okay, let me try to follow Jimmm's quote anyway.
obligatory setup:Row1 Detective, 1-shot Commuter, Goon Cop; 1-shot Investigation Immune + Serial Killer
Row2 Watcher, Jailkeeper, Psychologist; 2-shot JOAT
Row3 1-shot BP Townie, Jailkeeper, Bodyguard; Traitor Knows MafiaRow4 1-shot BP Commuter, Psychologist, Detective; Mafia Knows Traitor
Column1 Watcher, 1-shot BP Townie, 1-shot BP Commuter; 2-shot JOAT
Column2 Detective, Jailkeeper, Psychologist; Mafia Knows Traitor + Serial Killer
Column3 1-shot Commuter, Jailkeeper, Detective; Traitor Knows Mafia + Serial KillerColumn4 Goon Cop, Psychologist, Bodyguard; 1-shot Investigation Immune
If Ichi was a Mafia Traitor in a TKM setup, he knew that the Town PRs are either Commuter, JK and Detective (Column 3) or BP, JK and Bodyguard (Row 3).
that's right
In the case of Column 3, which we now know is the real one if Ichi is lying, then he's fine, Psychologist is a safe claim.
yes
But in the case of Row 3, [...] The four claims would then be BP, JK, Bodyguard and Psychologist, and there are no possible setups which have a Psychologist and two of the others - the only possible setup with these four claims is Row 3, which excludes Psychologist.
that's right too.
So a Traitor in TKM would absolutely not claim Psychologist without more information about what other roles are present.
So, the argument here is that, although he does not immediately get counterclaimed, his claim is still not good because it requires two of the other claimers to be false in order to be true. The other claims only require one claim to be false - the psychologist claim. Then they are in Row3. So, upon analyzing it, we would come to the conclusion that his claim is false, and lynch him, which means he really only had 50% safeclaim chance, not 100%.
That seems to be true, but I honestly doubt how relevant it is. I think whoever fakeclaimed analyzed his probability, like ash did, but I doubt that he thought this far. Maybe he did. This point is not completely irrelevant.
But it is a pain to follow, because you explain so little. that's why I refused to dig into your setup posts before.