If I soft-reset HGSS until I find a shiny starter, would my odds be 3/8192 per reset?

Question

Like, since there's three of them, and you see them all at once, so per encounter since there's 3 and the odds are 8192.

Like, would that mean my odds are like 0.03% per reset or am I really bad at math

Comments

Someone correct me if I am wrong, but shouldn't this be calculated as 1 - probability of none of them being shiny. i.e. 1 - (8191/8192)^3

Answer 1

A simple way to calculate this would be to find the probability of none of the starters being shiny, then subtracting it from 1. i.e. 1 - (8191/8192)^3
This comes out to be ~0.0003661 or 0..03661%. Ironically this value is quite close to 3/8192 which is ~0.03662%. However, this is just a coincidence. The difference widens as number of starters increase. So technically, you do get very similar odds (about 3 times the base value) but not for the reasons you think.

Answer 2

I've calculated and recalculated these values in particular, so here they are:
The chance of finding a shiny starter is A + B + C, where A is the chance of one Pokemon being shiny, B is the chance of two starters being shiny, and C is the chance of all three starters being shiny.
The chances of B and C happening are almost negligible, but for the sake of accuracy (and lowering the estimated amount of time), I will incorporate these values. (for the records, the chance of finding one shiny Pokemon is 1/8192.

A = 0.00000000018189894
B = 0.00000148993422000
C = 0.01220405120000000
(these are all probabilities)

Therefore, the probability of finding one shiny starter is 0.01220554131611894%.

Each soft reset gives you that chance of finding one. Now, with a bit more calculations, we can determine the approximate number of tries it'll take to find a shiny starter.
To do this simply, just enter XX/0.01220554131611894 into google, where XX is the percent you want.

For example..

After your 4,096th reset, you're more likely than not to have found a starter by this point.
After 7,373 resets, there's a 90% chance that you'll have found a shiny starter.
Just 800 more, and you have a 99% chance..you're basically guaranteed to find one by this point.

Source

I hope this was what you're asking, lol. Hope this helps :P

Comments

Is this the same for resetting 5 pokemon at the same time at the game corner for example?

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This answer is very wrong. It says that the chance of finding a starter are A+B+C, which is fine, but then it completely miscalulates the values lmao.
C is the chance of one pokèmon being shiny and the other 2 not being shiny (they switched it up) which is:
1/8192 (the chance of a pokèmon being shiny) * 8191/8192 * 8191/8192 (chance of other two pokèmons being not shiny) * 100 (to make it a probability) = 0.012204051, which is their result, but this actually has to be multiplied by 3, because there's 3 ways in which this scenario could happen (only shiny chikorita, only shiny totodile, only shiny cyndaquil).
This error clearly propagates to the B case. Only the C case is correct, because there's a single way for the starters to all be shiny.
Also, this calculation is slow and can easily lead to errors (as you've just seen), so the smartest thing to do here would be to consider the complement: What's the chance for at least one pokèmon to be shiny? I don't know, but i know that:
(chance of at least one shiny pokèmon) + (chance of no shiny pokèmon) = 1, because these two events cover all the available possibilities (the sampling space).
so, (chance of at least one shiny pokèmon) = 1 - (chance of no shiny pokèmon) = 1 - (8191/8192)^3 = 1 - 0.99963383376 = 0.00036616623, which corresponds to 0.036616623%, which is approximately a 1/2731 chance

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1/2731 is basically the simplified version of 3/8192, if we round the decimals into the nearest whole number

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Yes, the value is pretty close but that is just a coincidence. Any number other than 3 will have very different answers

Answer 3

Yes, it would be. Since the odds of getting a shiny Pokemon in gen IV is a 1/8192, or a .01220703%; .012% rounded. So, it's not a lot. Since you are encountering 3 Pokemon at the same time, each has that 1/8192 chance, so It'd be a 3/8192, or a .0366% for each soft reset. And sadly, no, percentages and probabilities are different. Say you have 1/8192 for a shiny. You could SR 10,000 times and still not have it shiny, because each encounter has the 1/8192. I did Lugia in SS, didn't, get it until 12,777 SR's.

Good luck on your hunt!
I'm on 700 for starter in HG.
Happy Shiny hunting,

~Freezee

Comments

You're off. Following your reasoning, if there were 8192 starters in hgss, then you'd have a 8192/8192 chance, which is 100%. But as you stated, "each encounter has the 1/819"), so it's possible to have 8192 non shiny starter pokèmon, even if you checked them all at once.