No black box
Every class has a single-spin chance shown right in the game's spin screen. The chance of hitting your target at least once in N spins is 1 - (1-p)^N, and the table flips that formula around to find the spins each confidence level needs. Gems are spins × 40.
No pity system is visible in the current build, so the calculator assumes every roll is independent. That's an assumption, not a fact about hidden game code — if the game ever adds a pity meter, we'll rebuild the math.