Pity timer
Also said as Pity system, Hard pity, Soft pity, Bad luck protection
A guarantee that after so many failed rolls, the next one pays out. It cuts off the worst luck anyone can have, without changing the rate for everyone else very much.
At a 1% drop rate, some players will go hundreds of rolls with nothing, and they are the ones who quit or write the angry post. A pity timer sets a worst case you can state in public, and it matters more when real money is involved.
Say it
“Legendary drop stays at 1%, but add a pity timer: guaranteed by roll 150. Show the counter, because being able to see it is half of why it works.”
Where you’ve seen it
Genshin Impact lists a 0.6% base rate for a 5-star character and guarantees one by the 90th wish. Counting the guarantee, it states an overall rate of 1.6%.
Not to be confused with pseudo-random distribution
PRD nudges the odds up a little after every miss. A pity timer usually leaves the odds alone and then steps in once, at a fixed count. Some games use both.