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 :)