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The chance of finding a shiny starter (and how long it could take!)

#11Oak_Tea(Topic Creator)Posted 9/24/2009 4:31:03 PM
Orrrrrrrr, we can say that you either get a shiny or you don't

You either die or you don't die when you jump off a bridge...it depends on many factors.


You need to save right before choosing from the 3 Poke Balls. And then you SR when you see your starter behind you for the first time.

Does the starter appear behind you before you /finalize/ your starter? So, will it actually work to check all three before soft resetting?


how many SRs would it take for all three starters to be shiny?

After 274,877,907,000 resets, you're more likely than not to have gotten all three to be shiny.
To be in the 95% confidence interval... 522,268,024,000. Wow. Not that it matters. =)


But don't the chances of finding a starter reset every time, making it so no matter how many times you soft reset you will always have the same percent of chance of getting a shiny?

While you are technically correct, the chances /do/ reset, but since we're looking at averages and large amounts of data, we can calculate estimations of how long/how many tries it'll take. Both are correct ways of looking at this. What would be incorrect would be to say "It'll take within 8192 tries, but no more, and you'll have one by then". These are rough averages, and it's basically saying "If you do procedure x exactly y amount of times, you are z% likely to have found one by this point".


I'm glad to know that I'm not the only one doing tons of resets for a fairly arbitrary thing in a game. ;D
Of course, I should've known that, what with IVs and EVs and natures, too. Can't wait to get mildly into that stuff. (though I plan on staying away from IV breeding; too much work.)
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#12Blingya25Posted 9/24/2009 4:32:53 PM
Mr. Owl, how many licks does it take to get into the center of Rhode Island State Prison?

JUST ONE!
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I remember that i had one, but when it came, two was there, then three was nowhere to be find with four, but five and six was like nine dude, and eight seven :\
#13jayman7Posted 9/24/2009 4:43:29 PM
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.

A = 0.00000000018189894
B = 0.00000148993422000
C = 0.01220405120000000


Something is wrong here. (Actually, you just reversed A and C somewhere along the line, but it's still funny.)
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#14jayman7Posted 9/24/2009 4:45:38 PM
Orrrrrrrr, we can say that you either get a shiny or you don't.

I love it when people who don't understand probability say that "it happens or it doesn't" like it's a 50-50 chance - even sillier here than most, because everyone knows it's not anywhere near a 50-50 chance.
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Creator of Jay's Journey (see quote!)
"Game Series 1 is the best because it set the stage for better games!" - Nostalgia whores everywhere
#15agooguaPosted 9/24/2009 4:46:34 PM
doesn't whether it's shiny or not depend on an RNG and what time you click on it?
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#16jayman7Posted 9/24/2009 4:49:31 PM
doesn't whether it's shiny or not depend on an RNG and what time you click on it?

Strictly speaking, yes, it's determined by an RNG.

Do you know how to manipulate an RNG to get a shiny?

Pokemon has a strong enough RNG that, unless you outright cheat with hacking tools, it may as well be random as far as any human could easily figure.
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Creator of Jay's Journey (see quote!)
"Game Series 1 is the best because it set the stage for better games!" - Nostalgia whores everywhere
#17Ampharos64Posted 9/24/2009 4:50:53 PM
^ Yup, indeed. 'Tis why I just abuse the RNG for shinies usually, though I won't for Lugia since that seems too easy.

Does the starter appear behind you before you /finalize/ your starter? So, will it actually work to check all three before soft resetting?

Apparently you can now see whether the starter is shiny on the screen (when you're asked to choose, and can cycle between their Pokeballs), so yep, should be fine.

Still no three perfect IVs Eevee, so I wish you much luck in a quest which has an even lower chance of success than mine (will need it myself when I go after Lugia, wonder how long that'll take).
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#18agooguaPosted 9/24/2009 4:51:16 PM
I don't understand the manipulation of the RNG, but I have heard it's based on your Secret ID which is determined when you start the game, so wouldn't you have a better chance of getting a shiny each time if you clicked on the pokemon a second later than before?
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#19jayman7Posted 9/24/2009 4:52:59 PM
I don't understand the manipulation of the RNG, but I have heard it's based on your Secret ID which is determined when you start the game, so wouldn't you have a better chance of getting a shiny each time if you clicked on the pokemon a second later than before?

No, because Pokemon has a strong RNG. I believe the actual time on the DS's clock is a factor.

I'm guessing you've been hanging out on the Final Fantasy IV: The After Years board? That game has a really weak RNG, leaving it wide open for exploits.
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Creator of Jay's Journey (see quote!)
"Game Series 1 is the best because it set the stage for better games!" - Nostalgia whores everywhere
#20logic_use_itPosted 9/24/2009 4:56:42 PM
Your formula is incorrect.

Your error is that each soft reset, you actually get three tries for a shiny.

This is because if a pokemon is shiny, the preview sprite will be shiny. That is, you can tell that it is shiny before you actually select it.

The actual solution is a geometric distribution.

The probability of getting no shinies in one soft reset is the probability of the first one not being shiny, times the probability of the second one not being shiny, times the probability of the third one not being shiny, or: (8191/8192)^3.

The probability then, of getting at least one shiny in one soft reset is 1-(8191/8192)^3.

Let x be the number of SRs. Then the probability of getting at least one shiny in x or less tries is

1-(8191/8192)^(3*x)


If we want a 50% chance of finding a shiny, then we need 0.5 = 1 - (8191/9192)^(3*x)

solving for x we get

(log(0.5)/log(8191/8192))*(1/3) = x.

That is, x = 1892.638568.

In order to have a better than not chance of getting a shiny, you need to do 1893 soft resets, not 4096.

If you can do 3 soft resets in 1 minute, then you can do 180 soft resets per hour. Then it will take you approximately 10.5 hours to have a better than not chance of finding a shiny.

To have a 99% chance of finding a shiny,

(log(0.01)/log(8191/8192))*(1/3) = 12574.41847

you need 12575 tries, which, at 3 soft resets per minute, will take you about 70 hours.


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