Plan your Dota 2 pulls around the pity system
Loot systems with a pity mechanic guarantee a rare drop after enough opens, which changes how you should budget your pulls. This calculator combines the base drop rate with a hard-pity guarantee so you can see your true odds for the next batch of opens and know exactly when the item becomes certain.
How it works
Each open is a trial at the base rate p, until you reach the hard-pity threshold H, where the drop becomes guaranteed. Given your current pity count c, the chance of getting the rare within the next N opens is:
P(at least once) = 1 - PRODUCT over slots (1 - q_slot)For each future open, its absolute pity slot is c + i. If that slot is at or past H, its chance q is 1 (guaranteed); otherwise it is the base rate p. The pulls remaining until the guarantee is simply H − c, and the expected number of opens to get the item is the smaller of 1 / p and that remaining count.
Example and tips
With a 2% base rate, a hard pity of 50, and a current pity count of 10, you are guaranteed the rare within 40 more opens. Across just the next 10 opens your at-least-once chance is about 18%, because each open is still only 2% — the guarantee only kicks in near the threshold. If you are close to hard pity, it is often worth pushing through to the guaranteed slot rather than stopping early. Always re-enter your real pity count, since it resets to zero the moment the rare drops.