[SETUP] Trust Fall

[Kanna]

From [CHALLENGE] May Challenge! Has been run once here.

Trust Fall

7 Vanilla Townies

2 Mafia Goons

Nightless.
There are no eliminations during the day; instead, there is a Trust Fall mechanic. To Trust Fall, one player must post in bold: “I trust X” and the trustee, X, must reciprocate. Together, they will exit the game and their alignments are revealed.
Mafia cannot Trust Fall together.
Mafia win when they have both exited the game. Town win when Mafia outnumbers them.

[T-Bone]

I've queued it in the open queue for 9 players.

I saw someone suggest it might work better as a 10 player setup? Anyone out there thought about that?

[the worst]

ego
I like your setup kanna

[implosion]

This is neat. I think the one big problem is of course that if you screw up as town it is squarely your fault, but that's ultimately not an actual problem, just that I wouldn't want to play this with people who are going to be harsh about placing blame on someone. It's a good idea for another sort of different-angle-on-things type setup like purgatory and so on.

EV-wise... there are a few ways to approach this. It would depend on the strategy that the town uses and in practice they probably won't purely use a simple strategy but. I'm not sure if it's possible to do better than the strategy of town decides to collectively choose two people and force them to trust-fall each other each day, EV-wise. No matter what happens each day will end in a trust fall and so this is probably the only way to think about it from an EV standpoint. This does have an interesting side-effect which is that if the town picked both mafia then they would... immediately win, because the two mafia would refuse to trust fall together and presumably the town could infer that they're both scum.

With this in mind:

D1: 9 choose 2 = 36 pairs. 1 is scum-scum, 14 are scum-town, 21 are town-town. Thus,

1/36: town wins
14/36: go to 1:6
21/36: go to 2:5

At 1:6, town has to pair correctly 3 times in a row to win, which is equivalent to correctly picking the single mafioso to leave out of pairing. So their odds of winning would be 1/7.

At 2:5, similar recursive math applies:
1/21: town wins
10/21: go to 1:4
10/21: go to 2:3

At 1:4, town odds of winning are 1/5.

At 2:3,
1/10: town wins
6/10: go to 1:2
3/10: town wins

And at 1:2 the town's odds of winning are 1/3. So the total EV for town should be:

(1/36) * (1) + (14/36) * (1/7) + (21/36) * ((1/21) * (1) + (10/21) * (1/5) + (10/21) * ((1/10) * (1) + (6/10) * (1/3) + (3/10) * (1)))

Which is apparently *exactly* 1/3. I think this is entirely coincidental.

This setup actually might be significantly scumsided - I can't think of any factors intrinsic to the setup that would mitigate a scum-sided EV. And this is assuming that the town actually does get wins out of those cases where they force two scum to pair with each other and they refuse to pair, which in turn is assuming that townies are always willing to pair with whoever chance determines.

I guess the one mitigating factor is that you might be able to hunt for scumbuddies based on people that are really unwilling to pair with each other... but scum could also certainly townread each other or uni-directionally townread and just never pair.

[implosion]

If it were a 10-player setup the numbers will probably be nicer actually. The fact that town, to win, need to correctly pair when there's just one more town than scum alive is kind of brutal - they have to get to that point and then get a correct pairing. But in evens there would be two more town than scum alive on the last day. EV would work out as

(note that e.g. at 1:7, town's odds are 1/4 because they're effectively picking 2/8 people to not wind up pairing)

(1/45) + (16/45) * (1/4) + (28 / 45) * ((1/28) + (12 / 28) * (1/3) + (15 / 28) * ((1 / 15) + (8 / 15) * (1 / 2) + (6 / 15)))

This works out to 46.7%. Quite good in theory.

I'd say running it at 10 is better.

This is assuming the town win-con becomes "you win when there are as many mafia alive as there are town".

[Something_Smart]

If we're looking at different ratios, my EV program gives:

5:2 - 43%
8:3 - 52%
10:3 - 44%
(Pedit: I didn't think about even numbers, but as implosion points out, 8:2 is 47% as well.)

All of these seem to be close enough to the balanced range... that said, I also think that 33% can be balanced given practical factors. 8:4 nightless has a 33% EV and has a history of mostly town wins.

[implosion]

Part of the reason nightless is so town-favored is that a trusted, strong townie can take the reins and lead the entire game. Essentially if you get a pool of trusted townies you can break the game. Here if you get a pool of trusted townies that's great but they don't get to stay in control - they have to either leave the game or let less-trusted people pair off.

[Something_Smart]

Well, the way the first run of Trust Fall played out was Chef got proposed to and basically treated as conftown but they held out for a while and never ended up leaving. They didn't really take advantage of it but a more mechanically-inclined player in that position might set out to direct pairings or at least share some reads that are given a lot of weight.

[callforjudgement]

I think this setup wants an EV close to 50%, maybe even slightly higher. The mechanic isn't all that dissimilar from Vote For Town, which seems to be balanced at around 50% in practice. (Bear in mind that adding a player of a faction will hurt that faction's win rate, in the opposite of the normal rebalancing behaviour.)

It's also worth looking at odd numbers and even numbers separately, because they'll have very different endgame situations and one may be better than the other.

[implosion]

(Bear in mind that adding a player of a faction will hurt that faction's win rate, in the opposite of the normal rebalancing behaviour.)

Amusingly also in opposite of normal rebalancing behavior, this is true as a trend but each individual player will shift the win rate depending on whether they shift the game from odds to evens (making it more townsided) or evens to odds (making it more scumsided)

[T-Bone]

I can try this as a 10p setup. I'm always interested in more even number ones for the list.