Coupon Collector Calculator

Specify the drop rate of a coupon (decimal or fraction, e.g. 0.1 or 1/15), the total number of distinct coupons (e.g. 24), and the number of rolls per loot drop (e.g. 1). For a guaranteed coupon every roll, set the drop rate to 1.

Drop rate Number of coupons Rolls per loot Calculate

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Explanation

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]:

\[ \mathbb{E}[Y_n] = \frac{r}{k}n \sum_{i=1}^{n} \frac{1}{i}. \]

Unequal probabilities

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.

Number of coupons:

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Calculate

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Explanation

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]:

\[ \mathbb{E}[Y_n] = \sum_i \frac{1}{p_i} - \sum_{i < j} \frac{1}{p_i + p_j} + \dots + (-1)^{n+1} \frac{1}{p_1 + \dots + p_n}. \]