PokéBase - Pokémon Q&A
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In the FireRed/LeafGreen/Emerald Union Room, your trainer is represented to others with a trainer class. How do the gen 3 games determine which trainer class is assigned to each player? Is it something with the ID number or simply an RNG?

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I'm not sure about the gen 3 games, but in future generations (namely gen 5) I have found that your Union Room sprite depends on the trainer class selected on your Trainer Card.

Edit: I just checked Bulbapedia. It doesn't mention how the trainer class is selected for generation 3 games. I also checked Serebii. It doesn't mention it either... Whatever the case, it seems selecting it on your Trainer Card wasn't a feature until Gen 5.

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I couldn't find anything on the Union Room specifically, but I did find an article on Bulbapedia mentioning that the trainer class you are seen as in other games when other people visit your secret base is determined by the gender of the player and the 256 modulo 10 of your Trainer ID number. I also found a separate article stating that this same method was used when determining the trainer class of other players when you encounter them in the Battle Tower after mixing records with them. As a result, I think its safe to assume that this method is also used when determining trainer class within the Union Room, but if you want to test it for yourself, feel free to (I don't own any Gen 3 games, or else I would have already). Hope this helped!

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thx! u r the first person to actually help me with this! pretty sure this correct, too, so thx!
np, happy to help!
i have checked, and confirm that this is true.
Ah nice, thanks a bunch!