Arknights Pull Calculator: Estimate Your Orundum & Originium Needs
Plan your Arknights Headhunting strategy with precision. Our Arknights Pull Calculator helps you estimate the Orundum and Originium Prime required to acquire your desired 6-star operators, taking into account the game’s unique pity system.
Arknights Pull Calculator
Enter the number of pulls you’ve made on the current banner without getting a 6-star operator. This affects your pity. (Max 98)
How many 6-star operators are you aiming to acquire?
Select the confidence level you want for acquiring your target 6-star operators.
Standard cost is 600 Orundum per pull. Adjust if you have special permits.
Equivalent Originium Prime for one pull (1 OP = 180 Orundum, so 600/180 = 3.33 OP).
Calculation Results
Estimated Pulls Needed: 0 pulls
Estimated Originium Prime Needed: 0 OP
Average Pulls for One 6-Star (0 Pity): 0 pulls
The calculator estimates pulls based on cumulative probability, factoring in Arknights’ pity system (2% base rate, +2% per pull after 50 without a 6-star).
Arknights 6-Star Probability Table
Cumulative Probability of Obtaining at Least One 6-Star Operator
| Pulls | Prob (0 Pity) | Prob (40 Pity) | Orundum Cost |
|---|
Arknights 6-Star Pull Probability Chart
Visualizing Your Chances for a 6-Star Operator
Starting with 40 Pity
What is an Arknights Pull Calculator?
An Arknights Pull Calculator is an essential tool for players of the popular tower defense gacha game, Arknights. It helps estimate the amount of in-game currency, primarily Orundum and Originium Prime, required to acquire a desired number of 6-star operators from the Headhunting banners. By factoring in the game’s unique gacha mechanics, including the base 6-star drop rate and the progressive pity system, this calculator provides a data-driven approach to resource management.
Players who should use an Arknights Pull Calculator include:
- Free-to-Play (F2P) Players: To meticulously plan their limited resources for specific high-priority banners.
- “Dolphins” and “Whales”: To budget their spending and understand the potential costs for multiple copies or specific operators.
- Strategic Planners: Anyone looking to optimize their Orundum farming and Originium Prime conversion for future operator acquisitions.
Common misconceptions about an Arknights Pull Calculator:
- It guarantees an operator: The calculator provides probabilities and estimates, not certainties. Gacha remains a game of chance.
- It accounts for specific rate-up operators: This calculator focuses on the probability of getting *any* 6-star operator. While banners feature rate-up units, the underlying 6-star probability and pity system apply to the rarity itself.
- It replaces good resource management: It’s a tool to aid planning, not a substitute for consistent Orundum farming and wise Originium Prime usage.
Arknights Pull Calculator Formula and Mathematical Explanation
The core of the Arknights Pull Calculator lies in understanding cumulative probability and the game’s unique pity system for 6-star operators. Here’s a step-by-step breakdown:
Base Probability and Pity System
- Base 6-Star Rate: For any individual pull, there is a base 2% chance (0.02) of obtaining a 6-star operator.
- Pity System Activation: If you do not obtain a 6-star operator within the first 50 pulls on a banner, the pity system activates.
- Progressive Pity: Starting from the 51st pull, the chance of getting a 6-star operator increases by 2% for each subsequent pull.
- Pull 51: 2% (base) + 2% (pity) = 4%
- Pull 52: 2% (base) + 4% (pity) = 6%
- …and so on, until the rate reaches 100%.
- This means a 6-star operator is guaranteed by the 99th pull if you haven’t gotten one before.
Cumulative Probability Calculation
To find the probability of getting at least one 6-star within a certain number of pulls, we calculate the inverse: the probability of *not* getting a 6-star in any of those pulls, and subtract it from 1.
The formula for the probability of NOT getting a 6-star in ‘N’ pulls, considering pity, is:
P(No 6* in N pulls) = Product(1 - P(6* on pull i)) for i = 1 to N
Where P(6* on pull i) is the individual probability of getting a 6-star on pull ‘i’, adjusted for pity.
Therefore, the cumulative probability of getting at least one 6-star in ‘N’ pulls is:
P(At least one 6* in N pulls) = 1 - P(No 6* in N pulls)
For multiple target 6-star operators, the calculator approximates by multiplying the pulls needed for one 6-star (at the desired probability) by the target number of operators. This provides a practical estimate for resource planning.
Variables Table for Arknights Pull Calculator
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| Current Pulls Since Last 6-Star | Number of pulls made on the current banner since your last 6-star operator. Directly impacts pity. | Pulls | 0 – 98 |
| Target 6-Star Operators | The total number of 6-star operators you wish to acquire. | Operators | 1 – 10+ |
| Desired Probability of Success | Your confidence level for achieving the target (e.g., 75% means you want to be 75% sure). | % | 50% – 95% |
| Orundum Cost Per Pull | The amount of Orundum required for a single Headhunting pull. | Orundum | 600 (standard) |
| Originium Prime Cost Per Pull (Equivalent) | The equivalent amount of Originium Prime for a single pull, based on conversion rates. | Originium Prime (OP) | 3.33 (standard) |
Practical Examples (Real-World Use Cases)
Let’s look at a couple of scenarios where the Arknights Pull Calculator can be incredibly useful.
Example 1: F2P Player Saving for a New Operator
A Free-to-Play player, Doctor Amiya, is saving for an upcoming banner featuring a highly anticipated 6-star operator. She currently has 0 pulls since her last 6-star and wants to be 75% confident in acquiring at least one 6-star from the new banner.
- Current Pulls Since Last 6-Star: 0
- Target 6-Star Operators: 1
- Desired Probability of Success: 75%
- Orundum Cost Per Pull: 600
- Originium Prime Cost Per Pull (Equivalent): 3.33
Using the Arknights Pull Calculator, Doctor Amiya finds:
- Estimated Pulls Needed: Approximately 60 pulls
- Estimated Orundum Needed: 36,000 Orundum
- Estimated Originium Prime Needed: 199.8 OP
Interpretation: Amiya now knows she needs to save around 36,000 Orundum to have a good 75% chance of getting a 6-star. This helps her prioritize her Orundum farming (Annihilation, daily/weekly missions, events) and decide if she needs to convert any Originium Prime.
Example 2: Player Aiming for Multiple 6-Stars with Existing Pity
Doctor Kal’tsit is on a banner and has already made 40 pulls without a 6-star. She wants to acquire two 6-star operators from the current banner and wants a higher confidence level of 90%.
- Current Pulls Since Last 6-Star: 40
- Target 6-Star Operators: 2
- Desired Probability of Success: 90%
- Orundum Cost Per Pull: 600
- Originium Prime Cost Per Pull (Equivalent): 3.33
Inputting these values into the Arknights Pull Calculator yields:
- Estimated Pulls Needed: Approximately 100 pulls
- Estimated Orundum Needed: 60,000 Orundum
- Estimated Originium Prime Needed: 333 OP
Interpretation: With 40 pity, Kal’tsit is already close to activating the increased rates. To get two 6-stars with 90% confidence, she needs to prepare for about 100 more pulls. This helps her decide if she has enough resources or if she needs to purchase more Originium Prime.
How to Use This Arknights Pull Calculator
Using the Arknights Pull Calculator is straightforward. Follow these steps to get your resource estimates:
- Enter “Current Pulls Since Last 6-Star”: Input the number of pulls you’ve already made on the current Headhunting banner since your last 6-star operator. This is crucial for the pity system calculation. If you haven’t pulled on the current banner or just got a 6-star, enter 0.
- Set “Target 6-Star Operators”: Specify how many 6-star operators you are hoping to acquire. For a single new operator, enter 1.
- Choose “Desired Probability of Success”: Select your preferred confidence level. A higher percentage means the calculator will estimate more pulls to increase your chances. 75% is a good balance for planning.
- Verify “Orundum Cost Per Pull”: The standard cost is 600 Orundum. Only change this if you are using special Headhunting Permits that alter the Orundum equivalent.
- Verify “Originium Prime Cost Per Pull (Equivalent)”: This is the equivalent Originium Prime needed for one pull (standard 3.33 OP). Adjust if your conversion rates differ (unlikely for most players).
- Click “Calculate Pulls”: The calculator will instantly update the results based on your inputs.
- Click “Reset” (Optional): If you want to start over, click the “Reset” button to restore all fields to their default values.
How to Read the Results
- Estimated Orundum Needed: This is the primary highlighted result, showing the total Orundum you’ll likely need.
- Estimated Pulls Needed: The total number of Headhunting pulls required to meet your desired probability for your target 6-star operators.
- Estimated Originium Prime Needed: The equivalent amount of Originium Prime you would need to convert to Orundum to achieve your goal.
- Average Pulls for One 6-Star (0 Pity): This provides a general benchmark for how many pulls it typically takes to get a single 6-star operator from scratch, considering the pity system.
Decision-Making Guidance
Use these results to make informed decisions:
- Resource Allocation: Compare the estimated Orundum/Originium with your current reserves. Do you need to farm more?
- Banner Prioritization: If the cost is too high, you might decide to skip a banner or lower your target.
- Spending Budget: For players who spend, this helps set a realistic budget for acquiring operators.
- Risk Assessment: Understand the probability involved. Even with a 95% chance, there’s still a small risk of not getting your target.
Key Factors That Affect Arknights Pull Calculator Results
Several factors can significantly influence the outcomes of an Arknights Pull Calculator and your actual pulling experience:
- Current Pity Counter: This is perhaps the most critical factor. The higher your “Pulls Since Last 6-Star,” the fewer additional pulls you’ll need to reach a 6-star due to the escalating pity rate. Starting with 0 pity requires significantly more pulls on average than starting with 40 or 50 pity. Understanding the Arknights pity system is key.
- Desired Probability of Success: Your chosen confidence level directly impacts the estimated pulls. Aiming for a 95% chance will naturally require more resources than a 75% chance, as it accounts for less favorable luck scenarios.
- Target Number of 6-Star Operators: Each additional 6-star operator you aim for roughly multiplies the estimated pulls and resources needed. Acquiring multiple 6-stars can be very costly.
- Banner Type and Rate-Ups: While the base 6-star rate and pity system are consistent, specific banner types (e.g., Limited Banners, Joint Operations) might have different rate-up mechanics or spark systems that influence your strategy, even if the calculator focuses on the general 6-star probability. The calculator estimates *any* 6-star, not a specific rate-up.
- Orundum Farming Efficiency: Your ability to consistently farm Orundum through Annihilation, daily/weekly missions, and event rewards directly affects how quickly you can accumulate the necessary currency. A good Orundum farming guide can significantly reduce your reliance on Originium Prime.
- Originium Prime Conversion Strategy: How and when you convert Originium Prime to Orundum can impact your overall resource efficiency. Knowing the optimal Originium Prime conversion strategy is vital.
- Luck (Randomness): Despite probabilities, gacha is inherently random. You might get lucky and pull a 6-star early, or you might hit soft pity multiple times. The calculator provides an average expectation, but individual results will vary.
- Event Rewards and Free Pulls: Events often provide free Headhunting Permits or significant amounts of Orundum, which can reduce your overall resource expenditure. Always factor these into your planning.
Frequently Asked Questions (FAQ)
A: No, this calculator estimates the probability of acquiring *any* 6-star operator. While banners feature rate-up units, the underlying 6-star probability and pity system apply to the rarity itself. To guarantee a specific rate-up operator, you might need more pulls than estimated here, especially if you lose the 50/50.
A: Considering the pity system, the average number of pulls to acquire one 6-star operator from 0 pity is generally around 50-60 pulls. Our Arknights Pull Calculator provides this average as an intermediate result.
A: After 50 pulls on a Headhunting banner without receiving a 6-star, the probability of getting a 6-star increases by 2% for each subsequent pull. This means by the 99th pull, a 6-star is guaranteed.
A: Absolutely! The base chance for a 6-star is 2% per pull. Many players get 6-stars well before hitting the pity threshold. The pity system only guarantees one if you’re unlucky.
A: For 6-star probability, single pulls and 10-pulls are mathematically identical. However, 10-pulls guarantee at least one 5-star or higher operator, which can be beneficial for building your roster. For resource efficiency, it doesn’t matter.
A: Orundum can be acquired through various in-game activities: completing daily and weekly missions, clearing Annihilation stages, participating in events, and converting Originium Prime. Consistent farming is key to maximizing your Orundum income.
A: Orundum is the primary currency used for Headhunting (pulls). Originium Prime (OP) is a premium currency primarily used for buying skins, refilling Sanity, and can be converted into Orundum (1 OP = 180 Orundum). Our Arknights Pull Calculator helps you estimate both.
A: Yes, the pity counter for 6-star operators generally carries over between standard and joint operation Headhunting banners. However, specific limited banners might have their own separate spark systems, though the underlying 6-star pity still functions similarly.