Just like the simulations

[MURDERCAT]

Since I first joined the site I've gotten pretty good at this whole coding thing. A couple times since I've been back I've found it useful to run a simulation to understand something about a setup as it's a lot easier than actually doing math. This includes more difficult EV calculations, but also things like probability of different role combinations in semi open setups.

So, if there is something you want to know about a setup, request a simulation and I will do it for you. I am trusting you all to not break ongoing games rules.

[MURDERCAT]

Fae of Wishes

11 Townies

3 Mafia

During day 1, players may first/second/nth a motion to invite a player from outside the game to become a faerie. The moderator will contact users who are "6thed" and confirm up to three acceptances in the thread. Faeries win with the town.
Night 1, there is no factional nightkill and a random

Townie

becomes

Favoured by the Fae

. The following things are true about you if you are

Favoured by the Fae

for as long as you are

Favoured by the Fae

:

• You are eliminationproof
  
• You have daytalk and nighttalk in the Fae PT, where all three faeries also have daytalk and nighttalk
  
• You have a night action that will cause you to no longer be
  Favoured by the Fae
  and will cause your target to become
  Favoured by the Fae
  . It will fail if the target is mafia or is being visited by mafia.

The mafia are multiacting and have a factional roleblock. Faeries have no activity requirement and won't be replaced.

Assumptions

Elimination, robeblock, and kill targets are usually chosen randomly
If the favoured townie is an elim target, they will out themselves and another target will be selected
If a confirmed townie is targeted for an elim and another confirmed townie exists, all confirmed townies will out themselves and another target will be selected
If the favoured townie is outed, they will always be roleblocked and killed
If a confirmed townie is outed but the favoured townie is not, they will always be the kill target
No information is gained from night actions (because it's hard to simulate)
Scum will never fake claim (because it's hard to simulate)
The favoured townie always attempts to pass it (to create more confirmable townies)

Example Simulation 1

Day 1
Eliminating townie.
Night 1
Favoured townie chosen.
Day 2
Eliminating townie.
Night 2
Townie killed.
Pass successful.
Day 3
Eliminating townie.
Night 3
Townie killed.
Pass successful.
Day 4
Eliminating mafia.
Night 4
Townie killed.
Pass failed.
Day 5
Attempted to eliminate confirmable townie. Outted instead.
Eliminating mafia.
Night 5
Confirmed townie killed.
Pass successful.
Day 6
Eliminating mafia.
Town wins!

Example Simulation 2

Day 1
Eliminating townie.
Night 1
Favoured townie chosen.
Day 2
Eliminating townie.
Night 2
Townie killed.
Pass failed.
Day 3
Eliminating townie.
Night 3
Townie killed.
Pass successful.
Day 4
Attempted to eliminate favoured townie. Outted instead.
Eliminating townie.
Night 4
Favoured townie killed.
Day 5
Eliminating mafia.
Night 5
Former favoured townie killed.
Day 6
Eliminating townie.
Mafia wins!

Results

Simulations run = 100000
Total town wins = 33541
Expected town win percentage = ~33.5%

[MURDERCAT]

Fixed! That does change things a lot, I think because the favoured townie just kind dies sometimes and then town is in something like a 10:3 ratio with no help.

[MURDERCAT]

What if you remove the roleblock and make it so that a kill leads to no pass? Then town at least isn't randomly unable to pass sometimes, but they are still punished if the favoured is outed. Maybe that is actually worse though?

[MURDERCAT]

I think a lot of the time that the favoured is killed they are also RB'd because they were outed during the day. But in the cases where they are randomly killed that is really bad

[MURDERCAT]

Yes! I will do this tomorrow probably. This is two different sims, correct? Or both in one?

[MURDERCAT]

Ok!

[MURDERCAT]

With this method you end up with 49457/100000 town wins, so an EV of about 49.5%. Not sure if that is too townsided as the favoured townie is also basically getting cop investigations now that are unaccounted for. That is one problem with the bulletproof.

[MURDERCAT]

If you give me reasonable assumptions I will account for various interactions

[MURDERCAT]

It's possible, though probably that's the sort of thing EV/simulations do a bad job of capturing. If it's a closed setup you can send me pm and I'll let you if it seems feasible

[MURDERCAT]

Totally

[MURDERCAT]

Yeah I just did. 48%

[MURDERCAT]

Lol

[MURDERCAT]

I am joking that would be way too hard

[MURDERCAT]

Yeah that I could do

[MURDERCAT]

Yes but I'd have to code all of it

[MURDERCAT]

I played around with haskell a bit but was never any good at it. I usually use python or R depending on exactly what the simulation involves.

This looks like what Gypyx submitted to this month's setup challenge

[MURDERCAT]

I will have to think about how to do this one, as it's not clear when the game "ends." There's also a ton of abilities, so I'm not sure if random usage of them will really capture the setup well. But I can give it a shot this weekend.

[MURDERCAT]

This is a fun one, I will make a plot. 31-2 is only ~60% town win according to the EV project, which is surprising at first but also makes sense. 98-2 mountainous viable?

[MURDERCAT]

The numbers may be hard to see depending on your theme, if so you may need to download the figure. The x axis is the number of town players and the y axis is town win %

[MURDERCAT]

I'm sure there is some smart person like implosion or Ircher who knows or could figure out the exact formula. This is the relationship you'd expect though because at very high numbers of townies adding a single townie doesn't really do much to change the odds of hitting scum. Compared to lower numbers where obviously there is a big difference between 7:2 and 9:2.

[MURDERCAT]

I love that there is a literature on this

[MURDERCAT]

So basically, you prevent the mafia from being able to fake claim to out the cop.
This is an interesting question. Is counter claiming immediately ever actually the best strategy when you could instead just wait and see if the cop claim dies? I wonder if the general strategy in open setups should be to never counterclaim until elo.

pedit yeah I don't think people actually do that though. Also a 1:1 trade is kinda what you hope to get out of a PR (IMO)

[MURDERCAT]

Yeah I could give this a shot