Conqueror Kingmaker Situations

Test roles that have been suggested in simulated gameplay.

Conqueror Kingmaker Situations

Postby alex1234321 » Fri Jul 01, 2022 1:44 pm

One of the biggest reasons why Neutral Killing was removed from Ranked is the fact that they can form many kingmaker situations. Particularly, if there are three remaining players where one is Town, one is Mafia, and one is NK, the Town member usually gets to choose which of the other two players it wants to side with, arbitrarily determining the outcome of the game. Conqueror is supposed to be similar to an NK role but without the kingmaker problems. All vanilla 3-player Conqueror situations have a deterministic outcome, but some 4-player setups do not. Larger setups usually mean more confusion and make kingmakers less likely, but 4 players is still small enough that everyone knows each other's roles most of the time. The following 4-player setups allow one or more players to function as kingmakers.

Scenario 1: Town vs 2 Mafia vs Conqueror:

Mafia wins if Town is lynched.
Conqueror wins if Mafia is lynched.
Mafia wins if Conqueror is lynched.

If nobody is lynched, Conqueror attacks Mafia and heals Town, so Conqueror wins assuming no GF. If there is a GF and Conqueror attacks them, then it's back to the original situation. Repeated nolynches will always lead to a Conqueror victory.

Conqueror will always vote against Mafia, and Mafia will never vote against each other and will instead vote Conqueror since Conqueror will never vote Town. Town has the choice to either vote the Conqueror and hand the win to Mafia or vote nobody and let Conqueror win.

Outcome: Town decides between Mafia and Conqueror

Scenario 2: 2 Town vs Mafia vs Conqueror:

Conqueror wins if Town is lynched.
Town wins if Mafia is lynched.
Mafia wins if Conqueror is lynched.

If nobody is lynched, Conqueror attacks one Townie and heals the other, guaranteeing their victory.

All three teams have skin in the game and will likely vote the team they need to kill, causing a nolynch and Conqueror victory. However, the two Town members can vote against Conqueror and give the win to Mafia. If this were to happen, the Conqueror or Mafia might want to deviate to give the win to someone else. The game theory here gets pretty messy, but there are Nash equilibria that correspond to both Conqueror and Mafia victories. In other words, the Town cannot win because neither faction will help them, so they instead function as a kingmaker between Mafia and Conqueror. They can either vote Conqueror to give the win to Mafia, or have the voice between voting Town or stopping the lynch to give the win to Conqueror.

Outcome: Town decides between Mafia and Conqueror

With the current Conqueror wincon and abilities, both of these situations lead to kingmakers. But what if we tweak the role to fix this? I've thought about several possible changes to both the wincon and abilities, and the following change avoids any 3-4 player kingmaker situations.

Remove the heal. That's it.

Yes, it would basically turn Conqueror into SK. But there's nothing wrong with that. Rather than adding Conqueror into the game all you need to do is change SK's wincon and boom you've gotten rid of most kingmakers. Here is the same analysis but without the heal.

Scenario 1: Town vs 2 Mafia vs Conqueror:

Mafia wins if Town is lynched.
Conqueror wins if Mafia is lynched.
Mafia wins if Conqueror is lynched.

If nobody is lynched, Conqueror can no longer heal. Mafia will always win by attacking Town, and Conqueror can't do anything to stop it.

Conqueror will always vote against Mafia, and Mafia will never vote against each other and will instead vote Conqueror since Conqueror will never vote Town. Town can no longer hand Conqueror the win by stopping the lynch, so both opposing factions are powerless to stop the Mafia.

Outcome: Mafia wins

Scenario 2: 2 Town vs Mafia vs Conqueror:

Conqueror wins if Town is lynched.
Town wins if Mafia is lynched.
Mafia wins if Conqueror is lynched.

Things get complicated in the event of a nolynch. If Mafia attacks, Conqueror can win by doing nothing, and if Mafia does nothing, Conqueror can win by attacking. Meanwhile, Mafia can give themselves a chance if Conqueror attacks by trying to kill the other Town, which is better than a guaranteed loss. If Conqueror doesn't attack, Mafia can give themselves a chance by not attacking, which would bring things back to square one and be superior to a loss. The only Nash equilibrium here is when both Mafia and Conqueror both randomly decide whether or not to attack with a 50/50 chance of either. That way, both teams have a nonzero chance of winning, and Town has a minuscule but nonzero chance of getting a draw in the event that neither player attacks two nights in a row. The specific probabilities of each outcome don't matter, but what does matter is that all factions would prefer this option to a guaranteed loss, but they would also prefer a guaranteed win to this option.

If all factions vote the team that they need to lynch in order to win, nobody will get lynched. Meanwhile, any faction that deviates from this will either get nothing done or force themselves to lose, which would be worse than a nolynch for all factions. So nobody will ever deviate. Meanwhile, since no single faction can get anyone lynched alone, any faction that is currently deviating from this strategy can do better by stopping the lynch. The only equilibrium is if everyone follows this strategy, giving everyone a chance to win the game.

Outcome: Nobody is lynched and everyone has a chance to win or at least draw

The question becomes whether it's worth it to do something like this and whether mind games are a superior option to kingmaking. My answer to that question is yes, because in the final scenario both the Mafia and the Conqueror are making decisions that have an impact on their own outcome of the game. Even though the best strategy is to be as unpredictable as possible, both factions have an incentive to be unpredictable. Meanwhile, in kingmaker situations, no one has an incentive to do anything, and the game comes down to what the individual players feel like doing in the moment. Mind games aren't ideal, but this is a better outcome than a situation where players are making completely arbitrary decisions. The problem with Pirate is that it adds a layer of the game that is completely unrelated to everything else that is happening whereas endgame scenarios are an integral part of the game.
#SaveTheTG

Tired of trying to play discord Mafia games and not getting enough people? Join Town of Morons! We now have our own bot!


Credit to PurpleSidewalk1
User avatar
alex1234321
Role Ideas Moderator
Role Ideas Moderator
 
Posts: 4508
Joined: Sat Nov 28, 2015 4:20 pm
Location: Somewhere (UTC-5)

Return to Testing Grounds

Who is online

Users browsing this forum: No registered users and 2 guests