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Normally when you fight Team Go Rocket, you encounter their first Pokemon after you defeat them(example, I first fight a Snover so I encounter a Snover after I defeat them). However on a few occasions I have actually encountered their second Pokemon after beating them(I have encountered a couple Cloyster when it was the second Pokemon the team I faced). If that's possible, then I could possibly encounter their third(and usually most powerful) team member after defeating Team Go Rocket? What are the chances of each?

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Second is like 5 or 10% and third is like 1% don't have a source tho
hard. but if you battle the same one and defeat them over and over you get there other Pokémon.
Doesn't answer the question

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The exact chance is unknown, but some people say that for certain grunts is around 85% for the first pokémon, 15% for the second, and 0% for the third (meaning it's impossible). Others only give their first pokémon, this includes the Leaders. Giovanni always gives the last pokémon in non-event battles.

This bulpapedia article shows what the Team Go Rocket grunts can give:
https://bulbapedia.bulbagarden.net/wiki/Team_GO_Rocket_Grunt_(Trainer_class)#Trainer_list

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