Open Setup Certification Group

[Xylthixlm]

Huh... there's a really interesting pattern there. It seems there are fewer draws when the number of townies is a multiple of 3.

[Xylthixlm]

It might help if I make sure that double kills are handled correctly. One of these days I'm going to write a good simulator instead of the hackish Perl script I'm using

Code: Select all

--- 3 townies ---
Town 1002, Mafia1 4335, Mafia2 4321, Draw 342
Average length 2.16, std dev 0.52
--- 4 townies ---
Town 1178, Mafia1 3773, Mafia2 4024, Draw 1025
Average length 2.63, std dev 0.50
--- 5 townies ---
Town 1448, Mafia1 3909, Mafia2 3844, Draw 799
Average length 2.90, std dev 0.50
--- 6 townies ---
Town 1743, Mafia1 3932, Mafia2 3955, Draw 370
Average length 3.32, std dev 0.57
--- 7 townies ---
Town 1849, Mafia1 3661, Mafia2 3867, Draw 623
Average length 3.70, std dev 0.53
--- 8 townies ---
Town 2054, Mafia1 3617, Mafia2 3827, Draw 502
Average length 4.06, std dev 0.58
--- 9 townies ---
Town 2268, Mafia1 3618, Mafia2 3825, Draw 289
Average length 4.43, std dev 0.61
--- 10 townies ---
Town 2351, Mafia1 3539, Mafia2 3688, Draw 422
Average length 4.84, std dev 0.62
--- 11 townies ---
Town 2542, Mafia1 3543, Mafia2 3577, Draw 338
Average length 5.17, std dev 0.66
--- 12 townies ---
Town 2718, Mafia1 3500, Mafia2 3532, Draw 250
Average length 5.57, std dev 0.71
--- 13 townies ---
Town 2772, Mafia1 3372, Mafia2 3485, Draw 371
Average length 5.92, std dev 0.73
--- 14 townies ---
Town 2899, Mafia1 3422, Mafia2 3409, Draw 270
Average length 6.29, std dev 0.78
--- 15 townies ---
Town 3112, Mafia1 3305, Mafia2 3393, Draw 190
Average length 6.67, std dev 0.82

[Lord Gurgi]

(know-it-all dance)

[Xylthixlm]

One more time, this time with kingmaker endgames (1v1v1 or 2v2v1) counted in addition to wins/draws.

Code: Select all

--- 3 townies ---
Town 1003, Mafia1 4307, Mafia2 4376, Draw 314 (Kingmaker 3798)
Average length 2.15, std dev 0.52
--- 4 townies ---
Town 1175, Mafia1 3843, Mafia2 3960, Draw 1022 (Kingmaker 3052)
Average length 2.62, std dev 0.50
--- 5 townies ---
Town 1358, Mafia1 3961, Mafia2 3909, Draw 772 (Kingmaker 3287)
Average length 2.90, std dev 0.51
--- 6 townies ---
Town 1706, Mafia1 3937, Mafia2 4014, Draw 343 (Kingmaker 2422)
Average length 3.31, std dev 0.57
--- 7 townies ---
Town 1874, Mafia1 3707, Mafia2 3814, Draw 605 (Kingmaker 2083)
Average length 3.70, std dev 0.53
--- 8 townies ---
Town 1991, Mafia1 3724, Mafia2 3767, Draw 518 (Kingmaker 2207)
Average length 4.05, std dev 0.59
--- 9 townies ---
Town 2224, Mafia1 3708, Mafia2 3786, Draw 282 (Kingmaker 1739)
Average length 4.44, std dev 0.61
--- 10 townies ---
Town 2391, Mafia1 3484, Mafia2 3663, Draw 462 (Kingmaker 1593)
Average length 4.82, std dev 0.63
--- 11 townies ---
Town 2458, Mafia1 3542, Mafia2 3627, Draw 373 (Kingmaker 1682)
Average length 5.18, std dev 0.66
--- 12 townies ---
Town 2737, Mafia1 3490, Mafia2 3531, Draw 242 (Kingmaker 1382)
Average length 5.57, std dev 0.71
--- 13 townies ---
Town 2821, Mafia1 3333, Mafia2 3513, Draw 333 (Kingmaker 1253)
Average length 5.94, std dev 0.73
--- 14 townies ---
Town 2993, Mafia1 3310, Mafia2 3450, Draw 247 (Kingmaker 1328)
Average length 6.29, std dev 0.80
--- 15 townies ---
Town 3113, Mafia1 3317, Mafia2 3385, Draw 185 (Kingmaker 1115)
Average length 6.67, std dev 0.82

Now, actual play might avoid kingmaker endings - I don't know - but with random lynches/kills, they're actually more common than town wins for any setup under 9 players! Does that worry anyone else as much as it does me?

[shaft.ed]

Can town win a 1 v 1 v 1?

No Lynch, then cross kill?

Scum's going to lose (draw) if he lynches the townie. He can only win lynching the other scum, but the townie isn't going to let him do that. Scum doesn't want to look like the other scum, so he might push a No Lynch for WIFOMy puroposes going into the night phase.

I think as long as the win condition is clear that scorched earth is the draw scenario it shouldn't happen right?

[Xylthixlm]

The flaw in your plan is that you assume the scum will crosskill. Each scum knows they will lose anyways if there's a crosskill, so they may choose to shoot the townie and throw the game to the other scum. Not everyone takes the game-theoretical-optimal move if they think there's a 90% chance they'll lose anyways.

[shaft.ed]

I'm not saying there will be a crosskill, but that it's the only way a townie can win, so it's the move the townie would make. Thus if scum are still attempting to avoid being crosskilled for an outright win, they should also push for a no Lynch.

[Adel]

what is the past history of 2:2:n games? I recall town winning ~50% of those.

I think Kingmaker might end up usually going town's way (chance to win is better than guaranteed loss), and "good" scum play (the way most players approach multiball) results in earlier cross kills than random would indicate.

For vanilla then, my guess is that 2:2:11 will yield close to 25%:25%:50% in actual play.

[shaft.ed]

Yeah I agree with good scum play being better than random for crosskills. The mafia are trying to get rid of the other faction.

Is 25/25/50 what we should be after? Wouldn't something closer to 33/33/33 be more desiralbe?

[Xylthixlm]

It looks like there are natural sweet spots for minimum draws and for minimum kingmaker situations, in a repeating pattern of 3. Unfortunately, they're offset. 2v2v9 is good for minimizing draws, and 2v2v10 is good for minimizing kingmaker situations.

I think I'd go with 2v2v10.

[shaft.ed]

How about 2 v 2 v 10 for vanilla or limited scum abilities, and 2 v 2 v 9 for anything with town sided power roles?

[Adel]

sounds good to me, but I think we are getting ahead of ourselves.

What is balanced for 2:2:n?

[Adel]

Here is a tangent:
I designed an open game and posted it in the other thread.

Ballers in the Palace

3 Ballers (each can target one other player for a rendezvous)
11 Guards (tracker, finds out who a player targeted during the previous period of day.)
2 Princesses (each get 1 roleblock, and can target one player for a rendezvous per day)
Deep South.

Everyone knows who the Princesses are. If a Princess and the same Baller target each other two days in a row (successfully rendezvous), the Ballers and that Princess win. The Ballers can daytalk.

At the beginning of each day flavor will indicate if a rendezvous successfully occurred, and how many rendezvous occurred.

Baller

You are a Baller, you have disguised yourself as a Guard. _______ and ________ are the other ballers. You can talk ____here____.

Each day you can target one other player for a secret rendezvous. If you, or either of the other ballers, successfully rendezvous with a Princess two days in a row, the four of you will win.

Guard

You are a Guard, sworn to protect the Chasity of the Princesses. Each day you can follow the footprints of another player, and see who they visited the day before.

You win if all three Ballers are lynched before any of them successfully rendezvous with a princess two nights in a row.

Princess

You are a Princess. You can attempt to rendezvous with one other player once per day. You can also roleblock one other non-Princess player (preventing him from tracking another player or arranging a rendezvous with any Princess) once per day.

You win if you successfully rendezvous with a Baller two days in a row.

Moves can be submitted up 24 hours after the hammer. The death scene (about 24 hours after the hammer) will mark the end of day, indicate if a rendezvous happened (and how many) and reveal the role of the lynched player. The mod will send PMs indicating results from rendezvous and tracking attempts after he locks the game thread and before he posts the death scene.

The Princesses can't be lynched, obviously. The game is basically a race to see which Princess can break the setup (if they can) before the Ballers get lynched. The Princesses do not get a vote.

If a Guard tracks a Princess he will find out who she targeted, but will not know which player she targeted with which ability.

I think this design is a good test case for what an open game setup is or is not.

I can think of four objections to this setup being included:

• 1. The flavor is not Normal.
  2. It is probably breakable.
  3. Deep South is not normal.
  4. The informed minority does not have a kill.

On the other hand, with the role PMs written it would be fairly easy to mod. A pre-written rule-set would probably also help. I think Deep South is a format worth promoting, since I think it encourages a faster game with fewer replacements and a more enjoyable tempo. The role most likely to break the setup is probably the Princess, and there is a chance that by adding a third Princess the game could yield a really interesting meta-games of different Princess tactics, and different Baller tells.

Of the four objections (+ those y'all can think of) which are enough to disqualify a game?

[Korts]

It is also not mafia, per se. Which is more than enough to disqualify it.

I'll need to consider 2:2:n later, I just woke up.

[mith]

shaft.ed/Xyl, you both seem to be assuming in the case of an X:X:1 endgame that everyone knows who the townie is - we can't assume that, and whether we can determine it at all depends on how draws are counted (do we assume that if it gets down to two opposing scum, they kill each other and all three sides have an equal share of the "everyone dies" draw, do we assume that they kill each other and everyone loses - the same thing from the townie POV, since the townie's goal should be to maximize his own share of the win *and* minimize the share of the others - or do we assume that the scum automatically draw at that point to the exclusion of the town?).

If we assume the latter, the townie's best and only chance is to NL (which the scum must agree to/suggest themselves, to avoid giving away information about who the townie is), and hope for the best in a shoot out. Whichever scum side is better at missing the townie wins, (or they both hit the townie, draw, or they wipe each other out, town win). 1-1-1 would be 25% for the town (25% for each scum group, 25% draw).

In the former case (personally, if there are two scum groups left that can both kill each other, I make them play it out - it's only a draw if they can agree to not shoot each other and actually follow through with that agreement - so this is where my ruleset would bring us), the NL plan is even (33% total for each, counting the draw share), but so is the plan where the townie offers himself up to be lynched (since the correct play after that is for the scum to wipe each other out; it's Prisoner's Dilemma). However, while the townie is the only one that can offer himself to be lynched, I don't think there is any informational advantage to be gained by him doing so - correct play at that point for the scum is to lynch him, to avoid going to night X-X-1 and knowing who the townie is.

The more interesting case is 1-1-2, where correct play is for one of the townies to offer himself up for lynching, to actually follow through with that play some percentage of the time (determined to reduce the scum's chances of faking this), and then the rest of the time lynch the *other* townie (which the scum can't fake) since we have a high likelihood that the first claim is legit. The game theoretical value for this is surely very much in the town's favor (I've actually won a game similarly myself, though in that one everyone already knew I was innocent, I was just getting the other townie to offer herself up so I - and the scum - would know who she was, and thus who the scum were).

Anyway, the point is that no matter what the draw rules, I think it's far more likely 1-1-1 would go to a shootout than a "kingmaker" situation. Even halfway decent players don't give the game away when there is a 25% chance of them winning.

[Xylthixlm]

By the time it gets down to 1-1-1 it's usually pretty obvious who the townie is. If one of the scum can get away with fooling the other into thinking they're the townie, good for them. I've done that once or twice on IRC, but it's pretty hard.

The townie should just claim townie and no lynch, usually with a "fuck, you're both scum" in there for good measure.

[mith]

In practice? Sure. In determining balance? We can't assume that (see standard speech about random EVs).

The townie should claim townie. So should both scum. My point is that in 1-1-2, we can force some information to make it more of a Prisoner's Dilemma for the scum - in 1-1-1, we can't. The scum might have gained knowledge about which of the other two is the townie, and they might be wrong, and we can't assume anything for the balance of the game other than that they will shoot randomly.

[Xylthixlm]

That's why the EVs are based on random shooting

[mith]

Right. I'm just not sure why you're singling out 1-1-1 as a "Kingmaker" situation; it's not, in the standard sense of the term - it may be the case that scum A is killed by scum B, and thus scum A's choice has the effect of acting as the decider between scum B and townie, but scum A doesn't know this going in, and his choice isn't arbitrary (in the actual game) since shooting scum B is strictly better than shooting the townie, if he can figure out which is which.

[Xylthixlm]

1-1-1 generally comes down to whichever remaining player is dumbest throwing the game to one of the other two.

[shaft.ed]

The townie should just claim townie and no lynch, usually with a "fuck, you're both scum" in there for good measure.

Which makes this a really nice play for scum who wants to No Lynch and cross kill the other scum

I really think a scorched earth win (actually loss) condition the way to avoid kingmaker situations.

[mith]

I think any situation involving the word "dumbest" is still a game of skill.

After thinking on it in the shower, I've convinced myself that the best the town can do in a 1-1-2 situation is lynch a townie and go to 1-1-1 with no new information.

NL and randomly shooting at 1-1-2 yields: Town win (1/9), Scum A win (2/9), Scum B win (2/9), 1-1-1 (2/9), 1-1 (2/9). If 1-1 is a three-way draw (everyone dead), that's 7/27 for the town (compared to 1/3 = 9/27 if they lynch a townie). If 1-1 is a two-way scum draw, that's 1/6 (compared to 1/4 if they lynch a townie).

Now, consider a situation where a townie volunteers for lynching. If there is some chance that townie won't actually be lynched (because we assume we now know him to be innocent), we haven't gained anything, because it is now in all of the remaining three player's interest to claim to be the second townie (if the scum don't, they lose, under the assumption that a full-knowledge PD is a loss). If we NL, it is the same as if we went to night 1-1-1 (just ignoring the known townie), but doing so risks a scum offering himself as a sacrifice in the first place. Thus, we must lynch the claimed townie, even knowing that that claimed townie must be innocent, because that knowledge is based on always following through with the sacrifice and because nothing is gained by leaving that townie alive.

In practice, there would probably be some measure of "player A was online but didn't offer himself as a sacrifice, he must be scum", in which case it really could devolve into a kingmaker situation (with player A knowing he can't win because the other scum will shoot him). The theoretical perfect scum would avoid things like this, though.

[mith]

Moved over to the numbers thread. If my numbers are correct and I'm not missing anything, I've shown that the strategy up to 1-1-5 is either to NL or to sac a townie. I suppose it's still Mafia (you still want to be posting in such a way as to look townie, only now you're trying to persuade the scum not to shoot you, rather than the town not to lynch you).

[shaft.ed]

Moved over to the numbers thread. If my numbers are correct and I'm not missing anything, I've shown that the strategy up to 1-1-5 is either to NL or to sac a townie. I suppose it's still Mafia (you still want to be posting in such a way as to look townie, only now you're trying to persuade the scum not to shoot you, rather than the town not to lynch you).

You broke it This will be even more of an issue when you add power roles to the town.

[shaft.ed]

it is worth noting; however, that not all games progress to 1-1-X easily.