[SETUP] Unresistance

[BBmolla]

Unresistance

9 Players

1 Mafia Boss
2 Mafia Goons

1 Town Lord
5 Vanilla Townies

• See below for game instructions.

This game does not have lynches. There are five phases.

When the game begins, the Town Lord is immediately revealed.

Phases 1-3:

All players elect by majority someone to put into jail. The Town Lord can not be placed into jail. Once someone is elected, the Town Lord chooses another player to put into jail.

If the two people in jail are the Mafia Boss and a Mafia Goon, the game is over and town wins.

In any other case, one of the alignments of the jailed players is randomly revealed. It is not revealed which player that alignment belongs to, but the mod confirms that one of the players is of that alignment. After this, move onto the next phase.

Phase 4

All player elect by majority someone to kill.

If the Mafia Boss is killed, town wins.

If not move on to the next phase.

Phase 5

The Town Lord chooses a player to kill.

If the Mafia Boss is killed, town wins.

If not, town loses.

Visual

Jail 2 (Majority Jail 1, Lord Jail 1.) If Boss and Goon in jail, town wins. Reveal one alignment randomly, unspecified who.
Jail 2 (Majority Jail 1, Lord Jail 1.) If Boss and Goon in jail, town wins. Reveal one alignment randomly, unspecified who.
Jail 2 (Majority Jail 1, Lord Jail 1.) If Boss and Goon in jail, town wins. Reveal one alignment randomly, unspecified who.
Shoot 1 (Majority)
Shoot 1 (Lord)



I suck ass at math so someone double check my work, but if this EV is correct then the winrate for town should be 40% without bonuses of knowing alignments:

Code: Select all

C(8,2) [Because Town Lord can not be chosen] (8!) / (2! * 6!) = 28
2 out of the 28 result in a town win (Boss with each team mate)

1/14 - win
13/14 - next phase 

	2/27 - win
	25/27 - next phase

		1/13 - win
		12/13 - next phase

			1/8 - win
			7/8 - next phase

				1/7 - win
				6/7 - lose


(1/14) + (((2/27) * 13)/14) + (((((13/14) * 25)/27) * 1)/13) + (((((((13/14) * 25)/27) * 12)/13) * 1)/8) + (((((((((13/14) * 25)/27) * 12)/13) * 7)/8) * 1)/7) = ≈40% town winrate

13/14 * 25/27 * 12/13 * 7/8 * 6/7 = ≈60% mafia winrate

Would love thoughts, maybe it's just a bit too unforgiving to town? I didn't want to have both jailed players alignments revealed because it can easily cause four confirmed town after second phase. I didn't want to have one jailed player's alignment revealed because then you have confirmed scum which means they basically can't play anymore. So I settled for an in between, one of their alignments is revealed but you're not sure whose alignment it is. However that only is useful if one of them is scum. And even then, 50% it won't reveal them. And even if they're the two goons, one of them being confirmed scum doesn't actually help the Lord with the shooting at the end. So maybe that's actually completely useless?

Idk, just a concept I've been mulling over.

[Awoo]

Can you kill someone in jail.

[BBmolla]

Can you kill someone in jail.

The jailed status only happens during that phase, they're released once the phase ends.

[the worst]

This is pretty cool.

[Gamma Emerald]

Looks pretty interesting, do scum have control over which person’s alignment shows up (despite there not being a specific person tied to the reveal)?

[Sukima]

Is it possible to get the same result on one person even if you jail the same people 3 times? Also maybe something like a parity checker instead of randomly revealing one?

[Gamma Emerald]

I'd assume yes

[mith]

Looks pretty interesting, do scum have control over which person’s alignment shows up (despite there not being a specific person tied to the reveal)?

I don't see how that would work. If both Mafia are in, they already lose, otherwise they would always choose to reveal "town" if they had the choice.

The probabilities here are interesting.

Phase 1, if you jail boss and scum, you win, yay (probability 1/14). If you jail two town (probability 5/14), reveal is town. If you jail two goons (probability 1/28), reveal is scum. If you jail scum and town (probability 15/28), reveal is town or scum (15/56 for each).

If you get a town reveal, the likelihood of having two town is (5/14)/(5/14+15/56) = 5/7. So the probability of each individual player being town is 5/7 + 2/7*1/2 = 6/7. (Then the other non-TL players have probability of (5-12/7)/6 = 23/43 of being town.) Basically, after a town result, you don't want to pick these two players again during phases 2 and 3, and that will affect the likelihood of winning in those phases. (In fact, I don't think you want to pick these two players at all - which sucks if one happens to be the Boss, but the probability of picking Boss/Town and getting a town reveal is only 5/56, so you're not losing a whole lot there.)

If you get a scum reveal, the likelihood of having two scum is (1/28)/(1/28+15/56) = 2/17. So the probability of each individual player being scum is 2/17 + 15/17*1/2 = 19/34. (Then the other non-TL players have probability of (3-38/34)/6 = 16/51.) After a scum result, you want to pick one of the same players and pair with a different player in phase 2 - then if you get another scum result, keep that player and try again phase 3, otherwise pick the other player from phase 1 with a new player for phase 3.

If you haven't won after optimally playing the first three phases, you have a bunch of conditional probability information to determine your targets. For example, if you have had three town reveals, there are two players who haven't been chosen yet, and they are the most likely (equally) to be the Boss (even though you have obviously already chosen at least one scum and missed them in the reveal). If you had three scum reveals,

you are shooting the guy you kept picking; if they're the Boss, yay, if they're a Goon you have four players left who could be the Boss, and if they're Town then one of the three they were paired with is the Boss (and the other two are Goons).

[edit]This is actually incorrect - the original guy is much less likely to be the Boss, both because it's unlikely to keep getting scum results after pairing him with Town, and because you've ruled out three potential partners. You want to shoot from the four players not chosen yet.[/edit] It gets a lot messier if you get mixed results though, and I'm too lazy to figure out the exact EV right now. But I wouldn't be surprised if it's above 50%.

[mith]

Ok, this is a little surprising:

Phase 1: A&B, scum result
Phase 2: A&C, scum result
Phase 3: A&D, town result

It is equally likely that B, C, E, F, G, H are the Boss. There are five cases for Boss B (or C) to get these results, and C (or B) is a Goon in all of them; four of these cases get a certain result on Phase 3 (B+C+D scum is a coinflip on all three phases). There are six cases for Boss E-H to get these results, five paired with A and one paired with B+C; but only three of these get a certain result at some point (e.g.E+[two of A, B, C]).

(I got less lazy and am putting a spreadsheet together.)

[Flavor Leaf]

This seems to pull a nice amount from Resistance, but I'm assuming that's the point. That's always a plus for me, though. I love Resistance, and this seems to have enough variety to it to differentiate as not Resistance-Lite. A lot of stock is put onto the Lord.

[mith]

Finished the spreadsheet. EV is 123/224 (54.91%).

Strategy is as follows:

Code: Select all

Phase 1: A+B
    If win, you're done!
    If town, Phase 2: C+D
        If win, you're done!
        If town, Phase 3: E+F
            If win, you're done!
            If town, shoot G+H
            If scum, shoot G+H
        If scum, Phase 3: C+E
            If win, you're done!
            If town, shoot D+[one of E-H]
            If scum, shoot [two of F-H]
    If scum, Phase 2: A+C
        If win, you're done!
        If town, Phase 3: B+D
            If win, you're done!
            If town, shoot [two of A-B,E-H]
            If scum, shoot B+[one of E-H]
        If scum, Phase 3: A+D
            If win, you're done!
            If town, shoot [two of B-C,E-H]
            If scum, shoot [two of E-H]

At least on the first phase, you're better off scum hunting than town hunting... but a scum reveal is only barely better than a town reveal (51.47% EV vs. 51.43%). The advantage, of course, is that you can instant-win by picking two scum (EV given that you either won or got a scum reveal is 60.71%).

Removing the last kill entirely lowers the EV to 95/224 (42.41%). Adding another townie (without removing the kill) lowers the EV to 137/288 (47.57%). (Messing with scum count would be a much bigger change for the way I put this together, and it's late. Maybe some other time.)

Anyway, I think it's a pretty neat concept.

[mith]

Realized this morning that my spreadsheet failed to account for the first kill flip.

Ok, this is a little surprising:

Phase 1: A&B, scum result
Phase 2: A&C, scum result
Phase 3: A&D, town result

It is equally likely that B, C, E, F, G, H are the Boss. There are five cases for Boss B (or C) to get these results, and C (or B) is a Goon in all of them; four of these cases get a certain result on Phase 3 (B+C+D scum is a coinflip on all three phases). There are six cases for Boss E-H to get these results, five paired with A and one paired with B+C; but only three of these get a certain result at some point (e.g.E+[two of A, B, C]).

(I got less lazy and am putting a spreadsheet together.)

In this case, those six players are equally likely Boss after phase 3. But picking B or C for the first kill has a clear advantage: if B flips town, C cannot be the Boss; whereas if B flips scum, C is much more likely to be the Boss.

I don’t think any of the other cases change enough to affect the last kill decision, but that one will up the EV by a small amount.

[mith]

Ok, I was wrong about none of the other cases changing:

After scum, town, town, A&B are equally likely with E-H, but if A flips goon B cannot be the Boss (so pick from E-H), while if A flips town, B must be at least scum and is thus more likely to be the Boss than E-H.
After scum, town, scum, B is most likely and A/D are least likely, but if B flips town then A/D jump to most likely (since they must be scum); if B flips scum, again pick from E-H.
After town, scum, town, D is most likely and F-H are equally second, but if D flips town then C must be scum; if D flips scum, pick from F-H.

In the remaining four cases, the most likely Bosses are among the players who did not participate in the first three phases, so I'm doubtful that the first flip will tell us anything sufficiently useful. Might try some things later. Anyway, with the above changes, the EV is up to 761/1344 (56.62%). Which is a huge improvement over the naive approach (17/42, 40.48%).

[mith]

After further improvements, I got it up to 193/336 (57.44%):

After scum, scum, scum, shoot from E-H first, but a scum flip jumps A back to most likely (it eliminates the B+C+D case where A isn't scum at all, and also eliminates any case where A+[B-D] are both Goons; A must be scum, with equal probability to Boss or Goon, while the other three of E-H are a third as likely each to be the other scum).
After scum, scum, town, a B town flip does eliminate C, but also A is now the most likely (because as mentioned above, E-H must be paired with A in all cases except with B+C, which has been eliminated).
After scum, town, scum, see above.
After scum, town, town, see above.
After town, scum, scum, shoot from F-H first, but a scum flip makes C most likely (similar to scum, scum, scum argument above; it could still be D+E+[F-H], but otherwise C must be scum).
After town, scum, town, see above.
After town, town, scum, shoot from G-H first, but a scum flip makes E-F more likely than the remaining G-H.
The town, town, town case is the only one where it doesn't matter what the flip is. You're still shooting both of G-H.

That's a lot to keep track of. But there's really quite a lot of information generated. (Even a totally lazy strategy of picking three disjoint pairs and then shooting the other two players gets you to 13/28, and that's ignoring that those two players

can't

be scum if the got scum, scum, scum. A better but still lazy strategy is to shoot the unpaired players if you only got one scum result, and if you got more than one scum result shoot from distinct pairs that got scum results. That gets you to 85/168, just a hair over 50%.)

[mith]

With similar improvements to the 10 player case, EV is now 145/288 (also just a hair over 50%). The lazy strategy above only gets you to 3/7 here though.

(My suggestion to balance this would be to replace the Town Boss with another Townie, and just make all the choices by majority. Alternately, you might even keep the Town Boss but not allow them to vote or speak during the majority selection phases. Maybe give them a chance to make a single post when choosing their jailee, so that they can contribute to the discussion without controlling it due to their status as IC.)

[BBmolla]

What's the EV if I go with your suggestion?

Edit: The replacing Town Lord with VT.

[mith]

Same as 10p. Town Lord has no affect on EV.

[BBmolla]

Unresistance

9 Players

1 Mafia Boss
2 Mafia Goons

6 Vanilla Townies

• See below for game instructions.

This game does not have lynches. There are five phases.

Phases 1-3:

All players elect by majority someone to put into jail. Once someone is elected, they elect another player to place in jail with them.

If the two people in jail are the Mafia Boss and a Mafia Goon, the game is over and town wins.

In any other case, one of the alignments of the jailed players is randomly revealed. It is not revealed which player that alignment belongs to, but the mod confirms that one of the players is of that alignment. After this, move onto the next phase.

Phase 4

All player elect by majority someone to kill.

If the Mafia Boss is killed, town wins.

If not move on to the next phase.

Phase 5

All player elect by majority someone to kill.

If the Mafia Boss is killed, town wins.

If not, town loses.

Visual

Jail 2 (Majority Jail 2) If Boss and Goon in jail, town wins. Reveal one alignment randomly, unspecified who.
Jail 2 (Majority Jail 2) If Boss and Goon in jail, town wins. Reveal one alignment randomly, unspecified who.
Jail 2 (Majority Jail 2) If Boss and Goon in jail, town wins. Reveal one alignment randomly, unspecified who.
Shoot 1 (Majority)
Shoot 1 (Majority)

I think I'll try running it.