PokéBase - Pokémon Q&A

# What is the probability of getting three shinies in a horde?

1,637 views
If that happened to you, dude, buy a lottery ticket. No joke. Do whatever the hell you feel like, because either you are God, or the luckiest person alive. And either way BOOYAH!!
Unfortunately, you would have to KO two of the Shinies D:
True. But you still are either God, or the luckiest person alive.

There is a 1/4096 chance of finding one Shiny in a horde. Fortunately for you, I just finished a probability unit in Science. So you want the chances of finding three Shinies in a horde. Well, for that we multiply 1/4096 by itself… three times!

1/4096 x 1/4096 x 1/4096 = 1/68,719,476,736

You have approximately a one in 70 million chance of getting three Shinies in a horde.
(That's a really, really, really small chance.)

Just for the heck of it, here's the probability of finding five Shinies in a horde.

#1/1.152921504607e+18

(It's so small my calculator had to put in some form of notation.)

selected by
Let me know if I did my math wrong :)
5 shinies = 1/4096^5 = 1/1,152,921,504,606,846,976. This is what your calculator is trying to read.

The other answer given is ("fortunately") "completely" incorrect. Here's why;

The chance for a Pokemon to be shiny is 1/4096 (3/4096 if you have the Shiny Charm).
In a horde, there are 5 Pokemon, you have to consider 3 to be shiny and 2 to be non-shiny. That means you get 1/4096 1/4096 1/4096 4095/4096 4095/4096 = 16,769,025/1,152,921,504,606,846,976 = 1,4545 10^-11.
However, you have to consider picking them in a different order (if you had only two Pokemon and ask for one to be shiny, the orders AB and BA wouldbe equal for you ("one shiny"), but they are different possibilities nonetheless). For that reason, you have to multiply that number by 10 (different ordering possibilities - if shinies are A and non-shinies B, then all of those would be AAABB, AABAB, ABAAB, BAAAB, AABBA, ABABA, BAABA, ABBAA, BABAA, BBAAA <- 10 possibilities), so ultimately, you'd get
167,690,250/1,152,921,504,606,846,976, or roughly 1,4545
10^-10
. In percents, that's *1,4545 10^-8 %, or 0,000000014545 %.**

Now, with the Shiny Charm, the game generates another 2 codes trying for a shinies, which effectively means the chance of 3/4096 for a shiny. The calculation will be the same, except with the chance 3/4096 for shiny Pokemon and 4093/4096 for non-shiny Pokemon. The results you get is 4,523,215,230/1,152,921,504,606,846,976 which is equal to *3.9233 10^-9 % or 0,00000039233 %**.

edited

...