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Verification of Gacha Drop Rates (for consecutive gacha draws)

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In mobile games, when a certain item appears multiple times after spinning a consecutive gacha several times, this method simply verifies the drop rate of that item when it is a guaranteed prize.
The results are displayed for two types of consecutive gacha.
This calculation applies when the drop rate during normal play (when the item is not a guaranteed prize) is known in advance.

[Independent Guaranteed]: A consecutive gacha featuring regular slots and one independent guaranteed slot. The guaranteed slot has a different drop rate than the regular slots and only yields specific items. The drop rate for the guaranteed slot remains constant, regardless of the results from the regular slots.
[Dependent Guaranteed]: A gacha with a guaranteed drop where a certain number of slots are theoretically allocated for consecutive draws, and the drop rate for the remaining slot changes based on the results of the first (number of consecutive draws - 1) slots.When a guaranteed slot is actually displayed, it is for presentation purposes only. For example, suppose there is a 10-pull gacha that guarantees an SS-rarity item. If no SS-rarity item appears in the first 9 theoretical slots, an SS-rarity item is guaranteed to appear in the remaining theoretical slot; however, if one does appear, the drop rate for that remaining theoretical slot is the same as usual.When a “guaranteed slot” is actually displayed, one of the SS-rarity items that appeared in the 10 calculated slots will be shown in the actual guaranteed slot.
Number of consecutive gacha spins: n
Times
Number of times the verification item appeared: k
Times
Number of consecutive times L
Consecutive
Normal emission rate of verification items p
%
Normal drop rate for confirmed items p_R
%Use only for 【Dependent Determination】
[Confirmed as Independent] %
[Subordinate Determination] %

Since this is simply a direct solution to the equation “Expected number of appearances in a consecutive gacha = Actual number of appearances,” the resulting drop rates may be less than 0% or exceed 100%.

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