Calculating the Expected Value of a Gacha (for Gachas with a Cap)
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For gacha systems with a cap, such as those found in mobile games, this calculates the expected number of spins and the expected amount spent to obtain a single desired item.
Cap-based gacha: A gacha where, once a certain value associated with the gacha reaches the cap (i.e., the upper limit), you can obtain any item appearing in the gacha at your discretion.
Gacha with a cap based on the number of pulls: A cap-based gacha that sets a cap on the number of pulls.
Gacha with a cap based on spending: A cap-based gacha that sets a cap on the amount spent.The calculation results on this page do not take into account free gacha spins.
Point-Based Gacha with a Cap: A gacha that sets a cap based on points earned from spinning the gacha or points exchanged for items obtained from the gacha. Since the number of points earned per spin is likely to vary, calculations are based on an average value.
| Gacha | timesThe probability of getting the desired item from the gacha when you spin it just once % |
| The expected number of gacha spins required to obtain a desired item times | |
| The expected value of the amount spent when spinning the gacha until the desired item is obtained yen | |
| Price per gacha pull yen | |
| Expected number of pulls in a typical gacha times | |
| Ratio of expected number of pulls for gacha with a cap compared to standard gacha % |
Price per gacha pull = Number of premium stones per pull × Price per premium stone ÷ Number of premium stones purchased
When the cap is based on total spending
n = Total spending to reach the cap / Price per gacha pull
When the cap is based on points
n = Cap Amount in Points / Average Points Earned per Gacha Draw
- 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 collection 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 pulls)
- 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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