About how many phases would it take for me to see my static target?

Question

I need a math brain person to help me out here.

Now obviously, with shiny hunting, the numbers are not guaranteed at the odds, but for this question, let's assume they are.

Edit: I'll try to clear up this question so it's better to understand.

• I'm hunting three static encounters at 1/4096 odds (two Shelgon and an Amoonguss). In theory, it should take around 1365 encounters to see one one of my static encounters. These static encourage only serve as a baseline for how many resets I need to do, they aren't included in the random encounters.
• It's impossible to calculate how many random encounters I get per reset, since I'm playing on Violet. These encounters are random Pokemon at the shiny charm odds of 1/1365 that I'm seeing while checking the static encounters.
• Assuming I see 30 random encounters per reset, that means it would take around 46 resets to see one random encounter shiny.
• Assuming I see one of my static targets at 1365 resets, it should take around 30 random shinies before I see one of my targets

Is my math right? I'm trying to calculate the number of phases (random encounters) I would see before seeing one static encounter shiny, is that even possible to do based on the factors I've given?

It's important to mention that for my static encounter hunts in Violet, I count every random shiny I see as a phase. So hopefully that clears things up.

Comments

I am kind of confused about the situation you're describing since your 3rd and 4th paragraphs seem to talk about different things. Does every reset contain 3 encounters that each have a 1/4096 chance, or does every reset contain 30 encounters that each have a 1/1365 chance?
Those are very different scenarios, so while I get that you're saying that 3 attempts of 1/4096 is similar to 1 attempt of 1/1365, I'm unclear on the actual number of encounters per reset in the scenario you care about.

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I see how that's confusing, my bad. Basically, I was using the static encounters to say I would need to do about 1365 resets to see a shiny static, and within those 1365 resets, I would see 30 random shinies, given it takes 46 resets to see a shiny charm odds shiny with 30 random encounters per reset.

So that means I care about the random encounters, and the static encounters aren't a part of that math.

Again, I'm no math guy, so I'm not even sure if what I'm trying to do is even technically possible to calculate, but I hope that makes a bit more sense.

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The shiny odds you're hunting with don't matter at all when finding the odds of finding a shiny of your target vs a phase. The only thing that we would need to calculate your expected number of phases is the odds of encountering your target (shiny or not) vs anything other than your target.

From your question, it sounds like that, out of an encounter pool of 2 Shelgon and an Amoonguss, you've gotten shiny Amoonguss 19 times in a row, rather than your intended target of Shelgon. Considering this is about a 1 in a billion chance, I'm assuming this probably isn't the actual case and I'm misinterpreting something, but I'm having a hard time figuring out what the actual situation is.

What other Pokemon are you encountering other than Shelgon and Amoonguss (your secondary target?), and what are the odds of encountering all of them? Can you give us the encounter table for the area you're hunting in? If not, there are a few other ways we can try to answer the question, but I'm going to need a bit more context of where you are, and in which game.

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I edited my question to make it more clear. I think where's you're getting confused is that I count my random encounter shinies as phases, which I didn't directly mention.

I'm playing on Violet, and since I need to travel a little to see the Amoonguss and second Shelgon, that gives random Pokemon time to spawn in. I can't control how many random Pokemon spawn in, so I just gave a random number of 30 per reset (the average is probably lower than that, but we'll stick with it for the purpose of the question). These random Pokemon are the random encounters at charm odds, which I'm referring to as the phases.

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IT'S FINALLY OVER THANK THE HEAVENS!!!
I still want to know if I was doing this math right though.