Enter a drop rate (e.g. "0.1" or "1/15"), the number of coupons (e.g. "24"), and rolls per loot. If you get a coupon on every try, enter "1".
Given a drop rate \( \frac{1}{r} \), \( n \) coupons, and rolls per loot \(k\), the expected number of tries to collect all coupons is given by [1]:
\[ \mathbb{E}[Y_n] = \frac{r}{k}n \sum_{i=1}^{n} \frac{1}{i}. \]
For scenarios where each coupon does not have an equal chance of dropping, select the number of distinct coupons and input each coupon's probability. Ensure that all probabilities sum to 1.
When we have a more general non-uniform/categorical distribution for the coupons, the expected number of coupons for completing the collection is given by [2]:
\[ \mathbb{E}[Y_n] = \sum_i \frac{1}{p_i} - \sum_{i < j} \frac{1}{p_i + p_j} + \dots + (-1)^{n+1} \frac{1}{p_1 + \dots + p_n}. \]