Comparative analysis on theoretical and simulated data in Arknights Headhunting.

Developed by KaidenFrizu, SurfChu85, Ayane Satomi, and Eyenine.

Theoretical probabilities are important to predict your chances in getting 6★ Operators in Arknights. While the first 50 consecutive non-6★ pulls follow the conventional geometric pdf with fixed probability p, but it’s impossible in the case where the pity system starts and the p varies each pull.

A similar problem was found in StackExchange where it asks about the specific distribution similar to geometric pdf but with varying but deterministic probabilities. It is found out that the theoretical probabilities of pulling a 6★ Operator after consecutive non-6★ Operators follows a more general version of geometric distribution in which accounts for the varying probabilities.

The probability of getting a 6★ Operator is much sooner than you would expect. Upon calculation from the general version of geometric pdf, results show that there is a 76% chance that you will pull a 6★ Operator on your 55th pull or earlier in your streak, 95% on your 62nd pull or earlier, and 99% on your 67th pull or earlier. The probabilities shown accounts the near impossibility of making into pull 99 because the probability of ending the current streak (or getting a non-6★ Operator) decreases exponentially as you approach the 99th pull.

To validate, we tested each simulated data and determine whether they follow the theoretical probabilities. For this analysis, there are 6 sets of simulated data where their differences comes down to their RNGs and seeding methods. Results indicate that the all six sets of simulated data follow the calculated theoretical probabilities.

The computed theoretical probabilities can be used to accurately predict your chances of getting a 6★ Operator. This would highly benefit users to plan ahead on their rolls and their desired outcomes. Further research on other gacha rating system with varying rates could be possible using the general formula for geometric pdf.

arkfunc.R
A file containing all the custom codes used for simulation and analysis.

CODEBOOK.md
A markdown file that contains the function and variable details in arkfunc.R and Savedata.RData.

GachaPull.Rproj
File used to open this project in RStudio.

LICENSE
Contains the details on MIT License.

Savedata.RData
An RData that contains the saved global environment on its last render.

Detailed analysis can be found in RPubs.