I haven't had this problem since 1990, when I started a new campaign with mostly people I had only just met, and one of the players started off with a character who turned out to be a serial killer with serious pscho-sexual pathologies. After maybe half-a-dozen sessions it became clear that the character didn't fit the game, and she was written out and a new character who did fit the game was introduced.As a player, I also want to be the Grand Hero of Destiny, but every time our group talks to someone, it always ends up the same way. With a face palm, them muttering "these people are idiots", and wishing we would just GO AWAY already. Every. Single. Time. Doesn't matter if it's a prince or a shopkeep. Doesn't matter who's the DM or what genre game. Always ends up the same way. Always.
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So, open ended question - how do you keep this from happening?
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For DM's, the second side of the same coin. How can you keep up a truly "heroic" or "epic" feel when your Rogue is pickpocketing the rest of the party, the Bard is trying to sleep with everything in sight, the Barbarian is grappling random strangers hoping for a bar brawl, and you're trying to tell the story of "An elf, an orc, and a halfling walk into a bar" without it being the start of some joke?
I don't mandate that all PCs be connected - I leave this to the players, and sometimes it emerges organically and sometimes integrating the PCs is a challenge that I have to deal with as GM.The other thing I've found as a GM is that the PCs have to have something they care about in the game world written into the fiction. If they are truly rootless, vagabond murderhobos and they couldn't care less if the town next door is burnt to the ground, then they'll generally act like it. If you want players to not act like witless morons, they have to have something their characters value, something they're willing to protect, and make sacrifices to protect.
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In reference to the above, as a GM I now mandate that every PC will have some element of their background that ties them to every other PC in the party.
But I generally do require the players to give their PCs backstories and motivations that link them into the gameworld - and then, in play, I make these things matter (both as colour - eg NPCs will recognise a PC, or know something about his/her uncle, or notice that the PC is an out-of-towner and make a fuss about it - but also as elements in the situation that is driving the action). And in my experience that's enough.
The situation that I as GM set up doesn't have to be that interesting or engaging to be more engaging than wanting to pick pocket your fellow party members, or wanting to have your imaginary avatar have off-screen sex with imaginary people. In my experience it's been enough that it (i) speak to whatever concerns the players have built into their PCs, and (ii) not be a railroad.