Keltham borrows the coin at 0% interest!  That's the kind of trusting relationship they have!

(Anyone who recognizes Abadar's symbol should really know better than to ask this.)

The gold coin looks like the other 600 instances of this coin that he owns, with a picture of Abrogail's face on one side, and on the other side 'Sworn by Hell to be pure'.  At some point he needs to ask what Hell is swearing Abrogail to be pure about, but that's not important right now.

On close examination, a coin does look sufficiently physically symmetrical, with enough lingering asymmetry for identification purposes, to serve as a randomness source if spun.

"Okay, so this coin can land 'Abrogail' or 'Text'.  Now... actually, something else first..."

"First, I want you all to rescale your old lunch duck numbers to a 1-12 scale where 1 is super unlikely and 12 is super likely, so we're all on the same page about what the scale meant.  If you were picking a lunch duck number that meant something totally else, scale it instead."

"Raise your hands when you've done that, then let's say our commonly-scaled numbers once we've raised our hands."

"Oh, and don't update your estimate off what other people thought, this is just supposed to be your original estimate, but we're making sure all estimates are on the same scale."

3, 4, 4, 6, 4, 6, 6, 6, 8, 7, 4, 5!

And his is 3!

Now, again without taking others' opinions into account - especially considering that people might be using different real meanings for their scales, so who knows if anybody really disagrees - consider the chance that there will be duck for lunch, AND when Keltham spins this coin, it will fall Abrogail's-face-upward.  In other words, both things have to happen, so if the coin lands text-up, it doesn't matter if there's duck for lunch or not, the combined event didn't happen.

Generate new numbers for this combined event, same 1-12 scale from very unlikely to very likely.  Please stick to your original opinion and original scale, rather than guessing what others mean by their numbers and updating off those.

Raise your hand when you've got it, then everybody says their numbers.

2, 2, 3, 2, 4, 3, 4, 3, 3, 4, 2, 2

"And mine is 2."

"You may recall that shortly before the gods went to war - to be clear, I don't think there was actually a direct connection as such - I talked a bit on the Law of Dividing Gains From Trade, and one of the constraints was that identical agents receive identical pay."

"You've now generated two numbers, one for the chance that we have duck at lunch, and one for the chance that we have duck at lunch and that when I spin this coin it will land Abrogail's-face-up.  Raise your hand open if you think you could state an aspect of Law connecting these two numbers, raise your hand closed into a fist if you've given up on doing that."

Most of the hands go up into the air open, after a bit of hesitation.

He'll give a half-minute to anyone who doesn't have their hand raised in either way, and then ask people with raised-open hands to state whatever Law they had in mind when they raised their hand.

"...our numbers should have gone down. Because now it's two things that have to go right, not just one."

"They should have gone down by half," says Meritxell.

"Whether they go down by half depends on what the scale means.  Mine went from 3 to 2, because I'm taking the 1 of the scale to mean that something absolutely can't happen, and equal intervals to represent equal amounts of chance, so halving the interval from 1 to 3 gets me the interval from 1 to 2.  But it's fine if somebody else is interpreting their scale in some totally different way!"

"In fact, the aspect of Law I'd propose to govern here is that, when you have two events that both need to happen, the chance of that happening, cannot go up compared to the chance of just one event happening."

"Ione, for example, could've been tipped by the Whatchamacallit of Nethys that this coin is definitely going to land Abrogail's-face-up, in which case Ione could just give the exact same number she did before for the duck-lunch part.  But even Ione's number shouldn't go up.  By the way, Ione, thanks for being you, your mere presence here substantially expands the space of immediately relatable scenarios I can use for probability-theoretic examples."

"Thank you, I think."

The students seem persuaded that the number cannot go up. 

"Now, for the next demonstration... actually, task to run simultaneously while that's in progress.  Carissa, can your magic writing thingy copy what I write down on one paper scrap, to other paper scraps, without you knowing what was written?"

"There's supposedly a rare spell for that but Unseen Servant can't do it unfortunately."

"Noted, worth talking to Acquisitions about that or an item because this won't be the last time we run into this issue."

"For now, though, I first want to establish a common scale of probability before the next demonstration.  Please think of the chance we have a beef dish at lunch," that'd be around 3/12 in his own guess and memory, "on a scale where 1/5 means the same as the chance that you're first in line in a randomized line of five people, or 1/10 means the chance is around the same as first in line among 10 people.  If you're thinking something like, it's between 1/3 and 1/4, you're allowed to say 1 over 3-and-a-half, or even say 7/24, but you don't need to go complicated if you don't have a very exact notion of beef-lunch probability."

Raise hands when you have your number; when all hands raised, articulate guesses.  Keltham isn't tracking this one closely, he just wants to check that they're now working to an understood common scale of probability.

They do seem competent to use the scale, and to mostly assign beef-lunches between a third and a half chance of occurring today.

(Encouraging!  Like, not super encouraging or anything, but it could've gone wrong, and it didn't.)

Next, Keltham is going to distribute two propositions each to half the girls, to be assigned a probability on this kind of scale.

He'd be making 6 copies of each proposition, for everyone to look at privately, if he had easy copying.  Since he doesn't, he'll give each group a piece of paper to be passed around among themselves, and everybody writes down their own answer individually, on the same common scale they just used for beef-lunches.  Don't discuss it among yourselves and especially don't show your question to the other group.

Don't worry, it won't be a complicated proposition.  It's something that happens around here about a third as often as they have beef at a meal, going on his own memory.

On this occasion they will not-really-pseudorandomize by taking alternate girls from among 'desks', that is, if they were to be numbered in a seating chart, evens would go to one side of the room, odds to the other side, starting from Meritxell.  Can they sort themselves out while he writes the two propositions?

Here are Meritxell Jacme Pela Peranza Ione and Tonia, and here are Carissa Asmodia Gregoria Pilar Yaisa and Paxti.

Cool!  Keltham is writing on two scraps of paper while that occurs.

Meritxell et al get:

Chance over next 1 year that another god attacks Keltham, starting another god-war.

Carissa et al get:

Chance over next 1 year that another god-war starts.

They can take a minute to think, not much longer please.

When they're done, they can put their slips into two heaps.  Don't look at each other's propositions yet; Keltham will announce both groups' probability-sets first.

This is VERY STRESSFUL.

Security relays to Carissa that several girls are thinking whether to lie and if so what lie they're supposed to give.

This seems like PRECISELY the kind of situation where the lies would be discovered because they would have the WRONG UNDERLYING MATH SOMEHOW. Tell them NOT to.

Keltham could of course ask questions like these they'd all have no choice but to lie about, but hopefully first they can learn a bit more of the Law...

She puts down 1/3. The rest of her group puts it lower: 1/8, 1/4, 1/4, 1/10, 1/20.

The other group has 4/5, 1/4, 1/2, 1/3, 1/2, 1/8.

The 4/5 is Meritxell, reasoning that Keltham has been here three days and started one godwar so what are the odds they'll make it through the entire next year without a second one.

Keltham announces these results!  Whatever Group Evens (Carissa) was asked about, it was clearly something pretty unlikely; while whatever Group Odds (Meritxell) was asked about, it was clearly much more likely.

Okay, compare your propositions now!

So, all y'all consider yourselves to be 'Lawful' Evil, huh.

....wow, that's - 

It's a test you can't lie on, is what it is (though also even if you are telling the truth if you're bad at truth you'll get it wrong). 

"Can we argue with the other group about who is right?"