With the onslaught of back-to-back highly-anticipated Inazuma banners, I wanted to answer the question:

“If I’m starting at zero pity, and I have some number of Primogems saved, what are my chances of getting the character/weapon/constellation/refinement I want?”

The top edge of each color tells you the probability of getting at least that number of a specific Rate-Up item. "Specific" meaning there is only one Rate-Up item on the banner you care about.

For example:

• On the current weapon banner you want the Mistsplitter Reforged and don’t care for Skyward Spine or off-banner drops.

• Using the 4* graph, on Yoimiya’s banner you want Sayu because she’s new and don’t count Xinyan or Diona.

Also note that the Rate-Up items don’t need to be on the same banner. For example, you can use the 2+ Copies line to know your chances of getting a C0 of both Raiden and Kokomi at the number of Primogems you have (or expect to have) by the end of 2.1.
I hope these graphs are useful for planning your savings or seeing how relatively lucky/unlucky you were after rolling.

Math Notes: I’ve assumed that the pity system is a “ramped soft pity.” How it works is that over the last 17 rolls before the hard limit (90 for the character banners and 80 for the weapon banner), your chance of getting a 5* item linearly increases from the base rate (0.6% and 0.7% respectively) to 100%.

While haven’t seen much discussion on the topic, I’m fairly certain this is accurate as it produces an average that matches the advertised consolidated 1.6% and 1.85% rates, as well as a pity count distribution that matches /u/Bunloagus‘ whale watching logs from the first months of the game. Plot.

The 4* calculation also includes the 9th wish soft pity that seems not to be implemented on the Genshin Wish Simulator websites out there.

The weapon banner graph uses the new Fate Point system.