[DISCUSSION] One Day Lylo

[BNL]

N Mafia Lovers
N+1 Vanilla Townies

One Day only. If a Mafia Lover is lynched, town wins. If a Vanilla Townie is lynched, or there is no lynch, Mafia win.

Using typical EV calculations, the EV is N/(2N+1), which is 1/3 for N=1 and approaches 1/2 for large N.


However, I suspect that the actual win rate will approach 0 for large N. I believe this is possibly due to the large amount of control scum have in manipulating their votes, and townies needing to find each other to work together to lynch a scum.

If town win rate is so low, shouldn’t town lynch randomly to maximize their winrate? Well, I think town

can’t

lynch randomly. I can’t think of a way that lets every player contribute to a random number that also results in getting in a random number, especially in a forum setting, where posts are displayed one at a time. You see, if all players contribute equally, the player who is going last will have a large control on the generated random number. Hence in order to lynch scum, players need to be able to both come up with a good random number and let a town player go last.

This would be in fact different if there was a town treestump. While they cannot vote, they can produce a random number, bringing the game close to EV. However, without a treestump, I don’t think a random number can be produced, and the true EV may be lower than calculated by traditional methods.

[popsofctown]

Not mafia (no informed minority).

It is true a town actually can't lynch randomly.

I think people are more likely to have fun when they're playing mafia. You could maybe use vengeful townies to get a setup similar to this one that is actually mafia, like:
3 Lover Goons
2 Vengeful Townie with bastard town secret lover role pm.
4 Town secret lovers
(Vengeful townie shooting vengeful townie triggers vengeful townie)
I suspect this setup retains the "random lynching would actually be better than human meta D1 dayplay" paradox.

[BNL]

This isn’t a setup I plan to run. Instead, it’s more for theoretical discussion.

[popsofctown]

Oh.

Yeah I think conclusions in OP are correct.

[Ircher]

Actually, the setup is broken for scum as they can force a no lynch since there is an equal number of town and mafia. Even with plurality, it would be too easy for all the scum to vote the same person right at the start.

Town needs to at least outnumber the mafia unless I'm missing something.

[BNL]

Ah, there are N+1 Vanilla Townies. Typo, fixed.

[callforjudgement]

You could just use a dice tag or the like to collectively generate a tamper-proof random number. Many moderators have a rule against provable randomness, but that rule isn't universal yet (in particular, it isn't in the site rules).

Without that, the problem is pretty similar to the famous Byzantine Generals Problem, but different enough in the details that I don't think the same solutions work. It might not be impossible, though.

[callforjudgement]

Incidentally, there's also a cryptography-based solution (in addition to the provable-randomness-based solution). Everyone independently generates a random number, then uses a cryptographically secure breadcrumb to prove that they've committed to a number without other people being able to find out what it is until told. Then everyone reveals their numbers, you check them against the breadcrumbs to make sure players didn't lie about their numbers after seeing other players' numbers, and then you add them all together and take the result modulo the number of players in the playerlist.

[callforjudgement]

You could also just lynch the first player on the playerlist. (Sucks if you were excited for the game, I guess.)

[popsofctown]

Uh, CFJ, isn't #7 just, "also you could use cryptography to prove your provable randomness instead of using dice tags"?

[Irrelephant11]

You could also just lynch the first player on the playerlist. (Sucks if you were excited for the game, I guess.)

this is probably what would happen for maximum EV

[BNL]

You could also just lynch the first player on the playerlist. (Sucks if you were excited for the game, I guess.)

I don't think that works. No one would sign up for the game because the first to sign up will lose.

This extends to any "Lynch the xth player on the list" strategy.

[callforjudgement]

That doesn't prevent the strategy working. It just prevents the game getting players, which is unrelated to optimal strategy for town as it happens before alignments are randomized.

[popsofctown]

This isn’t a setup I plan to run. Instead, it’s more for theoretical discussion.