I don't understand how an odd or even number of players makes a difference, as a no lynch would still result in m/(n-1) regardless of the number of players.
In case of odd number of players players, an NL+NK brings the Mafia 1 step closer to victory as it reduces the number of players they have to NK.
Consider 4T vs 1M (odd number of players).
The Mafioso has to NK 2 players to win. If they decide on No-lynching, then Mafioso only needs to NK once.
Now consider 5T vs 1M (even)
Mafioso has to NK 2 players to win. If they decide to NL one Night, the Mafioso still has to NK twice.
For the most basic situation consider LYLO (odd), vs MYLO(even). In this case the Mafiosi have to NK once to win. In case of odd (LYLO), an NL reduces this to 0 and it's game over. In case of MYLO, an NL means they still have 1 Day.
I thought I understood more before
Or maybe you made a mistake. When you say "Consider 4T vs 1M (odd number of players). The Mafioso has to NK 2 players to win. If they decide on No-lynching, then Mafioso only needs to NK once
I'm sorry, but... in that scenario wouldn't that NL lead to a next Day 3vs1? Thus needing a mislynch and another NK for a Mafia victory?
(Unless you're considering the game ends with the mislynch because the Night+1's NK and thus the Mafia victory is a foregone conclusion)
Either way I parse your statement it looks like you're saying that a NL leads to less people the scum has to kill. I really don't get it, unless you wrote NL but actually meant to say mislynch.