[SETUP] [EV] Monty Hall 7p

[Mathdino]

Monty Hall Mafia 7p

Roles

:

• 5 Vanilla Townies
  
  
• 2 Mafia Goons

Mechanics

:

• Nightless. Day occurs in two phases: Protect Phase and Lynch Phase.
  
• Pre-game, the mafia must submit a kill list of all town players. They may update this kill list at any point during the game.
  
• During Protect Phase, players vote for a player to be protected from the mafia kill for that day. No player may be protected two days in a row.
  
• Once Protect Phase ends, the first unprotected living player on the mafia's kill list is revealed to be poisoned.
  
• During Lynch Phase, players vote for a player to be lynched.
  
• Once Lynch Phase ends, the lynched player and the poisoned player both die, and the next day begins.
  
• Lynches are compulsory. If there is no majority by the deadline for either phase, plurality lynch will occur.

Spoiler: Version 2

Monty Hall Mafia Draft 2

Roles

:

• 7 Vanilla Townies
  
  
• 2 Mafia Goons

Mechanics

:

• Nightless. Day occurs in two phases: Protect Phase and Lynch Phase.
  
• Pre-game, the mafia must submit a kill list of all the town players. They may update this kill list at any point during the game.
  
• During Protect Phase, players vote for a player to be protected from the mafia kill for that day. No player may be protected twice in a row.
  
• Once Protect Phase ends, the first alive/unprotected player at the top of the mafia's kill list is revealed to be Marked for Death.
  
• During Lynch Phase, players vote for someone to be lynched.
  
• Once Lynch Phase ends, the lynched player and the marked player both die, and the next day begins.
  
• Lynches are compulsory. If there is no majority by the deadline for either phase, plurality lynch will occur.

Spoiler: Version 1

Monty Hall Mafia

Roles

:

• 7 Vanilla Townies
  
  
• 2 Mafia Goons

Mechanics

:

• Nightless. Day occurs in two phases: Lynch Phase and Switch Phase.
  
• Pre-game, the mafia must submit a kill list of all the town players. They may update this kill list at any point during the game.
  
• Once any player receives a majority of votes, Lynch Phase ends, and the player at the top of the mafia's kill list is revealed to be Marked for Death. If the Lynch Phase target is at the top of the kill list, the next player is Marked.
  
• During Switch Phase, the town is given two voting options: The player with the most Lynch Phase votes, and the player with the second most votes (with ties broken by whomever received that many votes first).
  
• Once one of these two players receives a majority of votes, Switch Phase ends, that player is lynched, and the Marked player is killed by the mafia.
  
• Lynches are compulsory. If there is no majority by the deadline, plurality lynch will occur.

[Mathdino]

EV for 9p 2:7

Because of the Monty Hall Problem, in theory, it is always optimal for town to switch. I'm not sure how this would work in practice, and I'm not sure whether to determine the second Switch Phase choice by 2nd most votes, or just by randomness.

Either way, assuming town always switches, the expected value is actually somehow 57.0%. This is mostly because of LyLo turning into the actual Monty Hall Problem.

EDIT:

This has outdated assumptions from Draft 1 baked into it that make it not the real EV in practice. I'm not sure how to calculate EV given the partial doc clears, but I'm open to suggestions.

• 2:7. If town votes scum (2/9), switching after the Mark has a 1/7 chance of success. If town votes town (7/9), switching has 2/7. 16/63 chance of hitting scum.
  • 1:6 (16/63). If town votes scum (1/7), switching has 0/5 chance. If town votes town (6/7), switching has 1/5 chance. 6/35 chance of hitting scum.
    • 0:5 (16/63 * 6/35).
      WIN
      .
      
    • 1:4 (16/63 * 29/35). If scum (1/5), switch gives 0/3. If town (4/5), switch gives 1/3. 4/15 chance.
      • 0:3 (16/63 * 29/35 * 4/15).
        WIN
        .
        
      • 1:2 LyLo (16/63 * 29/35 * 11/15). The Monty Hall problem. 2/3 chance of town win.
        • 0:2 (16/63 * 29/35 * 11/15 * 2/3).
          WIN
          .
          
        • 1:1 (16/63 * 29/35 * 11/15 * 1/3). Loss.
  • 2:5 (47/63). If scum (2/7), switch gives 1/5. If town (5/7), switch gives 2/5. 12/35 chance.
    • 1:4 (47/63 * 12/35). See above 1:4 calculations.
      WINS
      here are (47/63 * 12/35 * 4/15) and (47/63 * 12/35 * 11/15 * 2/3).
      
    • 2:3 LyLo (47/63 * 23/35). If scum (2/5), switch gives 1/3. If town (3/5), switch gives 2/3. 8/15 chance.
      • 1:2 LyLo (47/63 * 23/35 * 8/15). See above.
        WIN
        is (47/63 * 23/35 * 8/15 * 2/3).
        
      • 2:2 (47/63 * 23/35 * 7/15). Loss.

(16/63 * 6/35) + (16/63 * 29/35 * 4/15) + (16/63 * 29/35 * 11/15 * 2/3) + (47/63 * 12/35 * 4/15) + (47/63 * 12/35 * 11/15 * 2/3) + (47/63 * 23/35 * 8/15 * 2/3) =

57.0%

.

EDIT

: For 2:5 town EV, take (12/35 * 4/15) + (12/35 * 11/15 * 2/3) + (23/35 * 8/15 * 2/3) =

49.3%

.

[Mathdino]

If the mechanic is dropped for 3p LyLo, which replaces all the 2/3s with 1/3, town EV drops to 36.9%.

I'm super open to any feedback that could balance it out, remove breaking strategies, or make the setup easier to understand. I'm not sure if either 57% or 37% EVs are playable, but I intend to run something with this mechanic if approved.

Edit: Another possibility might be to just instantly kill the "Marked" player at the end of the Lynch Phase, unless it's LyLo. This would give town less control over the votes during Switch Phase.

I think in practice, because the mafia kill is definitely not random (and it's probably never optimal to Mark the 2nd biggest wagon), the EV might actually be identical to Marked For Death. I'm not at all sure though.

[popsofctown]

I don't think it's a good setup. The problem with it is overlap between the factional mafia kill's incentives and the monty hall information.

Mathdino: Day 1 begins! With 9 players alive it takes 5 to lynch.
DarkIdeal2019: Hai everybody! So excited to play with you all. We are gonna have a fun game and lynch all the mafias LOL. By the way, just so you know, I am alive in four games, and I am town in only one of them. Makes it more exciting for all of you!! <33333
(GreenKitty: I revise our deathlist, MathDino. DarkIdeal2019 is now at the bottom of the deathlist)
Entire town: VOTE: DarkIdeal2019
Mathdino: Ok that's a lynch. But wait guys. I got some info for you. This is going to rock your world. It's a gamechanger. It's fantabulous.
Did you know the scumteam is disinterested in using up the factional nightkill on DarkIdeal2019? Let's all take some time to chew on this curveball here.
Entire town: No shit sherlock, even if she's town she's not an NK candidate.


You've acknowledged the same, more or less. But, yeah. It might eventually creep up to create a little bit of edge but I'm concerned about mechanics that are live all the time and meaningful 10% of the time.

It also seems like the mechanic generates benefit if and only if the town wants to lynch the same people the mafia want to NK, and I generally feel like those gamestates are the ones where mafia are outplaying, so I think it is unpalatable for those to be the ones where town is getting prizes. Opposite reward/punishment feedback loop from vig, etc.

Did you see Jingle's Monty Hall setup in Open Setup Reviews?

[popsofctown]

It's like, not really the Monty Hall problem because the leading wagon never ever could have been the NK. If the first door you pick is the door to a birdhouse that doesn't have room for a million dollars in it, it's not Monty Hall anymore.

[popsofctown]

There have been two other Monty Hall threads in the past few months ftr:
viewtopic.php?f=115&t=79926 - Something Smart
viewtopic.php?f=115&t=79846 - popsofctown

For the most part I have a pretty high level of concern that it is one of those setup concepts that is intriguing conceptually but not geared to deliver fun dayplay dynamics.

[Jingle]

I think it's more elegant as a vote for doc phase and vote for lynch phase with a public nightkill before the latter resolves, tbh. Should have the same EV as the always switch suggestion, doesn't run into the mess of organizing both the highest wagon and the second highest wagon to get the second highest wagon lynched.

[Mathdino]

Thanks for the feedback pops, you definitely articulated what I had a bad feeling about. And yeah, I found all the Monty Hall suggestions (and credit to them because they partially inspired this); I'm trying to see if it's workable as all-Mountainous without breakable mechanics.

I think Jingle rephrased it really really well. It seems like a more explicitly Monty Hall version of this idea, and still becomes the actual Monty Hall problem at 3p.

I'll edit the 2nd draft into the OP later. Pops, what do you think of Jingle's idea?

I can run EV calculations on 3:8 later. I'm wondering if in practice 2:7 isn't actually 57% townsided due to mafia influence on voting.

[Jingle]

57% EV is pretty damn good for an experimental setup. I mean, obviously if it runs at scum winning 80% of the time, numbers need to be tweaked, but I'd guess it's roughly balanced as is.

[Mathdino]

Fair enough. I'm more concerned about town winning too much.
I think i could significantly cut town EV by making it impossible to protect the same player twice, but the EV there sounds a bit monstrous given how that changes scum's kill calculus.

[Jingle]

I think i could significantly cut town EV by making it impossible to protect the same player twice, but the EV there sounds a bit monstrous given how that changes scum's kill calculus.

I'd support the change. I think the impact to actual chances would be lower than it sounds, but it would prevent having a powertown player walk in and roflstomp scum without scum being able to do ANYTHING (which is negative fun).

In the absence of a wide skill disparity, it shouldn't effect chances too much either, and I think (given random lynching) it would actually have a 0% change on EV because the doc shot is randomly determined anyway.

[RadiantCowbells]

As is, all you have to do is have one correct townread and not colossally fail at hitting 1/2 scum

Changing the rules so you can't have one TR you chain protect means that this game becomes colossally harder for town.

[Mathdino]

As is, all you have to do is have one correct townread and not colossally fail at hitting 1/2 scum

Changing the rules so you can't have one TR you chain protect means that this game becomes colossally harder for town.

Alright, I changed it per Jingle/RC feedback.

I think it's technically ideal play for scum to always NK yesterday's doc target when possible. But then leads to WIFOM in the case of mafia getting doc'd themselves.

In any case, the problem with EV is that each player's chance of being scum doesn't reset each day. It carries over from previous days. Which is why RC is right; the d1 doc target is more likely to be town the more you continue doccing them, so town EV snowballs. I don't think EV for the new situation is calculable without some serious game theory calculations for ideal play.

But more importantly, do you think it's fun/playable?

[popsofctown]

I'm kind of fuzzy on Jingle's suggestion but if I follow it properly he's proposing a setup where "look who got docced" is being used in place of "look who got NKed" to create the Monty Hall pattern, which would correct the issue with the original setup.

I think it sounds fun enough to run. I am a little wary of setups with partial clears, occasionally it's unfun to vote your brain over your heart and lose because there's a partial clear and sometimes it's correct play to be a misanthrope. But fullclears are even worse and therefore that must just be me complaining about all mechanics that aren't mountainous mafia

except vig is the best role

.

57% EV is pretty damn good for an experimental setup

I know my balance preferences are a lonely hill on forum.townsideiadum.net but good grief 57% town EV is not ok, experimental or not. Copping out on balancing your setup is not ok when it's an open setup and you can put in the work for your players if you want to.

[popsofctown]

Actually I'm going to backup and say I take no position on whether partial clears or full clears are better design.

Anyway I think this is a playable setup concept.

[Jingle]

I think your issue is that you’re conflating EV with win rates, pops. Just because the ev says town should win 57% of the time doesn’t mean they will. For a setup that I don’t think has a direct comparison to meter it, I’d try anywhere from 40-60 as decent and tweak from there because while we can talk about how well town will over/underperform we can’t really guarantee anything until it’s been run.

With an experimental open, the players know that balance is a work in progress, so giving it that wiggle room is completely reasonable.

[popsofctown]

40-60

I think the symmetry implication is flawed. Games centered around information asymmetry will be most fun when they are balanced to favor a particular side. The side you want favored is the one that has access to more information. That side's winrate can fall towards 50%, even below it, as they leak and fail to safeguard information.
There are two reasons the funness skews this way:
- lottery effect. To some extent, randomness and/or the unknown is inherently fun. Town can often believe they have a great chance of winning when they in fact do not. Town that is searching for the player in the unconfirmeds, ignoring the player who was "cleared" by a gunsmith but is actually a mafia doctor, is having fun. Each lynch feels like a chance to get red. Due to the information asymmetry this lottery effect does not work in reverse. A scum that sees the game's consensus lynchpool is gamewinning and knows it is only narrowly likely for scum to escape that lynchpool will be miserable. It is unfun to spend large amounts of time in a game you have a low chance of winning also have the information of that fact.
- player agency. There is a lot more player agency in trying to read clues and find information leaked from the high information team. When player agency is not enough to surmount the odds, it will still feel fun that you tried. There is not as much player agency in trying not to lose a game as the informed player, especially when the mechanics are such that random behavior will produce an informed loss, so the uninformed player has to be actively manipulated. There is no more information to gather, you already have all the information. That is not to say that playing high information doesn't require skill, of course it does, but it's such an interactive skill, you are trying to mislead the other player, all methods of doing so are contingent on the other player's participation. There is rarely a clear thing you "should have" done to earn a false townread as scum because you must anticipate future cooperation for that to work, and it can be debatable whether the victim would cooperate in their own gaslighting. As town the "should have" can be rather clear. It can be totally based on past events in the thread that would lead to a correct read, and no future behavior from the scum needs to be contemplated to think about that.


In Android Netrunner the release of new card sets often shifted the power between the informed player and the uninformed player. We had so many years that were so unfair to the uninformed player, sets where just a deception or two easily won the informed player the entire game, sets where phase 2 of the game was pretty consistently played with the low info player picking between strategies that yield a 15% chance of winning or a 25% chance of winning. People loved those years. They'd get nostalgic and reminisce about it. It did not remove deception from the game for the informed player to have this advantage, employing deception could secure an even higher winrate.

In the game's latest years, a couple card sets created a heavy amount of power for the uninformed player, and feedback was far more negative. It was incredibly miserable once a game set its way along a path that made it clear a loss for the informed player was -almost- guaranteed. It provided little to no extra enjoyment when playing the uninformed side. The answer to decepting choices, "pass up on the treasure, or fall into the trap?" was so often "I'm advantaged to win, I choose xyzzy". Every single individual player, of course, won 50% of the games that they played in either meta, because people take equal turns as the informed and uninformed player. But just as Jingle perhaps implies winrates are not what matters. The strategic consequences of the mechanics in the game are what matters.




Again I know I am lonely in my view. But these are my philosophies.

[Jingle]

Agree to disagree, I guess.

[Mathdino]

I'm extremely certain that 57% is not the actual EV. It only applies if town and mafia make their decisions completely independent of previous days, and completely randomly. I agree with RC's intuition that the change makes it super difficult for town, and town typically suffers a hit to winrate in mountainous setups by default.

Imo the partial clear is based on democracy anyway. If town votes to doc a mafia member in Lylo and then makes the mathematically correct play of not lynching them, that's town's fault for doccing mafia.

I'll ask around for a couple more opinions and then I might just queue it up!

[Jingle]

I'm extremely certain that 57% is not the actual EV. It only applies if town and mafia make their decisions completely independent of previous days, and completely randomly. I agree with RC's intuition that the change makes it super difficult for town, and town typically suffers a hit to winrate in mountainous setups by default.

Au contraire. It's almost certainly the actual EV assuming I didn't miss a logic gap. The problem is that EV =/= functional winrates because EV doesn't take into account things like skill. It's all about theoretical vs. practical, and I think in this case you're right that practical will undershoot theoretical.

I'd guess town would win about 40% of games of this over a large sample size. I also don't think there's a setup similar enough to make that subjective guess more concrete.

Hit me up if/when you hit signups. I'd probably be down to be a body in this one.

[RadiantCowbells]

Want me to calculate actual winrate

[Jingle]

I'll bite. How?

[Mathdino]

I can't believe I didn't think of this, but using the same calculations I already made, EV for 2:5 is 49.3%.

Would you guys sign off on this as a 7p?

[Jingle]

I'd play it.

[popsofctown]

I can't believe I didn't think of this, but using the same calculations I already made, EV for 2:5 is 49.3%.

Would you guys sign off on this as a 7p?

Hawt