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So I was playing Smash Bros with my pals and one of them (a fellow Pokemon enthusiast that sadly didn't have Z-A) asked me how Pokemon Legends Z-A worked. I agreed to show him and walked into Wild Zone 2 at night to demonstrate how to catch a Pokemon. While looking for a Pokemon to catch, I heard that heart stopping signature chime. Spinning around, I saw a shiny female Magikarp swimming in the water. I caught it and celebrated while my friend stared in awe. But then I heard the chime again. Turning around one last time, there: another shiny female Magikarp.

What are the chances of this happening?? Or am I an idiot and it's just adding the shiny chances or something? Please let me know!

ago by
Forgot to say, I don't have a shiny charm

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Best answer

Simple answer

Generally, the chance of finding 2 shiny Pokémon in succession is (1/4096)^2, which is 1 in 16,777,216, or about 0.000006%. This is found by just multiplying the rates of two independent events together.

With the shiny charm, it's (1/1024)^2 = 1 in 1,048,576, or about 0.000024%.

Detailed answer

The chance of the specific scenario of finding 2 shiny female Magikarp in Wild Zone 2 at night is a bit more complicated.

Firstly, there are 8 Magikarp in Wild Zone 2 at night (11 during daytime).

The chance of a shiny female is the shiny rate multiplied by the female rate: (1/4096)(1/2) = 1/8192.
The chance of a Magikarp not being shiny is 4095/4096.

You got 2 shiny female Magikarp and 6 non-shiny Magikarp.
Multiplying all the rates together, we get (1/8192)^(2)(4095/4096)^(6).

However, we need to account for the fact that there are multiple ways to spawn 2 shinies out of a group of 8 Pokémon. For example, if you imagine that each Magikarp is numbered as #1, #2, and so on, you could be in a situation where #1 and #3 were the shiny ones, or a different situation where it was #6 and #7, or any other pair. Since we don't care which ones were shiny, just that 2 of them were, all of these situations are valid possibilities.

There are (8!)/((2!)(6!)) = 28 ways your situation can happen. I won't get into it here but this is a good website to read if you want to know why (this is a combination without repetition).

Our final result is
(1/8192)^(2)(4095/4096)^(6)(28) =
33008172222147618234375/79228162514264337593543950336
or approximately 0.00004%.
With the shiny charm, it's about 0.0007%.

So your specific situation turns out to be a bit more likely than the simple answer, because it's accounting for the fact that you encountered a total of 8 Magikarp instead of just the 2 shiny ones, but it's still pretty unlikely. Nice find!

Source: WolframAlpha

ago by
selected ago by
Thank you so much!! You're always so great at your answers!
Seriously, how long did it take to calculate this? Or do you have a website that helps you or something?
Ah thanks a million