Pity & Contract rates
Official pity numbers straight from the in-game contract rules.
The short answer
There are 2 character contract types: Chance — if you haven't pulled a 5★ in 79 draws, the 80th is guaranteed, but the featured character only wins 50% of the time; and Targeted — a longer pity (110 draws), but the guaranteed 5★ IS the featured character, with no 50/50. Weapon contracts pity at 70. Every type guarantees a 4★ or higher every 10 draws. Pity does not carry between contract types.
Contract Planner
5★ Shoki Ikenami
Example featured 5★ — tap for build
pulls since your last 5★ (0–79)
150 = 1 pull
if on, your next 5★ is guaranteed to be the featured one
Pulls to guaranteed 5★—
Pulls you can afford—
Worst case for featured—
Jewels still needed—
How this was calculated
Official numbers (v4.4)
5★ hard pity: 80
4★ guarantee: 10
Featured rate: 50/50
300 draws = choose a 5★ (first time)
Source: the official in-game contract rules text (v4.4 game data). Note: unlike some gacha games, pity status does not transfer between different contracts of the same ticket type.