If you want to catch a SHINY Pikachu, look here!

[Calvin]

Well since you're here, I assume you are ready for the following...

A calculation of the chance of encountering a SHINY Pikachu

It's just some basic advance Mathematics in my opinion on probability.

First off, some basic facts:

Rate of a Pikachu being SHINY = 0.01%
Number of PIkachu per wave = 5
Number of waves per run = 30
Rate of a Pikachu wave = 1%
Number of runs to encounter a Pikachu wave = 10/3


Next, on to the probability calculations:

Probability of encountering 'n' Pikachus in a row that are NOT SHINY = (0.9999)ⁿ
Probability of encountering a SHINY Pikachu within 'n' Pikachus = 1-(0.9999)ⁿ

Therefore, when (0.9999)ⁿ = 0.01,

We can get the number of Pikachus required to be encountered in order to have a 99% chance of finding a SHINY Pikachu within them.

To find n, we take log_0.9999^0.01
= 46049 (corrected to the nearest integer)

Lastly, some simple calculations:

Number of waves to encounter 46049 Pikachus = 9210 (Corrected to the nearest integer)
Number of runs to encounter 9210 waves = 30700

Assume the time to complete VT 2 = 2.5 min
Time to find a SHINY Pikachu
= 76750 mins
= 1279 hours (corrected to nearest integer)
= 53 days of non stop SHINY Pikachu Hunting (corrected to nearest integer)

Conclusion:
Too all Shiny Pikachu Hunters out there, you are warned!
Remember, this 53 days is the Maximum
amount of time you have to spend to catch a SHINY Pikachu. If you're lucky , you can even get one on your first try within minutes.

Well good luck guys. (Though the enthusiasm seems to have died down)

Credits to me, myself, and I Mysticman89
For all his help and mighty calculations.
I simply summarised them here.

Sidenote: Sorry it took me so long to edit the post, my brain experienced an overload of information while processing your explanation.

By the way please correct me if I am wrong.
Hopefully not :X

This only applies to VT 2
And I believe 99% of the caught SHINY Pikachu out there are gotten through hacking.















The reason my old calculation was not accurate was because I assumed from 0.01% that one is guaranteed to encounter a shiny pikachu as his 10000^th pikachus.
While Mysticman89 calulation took into consideration of the chance of encountering a shiny pikachu WITHIN 10000 pikachus.
Some of you may think that the days should be shorten if this is the case and this is because my assumption was dead wrong, resulting in a FAR FROM ACCURATE result.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Old post - In case it's needed for future reference
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Hi guys,

Here are some facts to answer your doubts.

This only apply to vf2

Rate of a Pikachu being SHINY = 0.01%

Number of Pikachu per wave = 5

Number of wave to find a SHINY Pikachu = 2000

Rate of a Pikachu wave = 1%(wave rate) * 30(total no. of waves)
= 1 wave in 10/3 runs

Change of meeting a SHINY Pikachu =10/3 * 2000
= 6666 RUNS!

Estimated time to catch 1 SHINY Pikachu
=6666(runs) * 2mins(time to complete vt2) / 60mins(1 hour)
= 222 hours
= 9.25 days of hardcore screen staring

[dubstep]

yeah its pretty stupid

para have 0.5% and i see them all the time in vf2

[justaperson]

*9.25 days later* CRAP I KILLED A SHINY!

[hellra1ser]

Apr 17, 2011 10:36:16 GMT -5 justaperson said:

*9.25 days later* CRAP I KILLED A SHINY!

Me too.!!

[charmander]

yea, i hope you dont sit through 9.25 days of playing just to kill it.

[Krono]

I love this game and everything i don't think i could justify 9 days for a shiny pokemon >.<

[penguin]

to be honest, i think the odds are completely fair, what makes them so sqecial and unique is the fact that they are hard to get. If the odds were like paras, where everyone has them, a shiny pikachu wouldn't even be an achievement

[hirschi15]

Apr 17, 2011 18:30:34 GMT -5 penguin said:

to be honest, i think the odds are completely fair, what makes them so sqecial and unique is the fact that they are hard to get. If the odds were like paras, where everyone has them, a shiny pikachu wouldn't even be an achievement

I agree. Just like in the real game, they have to be rare or everybody will have one!

[charzard]

im pissed i cant beat mount moon

[hirschi15]

Lots of video guides on these forums if needed, for any starter

[quentin123abc]

......it's not that hard, why do people keep thinking that it will take forever to find one. I haven't found one yet because i'm not trying to but still, just play for a bit and one will show up sooner or later. P.S. it wont take 9.25 days -_-

[Mysticman89]

Theres some dubious assumptions and not entirely right use of probability at work here...

So, given an average of 1 wave of 5 pikachu's per 10/3 runs, and 0.01% chance of any given pikachu to be shiny, or alternatively, a 99.99% chance that a given pikachu is *not* shiny.

This gives the probability of seeing 'n' pikachus in a row that are *not* shiny to be (9999/10000)^n. The probability that you will see a shiny pikachu within n pikachus is thus 1-(9999/10000)^n. In order to have a 50% chance of seeing a pikachu then, you'll need to have encountered n=log(0.5)/[log(9999)-4]=6932 pikachus, rounded up.

That means, at 1 wave of 5 pikachus per 10/3 runs, you'll need to do 4622 runs (again, rounded up). At 2 minutes per run, that comes to just over 154 hours, or around 6.4 days of straight playing to even have a 50% chance of having seen a shiny pikachu. (Note that this is different from having a 50% chance that the 6932'nd pikachu is shiny, it's instead the chance that any one of the 6932 pikachu's you've seen is shiny, and it could well have been the first one you saw.)

Notice that even at 10k pikachu sightings you don't have a 100% chance of having seen a shiny pikachu (in fact, you only have about a 63% chance at 10k sightings). It'd also take infinite pikachu sightings before you were garunteed to have seen one, which is in line with what you'd expect for something random. In order to have a 90% chance of having seen one, you'd need to have seen closer to 23k pikachus, which would take 21.3 days or so of straight playing.

These numbers aren't any more encouraging that the ones given in the OP, but at least they take into account the random nature of things, since most of us won't be catching tons of shiny pikachus, so the long term average of 1/10k doesn't really apply to any one of us individually.

[quentin123abc]

Apr 17, 2011 20:05:38 GMT -5 Mysticman89 said:

Theres some dubious assumptions and not entirely right use of probability at work here...

So, given an average of 1 wave of 5 pikachu's per 10/3 runs, and 0.01% chance of any given pikachu to be shiny, or alternatively, a 99.99% chance that a given pikachu is *not* shiny.

This gives the probability of seeing 'n' pikachus in a row that are *not* shiny to be (9999/10000)^n. The probability that you will see a shiny pikachu within n pikachus is thus 1-(9999/10000)^n. In order to have a 50% chance of seeing a pikachu then, you'll need to have encountered n=log(0.5)/[log(9999)-4]=6932 pikachus, rounded up.

That means, at 1 wave of 5 pikachus per 10/3 runs, you'll need to do 4622 runs (again, rounded up). At 2 minutes per run, that comes to just over 154 hours, or around 6.4 days of straight playing to even have a 50% chance of having seen a shiny pikachu. (Note that this is different from having a 50% chance that the 6932'nd pikachu is shiny, it's instead the chance that any one of the 6932 pikachu's you've seen is shiny, and it could well have been the first one you saw.)

Notice that even at 10k pikachu sightings you don't have a 100% chance of having seen a shiny pikachu (in fact, you only have about a 63% chance at 10k sightings). It'd also take infinite pikachu sightings before you were garunteed to have seen one, which is in line with what you'd expect for something random. In order to have a 90% chance of having seen one, you'd need to have seen closer to 23k pikachus, which would take 21.3 days or so of straight playing.

These numbers aren't any more encouraging that the ones given in the OP, but at least they take into account the random nature of things, since most of us won't be catching tons of shiny pikachus, so the long term average of 1/10k doesn't really apply to any one of us individually.

Interesting, i understood most of what you said ;D

[charmander]

Apr 17, 2011 18:31:13 GMT -5 hirschi15 said:

Apr 17, 2011 18:30:34 GMT -5 penguin said:

to be honest, i think the odds are completely fair, what makes them so sqecial and unique is the fact that they are hard to get. If the odds were like paras, where everyone has them, a shiny pikachu wouldn't even be an achievement

I agree. Just like in the real game, they have to be rare or everybody will have one!

I never saw a shiny in any of the real games. I didnt even know they existed for a while.

[FireOpal]

Apr 17, 2011 23:57:45 GMT -5 @charmander said:

Apr 17, 2011 18:31:13 GMT -5 hirschi15 said:

I agree. Just like in the real game, they have to be rare or everybody will have one!

I never saw a shiny in any of the real games. I didnt even know they existed for a while.

Me too. Only when I started using the internet and interacting with other poke enthusiasts and rpers a few years ago did I realise.

My sister only found out a couple of months ago when one turned up on her game for the first time in 11 years...