[REVIEW] Open Setup Reviews

[Awoo]

The way to turn a vig into a lower agency role is have it as a "Double Day Enabler"

[Isis]

When players adopt a very deferential strategy with vig, it already is that. There's a strong argument for that strategy.

[callforjudgement]

The way to turn a vig into a lower agency role is have it as a "Double Day Enabler"

That would cause notable changes to the balance of the setup, though, because a town vig can "counterclaim with a bullet"; if scum claims your role, you just shoot them, keeping your identity hidden. If you're a double-day enabler and scum claims your role, then you have to either stay quiet or counterclaim publicly.

[Hoopla]

hello balance wizards!

i have a window of free time coming up that i was considering dedicating to modding a game. an old idea that i never ended up experimenting with was my trapdoors nightless setup. i was hoping to finally give this a whirl pending peer review.

the setup;

3 mafia, 7 townies. Nightless.

- Imagine all ten players lining up in a row
- At the start of each day the mafia selects which player to place the trapdoor under. That player is poised to be executed.
- The town can choose to execute that player or move the trapdoor under someone else
- If the trapdoor was under the player in position #5 and the town instead decides to execute player #7, it costs two moves to execute that player
- The town can only move the trapdoor ten times for the entire game
- For the purpose of this game, position #10 wraps back around to position #1, and when someone is executed the gap closes in the lineup, ie; if #8 is executed, #7 is now connected to #9
- The mafia can't place the trapdoor under the same player on consecutive days
- Mafia have daytalk
- The ten players' positions in the line up are randomised pregame

Mafia wins if they control 50% of the town. If the town has used all their moves while the mafia is still active, the town will be considered endgamed as mafia cannot be executed now.

~~

Scum will probably need to place the trapdoor under themselves at different points in the game, so it should create some tasty wifom about how the mafia think the town will react to their choices. For town, determining how to spend your resources could be an interesting mechanic -- how sure do you have to be for someone to be scum if it costs two or three moves to do it? Do you wait until the scum place the trapdoor closer on future days and execute a second or third best target today who is closer? Conserving moves and regularly executing scum's choice could be viable and as it gives the town more flexibility deeper in the game, but if scum thinks the town will be doing this, they might select townies for their trapdoor choice with a higher frequency, and so the wifom will flow.

is it balanced?
is it fun?
is 10 moves an appropriate amount of flexibility afforded to town?

[callforjudgement]

What matters for strategy in that setup is not so much the specific player you place the trapdoor under, as the concentration of town in that area of the playerlist (therefore, the "can't choose the same person twice in a row" doesn't have a huge balance impact, because placing it next door won't usually make much of a difference). There's likely to be a lot of swing-from-randomness because the scum have a clear advantage if they happen to be bunched up in the playerlist (repeatedly trapdoor the player opposite, and town need to play almost perfectly to win).

It's hard to know exactly where the balance lies. For full flexibility in voting, town would need 5+4+4+3+3+2+2+1 = 24 moves, and giving them half that initially seemed about right in terms of making the mechanic relevant, but in practice town may well not run out at all (especially as the game won't necessarily reach a 3p ending); the average movement is going to be less than half the maximum possible movement, I think. Perhaps the game would benefit from an additional townie, making the mechanic more relevant and probably helping out with win/loss balance too (it feels a little scumsided just in terms of the 7:3 nightless numbers, given the restrictions on voting).

I strongly suspect, though, that the Mafia's best play is to aim at the same area of the playerlist continuously all game, which might rather negate the idea you had for the mechanic. That means that players at the opposite end of the playerlist will always be expensive to vote for (less so late, but still more than they could be). Moving it around just gives town the opportunity to optimize their move expenditure by waiting for a player to be near the trapdoor before removing them.

[BBmolla]

Couple ideas

If worried about same area being targeted, have the eliminated townie reorder to their liking. If worried about taking too much time, plus making the mafia selecting harder, have a player vengeswap two players and have the mafia, as a day action, choose a position (#1-10) instead of a player.

I think starting with less, but giving town +1 move per day, could be useful to prevent "okay we literally spent all our moves and now we lose."

[Gamma Emerald]

Yeah, there should be 1 move free per day I’d say

[Hoopla]

There's likely to be a lot of swing-from-randomness because the scum have a clear advantage if they happen to be bunched up in the playerlist (repeatedly trapdoor the player opposite, and town need to play almost perfectly to win).

yes, this does seem to be where a lot of the swing lies.

can any math genius tell me how likely it is for scum to be randomised into three sequential slots? or three of four etc?

as a worse-case scenario (assuming a sequence of scum), scum choosing to continuously trapdoor the opposite half of the playerlist could very easily implicate the distribution of scum. the move-quota can easily accommodate two max-spend phases for town if the town spends zero or one move on all other days. so, my counter-strategy as town would be to conserve moves early until a genuine suspect arises - or until we observe a pattern of scum trapdooring a certain portion of the playerlist.

more information seeps into the game the longer it runs. by D3, the town observing scum place the trapdoor in one area may well be enough evidence to execute a player 3-4 moves away.

the setup has a similar psychology to nomination mafia. in this setup, mafia don't

have

to nominate themselves for even-day executions - but by choosing to avoid the noose on this day, they (theoretically) increase their odds of being executed on other days. do they throw town a bone and give them a chance to execute them on even-days, as a trade-off for late-game deception purposes? sometimes. well, at least that is what we see scum do in nomination mafia.

i suspect scumteams fearing PoE in trapdoors nightless would distance occasionally; or at least not make it obvious which part of the playerlist has the highest concentration of scum (if they were fortunate enough to draw a concentration of scum-positions).

another big source of swing in nightless setups is that when you execute scum, you gain an addition misexecute - not to mention all the juicy association tells that now come into the game. nightless setups have a real problem of obvtown players or strong scumhunters being unable to be eliminated by scum, which can be deadly for PoE. i suspect that is a main reason why nightless games historically had such a high town winrate.

usually by the back-end of a nightless game, the setup is pretty much solved from PoE. you almost never see scum win a 3p LYLO in nightless, because for such a situation to occur, it requires that a scum be in the top 2 most town-looking players for the whole game, which is incredibly hard to do when you're unable to remove obvtown players. scum -- on the rare occasion they win nightless -- usually do so in a sweep or losing just one member.

i suspect most trapdoor nightless games (if run as is) wouldn't make it to a 3p LYLO - but i see that as an advantage. the scarcity of moves forces towns to be proactive and win the game before then. is picking your top or second top suspect across 4-5 phases better than trying to win in it in 6-8 phases but accepting lower-percentage executions along the way? hard to say.

perhaps the game would benefit from an additional townie, making the mechanic more relevant and probably helping out with win/loss balance too (it feels a little scumsided just in terms of the 7:3 nightless numbers, given the restrictions on voting).

i can see an extra townie being the correct adjustment if people think this is scum-sided. i'm hesitant because my experience with nightless games is that as soon as one scum gets executed, it blows the whole game wide open, usually creating one or two obvtownies in the process. the positive feedback loop of getting an extra misexecute every time you hit scum usually allows town to brute-force a PoE win.

in this setup, town gets four misexecute chances to hit scum before earning another misexecution. yes, towns will have to accept conserving moves on some phases - but scum will have to risk trapdooring a teammate within 0 or 1 moves at some point, or else risk revealing where scum is concentrated in the playerlist, allowing town to break the setup wide open on d3 or d4.

[Hoopla]

If worried about same area being targeted, have the eliminated townie reorder to their liking.

this is also an interesting idea.

i suspect towns will end up spending a significant portion of the day debating how the playerlist should be ordered in the event of a misexecution, which somewhat detracts from the moving mechanic - or at least, introduces more complexity to what is intended to be a simple/elegant setup.

another thought that came to mind (if we're tinkering with the mechanic itself instead of the town:scum ratio), would be to not allow scum to trapdoor players who have received it before (instead of just non-consecutively). this way, if scum are in slots #1, #2, #4, scum can't just bounce between #7 and #8. they'll have used up the furthest-away slots, forcing them to bring the trapdoor closer. this also introduces town strategies of possibly leaving certain slots alive if they want to influence parts of the playerlist where the trapdoor can't go next.

[Gamma Emerald]

With 3 out of 10, the odds of being placed into 3 sequential slots is I believe 1/18 (2/9 * 2/8 = 4/72 = 1/18).

[Hoopla]

could be useful to prevent "okay we literally spent all our moves and now we lose."

i like this as a losing condition for town. it forces town to (probably) win the game in six phases or so. it's similar thematically to a white-flag type mechanic, where by shifting the endgame forward (or would it be backwards?) from a 3p LYLO, it changes the way people play earlier in the game, for example; bussing/distancing becomes much more high stakes in mid-game white flag.

[Hoopla]

With 3 out of 10, the odds of being placed into 3 sequential slots is I believe 1/18 (2/9 * 2/8 = 4/72 = 1/18).

how about a sequence of 3 in 4? i imagine that's a trickier calculation

[Gamma Emerald]

another thought that came to mind (if we're tinkering with the mechanic itself instead of the town:scum ratio), would be to not allow scum to trapdoor players who have received it before (instead of just non-consecutively). this way, if scum are in slots #1, #2, #4, scum can't just bounce between #7 and #8. they'll have used up the furthest-away slots, forcing them to bring the trapdoor closer. this also introduces town strategies of possibly leaving certain slots alive if they want to influence parts of the playerlist where the trapdoor can't go next.

Definitely don’t use the “free move a day” idea if this is used, as town can technically do that repeatedly until no options remain, though I’d assume a fail safe exists
Also I almost tried to dive into the math for 3 in 4 then I realized it was kinda a trick question.

[Hoopla]

Also I almost tried to dive into the math for 3 in 4 then I realized it was kinda a trick question.

how so?

[Gamma Emerald]

It’s 100% since you only ever have 1 negative spot, which with the circle formation results in them always being adjacent

[Hoopla]

It’s 100% since you only ever have 1 negative spot, which with the circle formation results in them always being adjacent

i mean 3 in 4 sequences like 1/2/4, 4/5/7, 4/6/7, 9/10/2 etc.

something like 1/5/8 or 2/3/7 doesn't qualify.

[Gamma Emerald]

Actually hold on I think my math was off since you can technically fill a gap with the third
Had you not clarified 3 in 4 that wouldn’t have clicked

[Gamma Emerald]

I’m gonna be posting unga bunga math post soon, covering both the updated logic for all three being together, as well as the chance of three being in a range of four adjacent seats with a space somewhere between.

[Gamma Emerald]

I'll start with covering the chance of all 3 scum being together. The stuff inside the spoiler= tag is me going through the minutiae of calculating the probability, skip it if you don’t care for it.

Spoiler: all 3 together

Let’s assume we start like this, starting person’s placement is where all probability starts, so to make things simple we’ll put them in a fixed location.

Code: Select all

ooooxooooo

Acceptable locations for the second person when going for all 3 together are (the newly placed person will be the one capital letter. These will be marked with unique letters for the next step

Code: Select all

A: ooXoxooooo
B: oooXxooooo
C: ooooxXoooo
D: ooooxoXooo

That ends up at 4/9 locations having the potential to have all 3 together. For the next step, take each valid outcome and calculate the outcomes that meet the final goal for each of those.

The letter notations will now be used to separate the outcomes that relate to each placement of 2, with each valid option having an extra letter added (so the first valid option for A will be AA)

Code: Select all

AA: ooxXxooooo
BA: ooXxxooooo
BB: oooxxXoooo
CA: oooXxxoooo
CB: ooooxxXooo
DA: ooooxXxooo

What is interesting to note is that we end up with 3 different distinct sets of locations (345, 456, and 567), each one just having 2 different orders of picking them, the commutative property (5, then 4, then 6 results in 456, while 5, then 6, then 4 achieves the same outcome). This results in 6 possible outcomes, assuming a fixed location for our first person, that result in the 3 subjects all being together.
This is taken out of the number of outcomes in general to find our true probability of this event. That is 9 times 8, which equals 72, because our second person would have 9 potential locations, while the third has 8. So we get 6/72, which we can simplify to get 1/12.

To put this simply (and provide an answer without needing to open the spoiler= tag), we have 3 valid arrangements assuming a fixed placement for our first person, and each arrangement can have the two variable spots filled in either order, resulting in 2 permutations of each valid arrangement. Thus there are 6 valid outcomes, with 72 possible outcomes, for a final probability of 1/12.
Let's put this in more tangible terms. Assume there is a circular table with 10 chairs around it, and someone is already seated. A second person comes in and sits down, and let's assume they know there's a third person coming and they all want to sit together. In this situation, the second person can either sit in one of the two seats directly next to person already seated, in which case the third person can sit in the seat next to the first or second person. The second person can also sit with a seat of space between them and the seated person, in which case the third person has to sit between them.

Now for the chance of 3 people being in a region of 4 adjacent spots with a gap in their placement, which isn't actually as complex as I initially thought it might be.]. By virtue of how this group is defined, no previously covered outcomes will show up again, which I'll be expanding on later.

Spoiler: 3 in 4 / xoxx

So we'll start with the same spot we did last time.

Code: Select all

ooooxooooo

Since we are now covering a range of 4 total spots with our arrangement, the possible ground to cover now becomes 7 spots instead of 5 from last time (the ground covered to cover is equal to the starting location plus the amount of possible distance away on each side). There's no condition regarding how the second person can be placed, they can be next to, one away, or two away from the first. Like so, once again using letters to make it easier to distinguish outcome branches in the next step.

Code: Select all

A: oXooxooooo
B: ooXoxooooo
C: oooXxooooo
D: ooooxXoooo
E: ooooxoXooo
F: ooooxooXoo

With the second person placed, the third person now has to be placed in a way that will satisfy the 3 in 4 with a gap. I will go over the logic for where the third person can go after the possible locations. As you probably guessed, these outcomes will be marked as a pair of letters with the first representing a placement of the second person and the second being representative of a viable placement of the third.

Code: Select all

AA: oxXoxooooo
AB: oxoXxooooo
BA: oXxoxooooo
BB: ooxoxXoooo
CA: oXoxxooooo
CB: oooxxoXooo
DA: ooXoxxoooo
DB: ooooxxoXoo
EA: oooXxoxooo
EB: ooooxoxXoo
FA: ooooxXoxoo
FB: ooooxoXxoo

Now, let's get into the meat of why the third has to be in the places it goes. Let's start with the cases of the first and second being adjacent (C and D). In this scenario there is no existing gap so it must be between the third and the person they're on the side of (the first for CB and DA, the second for CA and DB). Next up is the case of there being a one-spot gap between the first and second (B and E). In this case, the third now has to be in a location that is directly adjacent to either only the first (BB and EA) or the second (BA and EB). Finally, when we have two spots between the first and second (A and F), the third has to go somewhere in that in-between space, either being next to the first (AB and FA) or the second (AA and FB).

So we end up with 2 possible placements of the third for each placement of the second, which we had 6 of, giving us 12 placements that meet the "3 in 4 with a gap" criteria. Once again taking this out of 72, we have 12/72 which reduces to 1/6.
Now interestingly we once again have 2 possible permutations of each arrangement, which when you divide 12 by six, you get 6 unique arrangements. These are 235 (AA and BA), 245 (AB and CA), 356 (BB and DA), 457 (CB and EA), 568 (DB and FA), and 578 (EB and FB). If you're interested in a better visualization of these, I'll put it in a spoiler at the very end along with ones for the permutations for "all 3 together"

Again summing up for those who didn't read the complex math dive, the second person can now be one space farther away from the first person for a total of 6 spots the second person can be in, and the third will always have 2 spaces they can be for each possible location of the second, defined by being on the side of the first or second, for 12 viable "3 in 4 with a gap somewhere" outcomes, being taken out of the 72 overall possible outcomes for a total probability of 1/6. I won't be diving into the chair metaphor again, if you want to see me go into that deep logic without focusing on the full math behind it, I colored the text within the spoiler= tag that does so.

Now I'm going to flex my statistics muscles a bit. Let's say we want to find out the plain odds of the 3 being within 4 spaces at all with a fixed location of the first. This doesn't necessitate a gap, mean the first 6 are valid, and also doesn't require them all to be bunched together completely, allowing the other 12 that have that one extra bit of space. since the events are exclusive, you just add them, which is 6 + 12 = 18, and again take it out of your 72 overall outcomes for a 18 in 72, or 1/4, chance. That's about it for the math.

Spoiler: enhanced displays of the arrangements and permutations for those who care

For these, I'm using numbers to fill out the ten spots, o's becoming zeroes and the x's becoming 1, 2, or 3, showing the order they're placed. While the letter notations are gone the results will be in the same order as when they were there, for ease of reference.

"all 3 together":

Code: Select all

0023100000
0032100000
0002130000
0003120000
0000123000
0000132000

"3 in 4 with a gap":

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0230100000
0203100000
0320100000
0020130000
0302100000
0002103000
0030120000
0000120300
0003102000
0000102300
0000130200
0000103200

[Isis]

hello balance wizards!

i have a window of free time coming up that i was considering dedicating to modding a game. an old idea that i never ended up experimenting with was my trapdoors nightless setup. i was hoping to finally give this a whirl pending peer review.

the setup;

3 mafia, 7 townies. Nightless.

- Imagine all ten players lining up in a row
- At the start of each day the mafia selects which player to place the trapdoor under. That player is poised to be executed.
- The town can choose to execute that player or move the trapdoor under someone else
- If the trapdoor was under the player in position #5 and the town instead decides to execute player #7, it costs two moves to execute that player
- The town can only move the trapdoor ten times for the entire game
- For the purpose of this game, position #10 wraps back around to position #1, and when someone is executed the gap closes in the lineup, ie; if #8 is executed, #7 is now connected to #9
- The mafia can't place the trapdoor under the same player on consecutive days
- Mafia have daytalk
- The ten players' positions in the line up are randomised pregame

Mafia wins if they control 50% of the town. If the town has used all their moves while the mafia is still active, the town will be considered endgamed as mafia cannot be executed now.

~~

Scum will probably need to place the trapdoor under themselves at different points in the game, so it should create some tasty wifom about how the mafia think the town will react to their choices. For town, determining how to spend your resources could be an interesting mechanic -- how sure do you have to be for someone to be scum if it costs two or three moves to do it? Do you wait until the scum place the trapdoor closer on future days and execute a second or third best target today who is closer? Conserving moves and regularly executing scum's choice could be viable and as it gives the town more flexibility deeper in the game, but if scum thinks the town will be doing this, they might select townies for their trapdoor choice with a higher frequency, and so the wifom will flow.

is it balanced?
is it fun?
is 10 moves an appropriate amount of flexibility afforded to town?

You might be interested in skimming Deathlist since it was a somewhat similar setup. For assessing the 2nd and 3rd questions, that setup was horrendously scumsided so it won't say much about balance.

[Isis]

I got 1/12th for a straight row also and am just gonna assume gamma is correct for 3/4

[Gamma Emerald]

3/4 is if you're doing straight row AND range of 4 with a gap
3 in 4 with a gap itself was 1/6

[Isis]

I think you should probably reshuffle the playerlist randomly every single day. Fixing a random swing by adding more randomness is an underrated option, large numbers of random events tend towards the mean.

The odds of worst-case-scenario scum positioning drops from 8% to 2% with daily reshuffles. 2% is like acceptable tolerance for some normal queue setups that become broken abominations if certain PRs die in the wrong order or whatever.

It will also be less swingy and unsatisfying in terms of there emerging a 3 card townbloc that happens to be sitting adjacent to eachother that gets picked over and over, etc, just better in general.

[Isis]

ebwop, "I am going to assume Gamma Emerald's final result of 1/6th for three mafias with one gap is correct without calculating for myself 3 mafias 1 gap"

[Gamma Emerald]

I like the statistical mindset, but I think that specific solution goes against the original setup idea
The setup seems based around the static locations of the players. Taking that away creates a chaotic not-really-system that just seems less interesting.