"Drought" is a bit fuzzy (e.g., Should we use the properties of 7 Bag as an indicator and consider the minimum condition for an I-piece drought to be >12 pieces before seeing that piece dealt? Should we consider anything beyond the expected value of 1/7?), but "sequence" I think we can get a better handle on. The length of the game before reaching the more-or-less unsustainable Level 29 is 230~290 lines depending on starting level. At 2.5 pieces per line, that makes the bare minimum piece count 575~725. If we allow for some play into Level 29+, you could start seeing piece counts around 750~850, but we have not seen much more than that. "A sequence" long enough to constitute an entire game for a human at current standards of play is certainly less than 1000, so we can use that as a very generous upper-bound.