It has been proven that the game of Tetris is unwinnable. This at least is true in the mathematically pure, infinite memory version of the game. The theorem states and proves that if you get enough s and z pieces in a row, it will force the player to lose, and if the game is played for a long enough time, then the law of big numbers states that such a sequence will eventually arrive. The number of s and z piece where this is guaranteed is at most 150, i.e. if you get 150 s or z shapes in a row, loss is guaranteed. The odd of that happening are one of those universe shattering numbers that's bigger than all the hydrogen atoms in the universe times billion trillions or whatever, so don't expect that happening anytime soon.
On the other hand it seems that the NES version got beaten in 2023!
I decided to try this out myself by writing my own Tetris game. This also served as a good project to teach myself the SDL graphics library. The result is a pretty basic Tetris clone with decent graphics and snappy gameplay since the SDL library is pretty low-level and light on resources. I also programmed in a way to get only alternating s and z pieces to see how long I could last. Unfortunately I forgot to put that in the version I uploaded to Sourceforge, and that functionality never got exposed in the game itself, i.e. it has to be changed programmatically. If I find the time I might change that. The source is available here: https://sourceforge.net/projects/tedris/. Or you could click any of the pictures on the screen.