PokéBase - Pokémon Q&A
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I've never encountered any shinies in Random Singles and Doubles, but in Random Triples I've encountered two shiny Pokemon in two different matches.

So, I want to know what is the chance of battle with a shiny Pokemon in random battle, random double battle and random triple battle per battle in Pokemon showdown?

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I'm pretty sure Smogon has each of those pokemon set for a move set and ability. Meaning that there are 0 shinies in random battles as of date.

I'm not sure, but it would be easiest to implement pokemon for random battles in that fashion.
recently when i was playing random triple battle,i got a shiny macargo.
Useless Q :P
I don't think it's a useless question.