end due to the "all possible sequences exist in an infinitely long random string of sequences" law doesn't actually apply, because Tetris is not truly random.
This does not apply to the original Tetris game on NES, which does use true-random.
This does not apply to the original Tetris game on NES, which does use true-random.