I used to think it might be possible to come up with some kind of general algorithm for playing Tet4 indefinitely, but I now suspect that no matter how tall the pit is and how many pieces you can look ahead, there are always sequences of pieces that will guarantee a loss - in particular, I don't think there is any way to place the sequence SSZ without adding a row every 6 pieces. This means that ultimately, Tet4 is a game of luck. However, most sequences that occur in practice do seem to be solvable - many years ago I wrote a program to play Tet4 automatically, and it seems to be able to play indefinitely. So in practice speed and accuracy are more important than luck for winning the game.
Side note: On the most recent occasion that I tried to figure this out, I attempted to resurrect my old Tet4-auto-player program (not trivial, since it's a graphical DOS program and hence doesn't work on Vista) and modify it to see if it could solve the SSZ repeated sequence. Once I'd got it running, I was amused to see that it was already set up to solve the SSZ repeated sequence - I'd done the exact same thing before and forgotten all about it!
Talking of Tet4, it's had a couple of updates since I last mentioned it here. The original version has had a bug fix so that playback of games in which the curtain reaches the bottom works properly. Also, a second version has been added, which is exactly the same but with no undo (and which is therefore less forgiving). This may be one of very few occasions on which the second version of a piece of software is identical to the first version apart from the removal of a significant feature.
When I first wrote the Javascript version of Tet4, I took the opportunity to change the keys from the DOS version a bit, to make them more logical and faster (so that if there were 5 or fewer possible positions for a piece, either hand could be used, for example). This meant that I kept making mistakes because (although I hadn't played Tet4 for years) my muscle memory was still trained with the old keys. Hence I added the undo feature. But in making the game more forgiving, I changed its nature significantly.
There's two ways I could have added undo to Tet4. One way is to undo the random number generator one step when undoing. The other is not to. Undoing the random number generator essentially gives you unlimited lookahead capability. To look ahead n pieces, drop those n pieces (anywhere) and then undo n times. I didn't want to grant that power, so I wrote it in such a way that dropping n pieces and undoing them changes the random number generator state. However, this gives an even stronger ability - now you can essentially choose which piece comes next by dropping and undoing until you get the piece you want. I think this makes the game too easy (at least until it gets really fast), hence the new version.