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Finally caught this sucker! Alright! And this shiny magikarp too Recent Shuffle addict here. - HaHa. Share your pokes here! I'd love to see them ")

Those pokemon with the PID reroll are marked as illegal because they ARE illegal. Is not a bug to report an illegal pokemon as illegal, bugs are legal pokemon marked as illegal and illegal pokemon marked as legal. Just because older release did not check this legal cases that not means those pokemon are legal, this pokemon always were illegal but now PKHeX have been updated to detect those cases. The check is not the same in gen 3, 4 and 5 pokemon because the PID and IV is generated with different methods depending on the origin game or type of encounter, in facti in most of the gen 5 cases all PID-IV relations are possible, because the RNG was better than older games, that is way gen5 are not illegal after reroll. The same happens with gen 3 and 4 pokemon hatched from eggs, probably a PID reroll wont make them illegal because eggs can have almost any PID-IV value if they were day care eggs. It could be helpfull to have a PID generator in PKHex like Pokegen, but there is none yet and those programs have working generators that can be used, that is why PID generator have not a mojor priority. Keep in mind even with that it would not be possible to make a PID reroll like the current button that instantanly gives a valid PID for any values, in most PID generation methods not every values are possible, and even that to find one in particular would require a brute force algorithm that could take minutes or more. From now if you just want to make a gen3/4 into shiny you can try to reroll the SID instead of the PID, in recent commits a feature was added to make the pokemon shiny chaning the SID instead of the PID, and that would allow a shiny reroll for most encounters without making the pokemon illegal. To use that you only need to control-click the shiny button.

As suggested above, use RNG Reporter to generate something legal. New features require effort; if possible features are already done sufficiently by another tool (PID search/generation via RNG Reporter) it's better to spend my time doing other things rather than replicate something that works fine. Generation 3, 4, and 5 have these checks. Generation 1/2 checks are not implemented, and Gen6+ will never have any as any PIDIV/etc is possible.

Actually you can, but only using emulators, CFW and unofficial harware to read GB cart saves, none of that are accepted by Nintendo. You can play with N64 and GB emulator (unauthorized), then inject the save into the VC with CFW (unauthorized), or use a GB cart save reader (unauthorized) and inject the save into the VC with CFW (unauthorized). Both options will make the pokemon illegal. That means there is no issue to fix. Staidum pokemon are not possible to obtain in VC and Gen 7 saves with Nintendo official methods. An illegal pokemon marked as illegal, working as intended. Of course this could change, imagine if Nintendo release Stadium games in Switch/WiiU with connectivity with 3DS VC games, if that happens those pokemon will be legal from that moment. This is improbable but is similar to gen 2 pokemon, they are currently illegal in VC and gen 7 saves but from the day when gold/silver are released in VC mode gen 2 pokemon will change to legal...except crystal and stadium 2 (including move reminder) pokemon.

Stadium Pokemon are legal in GB Cart saves but illegal in VC saves or gen 7 saves. Gen 1 cart->Gen 1 VC is not possible with official Nintendo methods, and that make this pokemon illegan in vc or gen 7 saves. Online battles are irrelevant, the purpose of PKHex is to detect pokemon impossible without When you load a gen 1 save PKHex ask if you want the program to treat the save as a gb cart save or a vc save, the first allow any pokemon legal in GB saves, like gen 2 tradebacks and stadium gifts, the second option only allow pokemon available in VC games. If the pokemon is traded to a gen 7 game then it will be considered a VC pokemon making it illegal if it has a Stadium origin. I made an Stadium level 20 hitmonchan with last commit of PKHex and it is detected legal in a GB cart save.