Last updated: 2020-12-19
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Knit directory: gacha/
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Now that the Zhongli banner is almost over, I’m sure a lot of you are saving up those precious primogems for our next white (silver?) haired twink Albedo. In this investigation we look for the number of pulls needed to achieve 95% probability of pulling one SSR character using the Genshin Impact.
I would like to state that we are very unsure about how the Genshin Impact (referred to as “Genshin”) algorithm actually works. Unlike Arknights, the gacha statistics given in the game offers very little insights on when the pity mechanism kicks in, and the size of the increment in probability. However, an empirical study on reddit has stated that the pity mechanism is likely to take effect at the 76th pull, and the SSR rate increases to 100% at the 90th pull (as described in gacha rules). We will assume that this scenario is true in our calculations.
Genshin Impact also includes the 10-pull bonus in their gacha mechanism. However, since we are not sure if the 10-pull bonus only affects 4-star (SR) items or both 4-star and 5-star (SSR) items, we will perform separate calculations for both of them.
The Genshin gacha rules state that
sessionInfo()R version 3.6.2 (2019-12-12)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS 10.16
Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] workflowr_1.6.2
loaded via a namespace (and not attached):
[1] Rcpp_1.0.3 rprojroot_1.3-2 digest_0.6.25 later_1.0.0
[5] R6_2.4.1 backports_1.1.5 git2r_0.26.1 magrittr_1.5
[9] evaluate_0.14 stringi_1.4.6 rlang_0.4.5 fs_1.3.2
[13] promises_1.1.0 whisker_0.4 rmarkdown_2.1 tools_3.6.2
[17] stringr_1.4.0 glue_1.3.2 httpuv_1.5.2 xfun_0.12
[21] yaml_2.2.1 compiler_3.6.2 htmltools_0.4.0 knitr_1.28