For the CC case, if it is truly Nightless (rather than the OP setup) then you lynch one at a time until you have lynched the fakes. This means you are either in 2:8 Nightless (60%), 2:8:1 Nightless with IC (EV = 7/9, ~78%), or 2:8:2 Nightless with ICs (EV = 14/15, ~93%) with equal probability, for a total EV of ~84% (113/135).
Two fake claims would be 1/2 1:8 Nightless (7/9), 1/3 1:8:1 Nightless (8/9), and 1/6 1:8:2 Nightless (1), for a total EV of 23/27, ~85%, so 1 fake claim is best.
Basically, don't used named townies in Nightless unless you are very careful about it.
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