Calculating the Expected Value of a Gacha (for Consecutive Gacha Runs)
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[No Guaranteed Drop]: A consecutive gacha with no guaranteed drops. All slots have the same drop rate.
[Independent Guaranteed Drop]: 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 slot where, based on a calculated number of consecutive slots, the drop rate for the remaining slot changes depending on the results of the first (consecutive count - 1) slots.When a guaranteed slot is actually displayed, it is purely for presentation purposes. 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.
Probability of Appearance: The probability that the desired item will appear at least once when a single consecutive gacha pull is made
Expected number of gacha pulls: The expected number of consecutive gacha pulls required before the desired item appears at least once
Expected amount spent: The expected amount spent on consecutive gacha pulls before the desired item appears at least once
Expected number of appearances: The expected number of times the desired item appears when performing one consecutive gacha pull
| Price per consecutive gacha pull | yen |
| Probability of occurrence | % % % |
| Expected Value of Gacha Attempts | Times Times Times |
| Expected Value of the Charge Amount | yen yen yen |
| Expected number of occurrences | Times Times Times |
*The expected number of consecutive gacha spins required for the desired item to appear at least once is denoted as E_gacha, [Type],
and the expected number of times the desired item appears per consecutive gacha spin is denoted as E_appearance, [Type].
*
When the normal drop rate of the desired item < the drop rate of the desired item when it is a guaranteed drop,
the following holds true for the probability of appearance and the expected number of appearances:
[No Guarantee] < [Dependent Guarantee] < [Independent Guarantee].
On the other hand, for the expected number of spins and the expected amount spent,
[No Guaranteed Drop] > [Dependent Guaranteed Drop] > [Independent Guaranteed Drop]
holds true.
Price of one consecutive gacha = Number of premium stones per consecutive gacha × Price per premium stone ÷ Number of premium stones purchased
and the expected number of times the desired item appears per consecutive gacha spin is denoted as E_appearance, [Type].
*
When the normal drop rate of the desired item < the drop rate of the desired item when it is a guaranteed drop,
the following holds true for the probability of appearance and the expected number of appearances:
[No Guarantee] < [Dependent Guarantee] < [Independent Guarantee].
On the other hand, for the expected number of spins and the expected amount spent,
[No Guaranteed Drop] > [Dependent Guaranteed Drop] > [Independent Guaranteed Drop]
holds true.
Price of one consecutive gacha = Number of premium stones per consecutive gacha × Price per premium stone ÷ Number of premium stones purchased
- Related links
Calculating Probability Distributions for Gacha (for General Gacha)- Calculating Probability Distributions for Gacha (for Box Gacha)
- Calculating Probability Distributions for Gacha (for Continuous Gacha)
- Calculating the Expected Value of a Gacha (for General Gachas)
- Calculating the Expected Value of Gacha (for Rerolling)
- Calculating the Expected Value of a Gacha (for Gachas with a Cap)
- Calculating the expected value of a gacha (for collection gachas with varying drop rates)
- Calculating the Expected Value of a Gacha (for Box Gachas)
- Verification of Gacha Drop Rates (for General Gacha)
- Verification of Gacha Drop Rates (for Consecutive Gacha Runs)
- Calculating the Number of Gacha Pulls (for General Gacha)
- Calculating the Number of Runs and Time Per Run in a Game
- Calculating Stamina in Games
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It displays the results for three different types of consecutive gacha draws.