I really depends on the difficulty of answering correctly to a calamity. The way I’d structure it would be to split up the game into rounds, with more calamities (and remedies) getting unlocked each round. Then maybe each round would be 8 total turns (maybe 5 successful turns). But that’s really only an out of the arse guess.
What matters more is the process. The way I’d actually would go about implementing it would be to set up the system for turns, then shove in the numbers (how many new calamities to add to each round, how many successful turns are needed, how many turns do you have before dying). Then I’d sit down and play the game, observe how the game feels (“this feels slow” “now there is an overwhelming amount of new stuff”) and tweak the numbers based on that.
When it comes to making the systems I usually spend more time programming than playing, but when I’ve made my systems I usually play the game more than I work in the engine. So I try the game, take two seconds to change a number, play the game again and so on.