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The hero and his arch rival are staring each other down! This is it! We're getting the Ultimate Showdown of Ultimate Destiny... wait, why are they sitting down and playing a game of UNO?
Not all heroes and villains are actively out for each others' blood, some heroes are reasonable and tolerant, and a few baddies can be perfectly civil. On more extreme ends, enemies who are opposites (ideologically or otherwise) can engage in a peaceful activity to have a bout of diplomacy. But some scenes can show even the antagonists have a good side, likewise rivals can sit down and have a nice chat every so often. In the end, they're not there to engage in fisticuffs, though they may engage in a bout or two of social combat. Rather, they're there just to meet as friendly rivals and maybe, just maybe, win the other person over to their point of view.
Essentially, the heroes join the Villains Out Shopping. Occasionally, it will be a dinner date, and it can happen frequently when the hero is Living With The Villain. If the bout is meant to emphasize their mutual intelligence, they'll probably play chess.
Now, this all sounds very nice and cheerful, right? Maybe people don't have to hate each other, even if they're opposed? However, this can take an entirely different feel if the villain is a Houdini of Karma who has committed horrible crimes and is getting special consideration because he and the Hero share history.
This is used alot in the video game Super Mario, where Mario appears to be inviting Bowser to games such as Golf or Race Cars.
However the creator of Super Mario, Shigeru Miyamoto says, "If you're familiar with things like Popeye and some of the old comic characters, you would oftentimes see this cast of characters that takes on different roles depending on the comic or cartoon. They might be businessman in one cartoon or a pirate in another. Depending on the story that was being told, they would change roles. So, to a certain degree, I look at our characters in a similar way and feel that they can take on different roles in different games. It's more like they're one big family, or maybe a troupe of actors."
This means that Bowser will play the part of a brutal usurper one game, then just a large racer the next.
Mario and Peach don't hate Bowser. The whole cast likes getting together for friendly games.