Using mathematical estimation, how many shiny Sinistea will I find before I find a shiny Authentic?

Question

This is for you krlw…?

I have shiny charm and am slowly working up to 500+ chain

Given this, shiny odds, authentic Sinistea odds, what would be the formula to estimate how many Shiny Sinisteas will I find until a shiny Authentic? Excluding outside factors (eg. Other phases)

I swear to god if any of you say “may be one, may be a hundred bc shiny odds work like that” I will downvote you into oblivion because I want math. I know how shiny odds work. I want this to compare for when I’m done the hunt

Comments

Should we assume that you've already hit the 500 chain? I believe that affects shiny rates

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Yeah sure; assume max possible odds already hit. Just be sure to add that in the answer (eg. Assuming you have this, this, or this to get this)

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Yeah, thanks

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That doesn't affect how many shiny Sinistea you will find before an authentic

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If you're still hunting Shiny Antique Sinistea, then this will interest you: https://twitter.com/sibuna_switch/status/1414068195544215553

Answer 1

I didn't even know that it can be fake, wtf. I hope I don't get this wrong

Assumptions

I am assuming that you have reached the 500 mark
I am assuming that you are hunting in the Old Cemetery in Clear Weather (Confirmed on discord about the old cemetery, clear weather is an assumption)

Calculations

Ok, SO. First, let's see what the rate is of getting an authentic sinistea in the first place is. So, assuming that there is clear weather, you would have a 1:19 ratio of authentic to fake. This means that you have a 5% chance of getting a pogtea from any encounter. Quite the development. This does change, however, based on weather. So, with permission from smoothie, I can, in fact, just average the percentage chances, this makes it a crapton easier, so don't judge smh. So, the average rate of finding it as an overworld encounter, as that's what OP wants. However, I'm going to use a weighted average to find this, as some percentages only happen a certain amount of time. I am assuming that the chances of all types of weather are the same (there's a really complex thing that depends on date and stuff, and I'm just, not going to. I'm not a masochist. So in blizzard or fog, the chance is 1/21. These are two of the nine weathers. The other 7 have a 5% chance of happening. So, the weighted average would be as follows:

Ok, so 4.9 is our number from that (approximately). However, I think there is one thing that is still missing. Probability is randomness quantified. Therefore, you could get 192386501623750176235016238506253 shiny normal sinistea before you get a normal sinistea. Therefore, I will give an estimate, but also a chart showing the places wherein you should be trying to get to. My estimation is 19. Here is the number line (yeah I did round 4.9 to 5 silence mortal):

Alright, so you see this number line. The base numbers are the number of shinies that you can get. The green represents low, yellow is medium, orange is high, and red is basically guaranteed. Again, this is probably, but not guaranteed.

Hopefully this helps.

Sources:
A crapton of bulbapedia and asking Smoothie stuff on discord :)

Comments

man i love ur handwriting even if its on ms paint <3

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Why thank you

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Dude just letting ya know your answer is very confusing and I can't tell what you mean

Answer 2

19

Fake Sinistea has a 19% encounter rate, (at best) in the Old Cemetery, while Antique Sinistea has a 1% encounter rate. For every 20 Sinisteas you encounter, one will be antique, theoretically.

So quite simply this is applied to the shininess too. If you encounter a Shiny Sinistea, there is a 1/20 chance for it to be antique. So theoretically, you will encounter 19 Shiny Sinistea before encountering a Shiny Antique Sinistea.

This is the same as how, theoretically, it takes 4096 encounters to get a shiny, but it could happen at any point up to 4096.

Brilliant Pokemon will not increase the chance of specifically Antique Sinistea to be shiny, it will just increase the chance of Sinistea in general to be shiny.

Comments

Just want to put it out there that this answer has the better mathematical representation of the problem. Adding shininess into the equation doesn't change the proportion of Antique Sinistea you'll find, so you don't need to do any calculations.