OK, a shorter quick version of what I wrote before that was lost.
FlockeSchnee: Because going with a no-NK wouldn't make sense for the Mafia team?
Yes, this works off the assumption that there is always exactly one NK every Night. This means that even number of players will remain even and odd will remain odd. And if we have an even number of players we should use NL to change it to odd, which gives us better odds without reducing the number of lynch-attempts that we have.
FlockeSchnee: Generally, or just in this setup?
In any setup where there is a guaranteed odd number of NKs every Night. So nothing that can cause 0 NKs (Doctor, Blocker...) and nothing that can cause 2 NKs (Vig, Serial Killer...). In all setups where this is not guaranteed (including all closed setups), NL is very bad because we could potentially be wasting a valuable lynch-attempt:
e.g. (Good NL)
5 vs 1 - we have 2 lynch attempts before it's game over. If we first go NL and one person dies in the Night, then it's 4 vs 1 next Day and we still have 2 attempts with slightly better odds.
but
(Bad NL)
5 vs 1 - we have 2 lynch attempts. If we go NL and
two[ people die in the Night, then it's 3 vs 1 next Day and we only have 1 attempt left. Our NL wasted an attempt.
OR
(Bad NL)
5 vs 1 - we have 2 attempts. We use up one (mislynch), but during the Night the Doctor saves us and no NK takes place. Next Day it's 4 vs 1 which means we still have 2 attempts (3 total).
5 vs 1 - we 2 attempts. We NL, Doctor saves at Night, and it's 5 vs 1 next Day. We still have 2 attempts; the potential extra attempt that Doctor's save could have given us got wasted.
In both those later cases NL was a terrible decision. We got less attempts than we'd have gotten otherwise.
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And finally
Since NK is not compulsory, then depending on a payout from a Draw, a single-NK-setup like this one with an even number of players can be game over immediately with an nevereding NL-noNK-NL-noNK... cycle. e.g. 3T vs 1M game. Town should NL to increase their chances from 25% to 33%, but then Mafia doesn't NK to keep those chances at 25%. If neither team budges, the game ends in a draw. This leads to an interesting quasi paradox, where it's better for Mafia's overall expected payout to have smaller payouts for both win and draw. See posts 51 and 58 here:
https://www.quicktopic.com/53/H/e29TzE9YP6Ra