The SWORD for 6 players?

Use the Lifepaths and Settings
When bringing in NPCs, use the lifepaths and settings as a guide. You can bring in someone who shares the same lifepath with you. You can bring in NPCs from your [lifepath] setting – so long as it makes sense.

I Don’t Know You
If you don’t share a lifepath or a [lifepath] setting with an NPC, then you cannot use Circles to bring him into play.

The Burning Wheel​, page 379

Whoops. Looks like the correct answer was “say no”?

There’s also the “is it reasonable” test. Circles is for bringing NPCs into play. Sometimes it’s used off-label for retroactively establishing relationships with NPCs. It’s not for turning enemies into friends. That requires a social skill at the least, and during combat? I’d say no.

The way I see it is this: the player states their task and intent, and then the GM arbitrates who those two things interact with the game mechanics and the fiction. Often, this will involve breaking tasks and intents down into multiple subtasks and subintents. The task must be something that could reasonable accomplish the intent, given the established fiction Sometimes, a player (especially one who is unfamiliar with how Burning Wheel works) will state a task that is not compatible with the intent or the fiction. In that case, the GM is authorized to disallow that particular combination of task and intent. You are allowed, for example, to disallow a player from attempting to fly to the moon by simply flapping his arms.

Returning to the pet spider example, let’s ask the question: what was the task and intent? The players intent appears to have been something along the lines of “get this spider to not be attacking me”. The proposed task seems to have been “recognize the spider as my long lost pet”. That doesn’t seem like something that is reasonable, given the fiction and the mechanics.

I think it all comes down to the ‘Intent and Task’ chapter in the Hub. So many issues that come up in BW can be resolved by going back to that chapter and making sure you are following it.

‘Say Yes’ only means anything if GM and player agree on the Intent and Task. There is no ‘Say No’, there is only ‘let’s back up a few steps and work out if there is an Intent and Task we will both agree on’.

This is the process I would be following in this case:

Ha ha, that’s a good one! But we need to back up a moment and figure out exactly how we can resolve this.

What is your Intent in declaring the spider is a pet? Do you actually want a pet? An ally? Do you want to declare a fact about the world? Do you simply want to survive this encounter?

Some of these Intents I may not be able to agree to because they violate an already established fact about the world, or interfere with plans I have in motion. But we can possibly agree on something more appropriate.

Once we’ve worked that out, how are you going to achieve your Intent? If you want to escape or make an ally, we will roll a physical or social skill (or Fight/Duel of Wits) as your Task. Other Intents may require out-of character/meta actions like a Wise or Circles roll.

If the failure result is not going to be interesting enough, I will Say Yes rather than have you make a roll, or give a low Ob roll for advancement.

Edit: took too long to write this post so did not see the previous response saying much the same thing!

Could the character dual of wits the intelligent spider to not eat him by telling a fictitious story about how the character once saved, nurtured and reared a baby giant spider?

What would the spider hope to get out of participating in such an argument? He was already going to eat the humans. In this case, I’d probably handle it as a straight-up Falsehood roll with the Spider’s Will as the Ob possibly with an added penalty on top, depending on how plausible such a story would be given the game’s established fiction. The character in question had better talk fast, and be very convincing; he only has a few seconds to sway the creature’s chamberless arachnid heart before it injects its venom into his neck.

This is no different than getting the bandits to spare you by spinning them a tale of how you did their fathers a great service once. Sometimes that’s acceptable in a game, but most of the time that’s not an acceptable intent, at least in my games. You can’t halt someone trying to kill you by talking; the enemy’s just not going to bother to stop and listen.