Use the formula only under these assumptions
Each opening must be independent and use the same success probability. 'Success' must mean the exact outcome you're counting. A tier-hit probability can't be substituted for one particular card's probability.
The chance of missing every opening is (1 − p)^n. Subtract it from one to get the chance of at least one hit. A changing, finite or weighted pool may require a different model.
A hypothetical 1% chase chance
At a constant 1% independent chance, 10 openings give about 9.6% chance of at least one hit; 50 openings give about 39.5% chance of at least one hit; 100 openings give about 63.4% chance of at least one hit. These are mathematical examples, not any platform's advertised odds.
After 100 independent openings there is still about a 36.6% chance of no hit. 'One in 100' describes the probability on each opening; it doesn't promise one success in every batch of 100.
Your next opening isn't due
After any number of misses, the next opening in this unchanged independent example remains a 1% chance. The cumulative chance grows when you count more attempts, but the cost grows too.
If packs cost a hypothetical $25, 100 attempts cost $2,500 before any proceeds from unwanted pulls. A higher cumulative chance isn't a recommendation to buy that many packs.
Keep probability separate from expected value
EV includes every outcome's estimated value and probability. The probability of one chase answers only whether that chase appears. A low chase chance can coexist with different floors, medians and mean returns.
Use the full disclosed distribution for value calculations, and use a fixed entertainment limit for spending. No fixed number of attempts guarantees recovery or a result close to EV.