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What is the chance of getting a Spinda in ORAS with full potential, Contrary ability, shiny, and possibly having Psycho Cut as a move (I don't really care about the level)? Should I just keep the shiny Spinda(s) I have collected and move on?

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Why would you want a Spinda in the first place? If you're a shiny hunter, just keep your shiny Spindas and move on. If you want to use it in battle, use a Malamar.
what did sumwun do to you with that comment
The person has their rights to use what they want.
I'm not saying he can't use Spinda; I'm just saying that Spinda is almost always worse than Malamar.
To be fair, it was worded a bit condescendingly.
Okay, I apologize if my comment offended anyone.
Hidden. (12 characters)

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Because you mentioned having several shinies already, I'm going to assume that you've already maxed out Spinda's search level at 999. This would make the probability of finding a shiny ~1/476 without the shiny charm, or 1/173 with it.
In case your search level is below 999, here's a handy DexNav shiny calculator.

At a search level >100, the probability of...

  • hidden ability: ~23%, or ~23/100.
  • 3-star potential: ~12%, or ~3/25.
  • an egg move: ~83%, or ~83/100.

(the three statistics above are from Bulbapedia. Statistics for lower search levels, if needed, are available there.)

With the egg move, however, there is the additional chance that the egg move will not be Psycho Cut. In ORAS, Spinda has 16 egg moves, therefore, the probability of Spinda having PC, on top of the probability it has an egg move at all is 1/16 x 83/100, which is 83/1600 or ~1/20.

Final Calculation

The probability that an encountered Spinda will have all of these properties would be the product of all the individual chances multiplied together.

Without Psycho Cut; no help from Shiny Charm:
1/476 x 23/100 x 3/25 = 69/1,190,000 or ~1/17,247.

Without Psycho Cut; help from Shiny Charm:
1/173 x 23/100 x 3/25 = 69/432,500 or ~1/6,268.

With Psycho Cut; no help from Shiny Charm:
1/476 x 23/100 x 3/25 x 1/20 = 69/23,800,000 or ~1/344,928.

With Psycho Cut; help from Shiny Charm:
1/173 x 23/100 x 3/25 x 1/20 = 69/8,650,000 or ~1/125,363.


So, yeah. Overall, your chances are not that great. However, keep in mind that these chances are for single encounters completely exempt from a chain. Chaining will, naturally, increase these chances, but it was hard enough finding the statistics for everything here (even Bulbapedia only had tested estimates, rather than exact figures). I'm not sure that I have enough patience to try and find out just exactly how much each part increases at which encounter intervals. So for now, here's what I got. Hope this helps.

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This helps a lot! Thanks for the various calculations and the time that you spent to write this response out!