Calculating the Number of Gacha Pulls (for General Gacha)
Author: ExpectedValueExecutions: 15250
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For standard gacha systems, such as those found in mobile games, this tool calculates the number of gacha pulls required to obtain a desired item with a given probability, along with the corresponding cost.
Price per gacha pull = Number of premium stones per pull × Price per premium stone ÷ Total number of premium stones purchased
The special bracket in the upper-right corner of the formula is the ceiling function, which means to round up to the nearest integer.
When x is sufficiently small, ln(1+x) can be approximated by x.
On this page, you can also calculate the number of runs required to obtain an item as a game reward with a certain probability. In that case,
please substitute “drop rate of the desired item,” “probability of obtaining it,” and “number of gacha pulls” for
“drop rate of the desired item,” “probability of obtaining it,” and “number of runs,” respectively.
- 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 completion gachas with varying drop rates)
- Calculating the Expected Value of a Gacha (for Box Gachas)
- Calculating the Expected Value of a Gacha (for Consecutive Gacha Runs)
- Verification of Gacha Drop Rates (for General Gacha)
- Verification of Gacha Drop Rates (for Consecutive Gacha Runs)
- Calculating the Number of Runs and Time Per Run in a Game
- Calculating Stamina in Games
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