[SETUP] Our Love Must Remain Hidden

[implosion]

8 Town Lovers

2 Mafia Lovers

All lovers are in pairs, and all pairs are the same alignment (one pair of mafia lovers, four pairs of town lovers). So town pairs are also masons.

Nightless.

If the mafia lovers are lynched, they have an opportunity to win the game if they can accurately name

every

lover pair still alive. For instance, if the town mislynches twice and then lynches the mafia pair at 2:4, the mafia would have to pair off those four players correctly to still win the game.

EV:

Assume that town never claims any lover pairs, because it's sort of strictly bad for them to from an EV perspective. An accurately-claimed lover pair might as well already be lynched.

There are 3 possible ways for 4 townies to be paired up, 3*5 ways for 6 townies, and 3*5*7 ways for 8 townies. Assume mafia guesses randomly among these options.

Then EV for mafia (a bit easier to calculate) is:

(1/5) * (1 / (3 * 5 * 7)) + (4/5) * ( (1/4) * (1 / (3 * 5)) + (3/4) * ( (1/3) * (1/3) + (2/3) ) )
≈.48. So town EV is ~.52.

Interestingly, of that 0.48 EV, 0.4 of it comes from the mafia getting 3 mislynches! So only ~8% of the time will mafia actually win off of figuring out the lovers... assuming random choices, which is probably pretty far-flung from reality. In reality, the merlin-inspired mafia last chance means that the town has a significant burden to obfuscate things.

[mith]

I feel like I've seen a similar suggestion before? It's a good one, though.

[Gamma Emerald]

I don't like that scum's job gets easier as town mislynches, sorta makes the game a slippery slope

[mith]

I mean, that's true of any* game. This one just has a different slope than, say, Vanilla Nightless.

*I'm sure a weird counterexample could be constructed.

[BBmolla]

This one is good

[Gamma Emerald]

but like the slope is much steeper, as with the last chance thing, in 6p it's like a 1/3 shot barring partner tells/untells

[mith]

It's actually less steep, in a sense. The balanced version of this without the extra Mafia win condition is 2:6 PairedLovers Nightless (aka True Love) - two mislynches there would already be a loss, which is as steep as you can get. Adding the extra condition here gives the town an extra mislynch for the trade off of a small chance of a loss on a successful lynch (about 8%; 40% of the Mafia EV is from winning normally).

The main downside to this setup is that there's less information for town to work with, in the sense that the Mafia pair should play similarly to the Town pairs (trying to keep their Lover alive). They are less concerned about being outed as a pair, but that's about it. In that sense, a bigger setup with two Mafia pairs might be more interesting (though also more prone to replacements and the like).

[callforjudgement]

I mean, that's true of any* game. This one just has a different slope than, say, Vanilla Nightless.

*I'm sure a weird counterexample could be constructed.

In Vote for Town Mafia, a mislynch makes things notably harder on scum for the rest of the game. (That said, they have to get the mislynches to win, so it's something that they're going to have to live with if they want to win.)

[mith]

Harder in the sense that it's easier for a scum to get mislynched if there are more of them, but not harder in the EV sense. Obviously it's easier to win if the first mislynch is day 1 (1:6, EV 5/7) vs. day 3 (1:4, EV 3/5), because the former reduces to the latter if the remaining scum doesn't take advantage of the extra two days.

(That's a neat setup, too, and obviously easy to balance since it's just flipped from Nightless.)