[OLD] Puzzle: Claiming Strategy

[Cogito Ergo Sum]

We don't do anything fancy, just the pointing. So 50% the Townie guesses correctly initially and if he guesses right, Mafia has a 50% chance of guessing correctly.

25% the Townie points at the Mafia and the Mafia points at the Townie -> town win.
25% the Townie points at the Mafia and the Mafia points at the Supercop -> 2 people are pointing at the Mafia, 1 at the Supercop.
50% the Townie points at the Supercop and the Mafia points at the Supercop -> 2 people are pointing at the Supercop, 1 at the Mafia.

Thus, instead of having the Townie guess when faced with a successful counterclaim, you just lynch the guy the Townie didn't point at for a 75% EV.

[Cogito Ergo Sum]

Probability of winning when cop actually has results: 3/4, from the previous problem.

This isn't necessarily true any more, since the scum can claim ignorant cop now instead of having to counterclaim the supercop fully.

There's also the added complication that in a certain scenario, getting the scum to claim first is probably beneficial for the town.

[Cogito Ergo Sum]

The strategy I proposed requires town to lynch any ignorant cop claim if there is a supercop claim pointing at an ignorant cop.

I don't see that anywhere?

And if that's true, how does the following hold:

-If the not-super-cop points at the mafia, we again have a 3/4 chance of winning (because it is the same result as if the cop were a supercop).

Surely, if supercop claims get believed over ignorant cop claims, the mafia has a 50% chance of winning in this scenario by claiming supercop. From a larger perspective, it's also not clear this situation is distinguishable for the town from the other scenarios (if ignorant cop points at mafia and mafia claims ignorant cop pointing at townie, the town has no way of knowing the made up result was correct).

[Cogito Ergo Sum]

Yeah, that is a lot of detail to leave out. I'd reconsider point 2 since town could benefit from arranging it so the scum claims first in certain scenarios (specifically, if there are two people pointing at him).