Tales & Trails of a Traveling Wiseguy

Yes, if one person in the group is ill, it's better they expose 13 other people in the room versus 19. But what's the chance that someone is ill? Your model ignores that factor. I get it, it's infeasible to determine with certainty. But it can overwhelm everything else in the equation. To ignore it just because it's not trivial to quantify, and instead fall back to heuristics like "Fewer people in each room, that's a big win", is a form of the fallacy of binary thinking.

Moreover, if your model rests on the assumption that one person is sick with Covid to prove its payoff matrix is a big win, really that proves the model is flawed. If it can be assumed that one person in the group is sick then you should identify that person and exclude them. Otherwise you're just rearranging deck chairs on the Iitanic.