When setting up scenarios for your game, do you figure out what the mission objectives are?
Mostly, yes. How the players go about meeting the objective, or if they really do at all, is entirely up to them. If they get stuck I don't drop hints on how they're supposed to proceed, and I stay open to ideas and solutions I hadn't anticipated. But in principle, the job is the job.
I especially always have a mission/adventure ready to go for the beginning of a campaign. Even in a sandbox campaign, a new group doesn't have the information needed to make really informed choices as players, so I still start with something directed as they get their feet under them.
As time goes on some groups start picking their own goals. In D&D I've had groups decide to start a mercenary company, or build a castle at low levels before name level. In Traveller its been things more like "you know, we should get out of this system for a while," or "can we do a salvage mission to earn some credits? Is there word about anything like that going around?" and then I can generate an adventure around that, either directly related ("funny you should mention that, there is a ship overdue") or just at the same time/place ("first thing you get in the new system is an SOS broadcast that they're evacuating the highport and need all ships"). So that's player directed gaming of a kind, but it emerges organically over time rather than being something I start with.
Once and only once I GMed for a group that had talked during the week about how to pull off a heist of an NPC they'd met, without warning me ahead of time. I had enough prepped I didn't have to break and generate anything new so I just ran for it. One of the better sessions I've run, but not due to being my idea, just due to having proactive players and me keeping up.
Similarly, I'd run for players signing up with the villain, pulling a Yojimbo and playing both sides against the middle, stealing a ship, robbing a bank... but its not the way to bet on a weekly basis, and I don't suggest all those things or it would just be me playing for the players.
And how do you set those mission objectives?
Typically they're intrinsic to the concept. If the job is keep a patron alive while he hunts a neo-Tyrannosaurus Rex, then that's the mission objective. Keep the patron alive, help him bag a genetically re-engineered T-Rex. What could go wrong?
The challenge with Traveller GMing is more coming up with enough complications and twists to have a satisfying adventure. Instead of a simple "go out, find the T Rex, shoot the T Rex, come back" adventure (what could go wrong? have a rival hunter after the same game and only the first one wins, have some attempted sabotage from that quarter, have terrain difficulties, have a forest fire to survive or a solar flare disrupting comms and electronics, whatever you can think of and more.
Added:
Not mine, and not directly what you're asking, but here's an old post about someone else's approach to mission generation. I don't actually share his mania for last minute adventures, but I still found it useful.
In my gaming career the only sessions I could easily improvise were those for cyberpunk games. I could create a scenario with 5 minutes notice, and extend on the fly. I had a blast, and played alot. More recently, with some old school D&D and now Traveller (players are my two sons) I've been...
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