Loot Drop Calculator (With Pity Timer)
This calculator compares loot drop odds with and without a pity timer (a guaranteed drop by a set attempt number), and shows the expected number of attempts to first drop in both cases. For the general probability math this is built on, see the probability calculator; for design guidance on tuning the pity threshold, see the loot table design guide.
The Math Behind This
Without a pity timer, this uses the same "at least one success" formula as the probability calculator. With a pity timer, expected attempts to first drop is the sum of survival probabilities up to the pity threshold — a standard result for a geometric distribution capped at a fixed limit. This assumes independent, unchanging odds on every attempt below the pity threshold; if your game uses a dynamically increasing drop rate instead of a hard guarantee, the numbers here will be directionally useful but not exact.
FAQ: Loot Drop Calculator
What is a pity timer, exactly?
A pity timer is a hard guarantee that a rare drop happens by a certain attempt number, even if pure random rolls haven't produced it yet. It caps the worst-case bad luck a player can experience without changing the odds on any individual roll below that threshold.
Why does the pity timer lower the expected attempts to first drop?
Without a pity timer, a small percentage of players get extremely unlucky and take far more attempts than average, which pulls the mathematical average up. A pity timer caps that worst case, which pulls the average down even though most players were never going to hit the cap anyway.
Should I tell players the pity timer exists?
That's a design and trust decision more than a math one — see the loot table design guide (linked below) for the tradeoffs. Mathematically, this calculator works the same either way.
Does this model duplicate protection too?
No — this models the odds of getting the item at all, not what happens on a repeat drop. Duplicate protection (converting repeat drops into partial progress toward something else) is a separate design lever covered in the loot table design checklist.