The EV Project

[Vi]

The EV Project is a wiki page I started messing with in my spare time about two or three weeks ago to determine the theoretical chances of a given faction winning Open setups. Right now I've only really considered passive roles - Lovers, I.Children, Masons, and the like - because once you start adding active roles into the mix things balloon out of control pretty quickly.

It's full of :math:, probably not quite as organized as it could be, and will give most people a severe case of tealdeer; so I'll introduce it wiiiiiiith... a POP QUIZ! No cheating by looking at the page.

1. 10:2 Mountainous. You've heard of it before. How balanced is it?
(A) Extremely Town-sided (>75% Town win)
(B) Leaning Town-sided (60-75% Town win)
(C) Balanced (40-60% Town win)
(D) Leaning Scum-sided (25-40% Town win)
(E) Extremely Scum-sided (<25% Town win)

2. Well then, what about 11:2 Mountainous? How much more likely is Town to win an 11:2 Mountainous game than a 10:2 Mountainous game?
(A) Very much more (>10%)
(B) Not a lot more (7-10%)
(C) Barely more (4 - 7%)
(D) Like it even matters (1 - 4%)
(E) How about "not"? (<1%)

3. In White Flag, the Town wins if only one scum is alive. In the case of 10:3 Mountainous, how much does this improve the Town win rate?
(A) Like, a lot (>20%)
(B) Quite a bit (15-20%)
(C) You'd be surprised (10-15%)
(D) A fair amount (5-10%)
(E) Actually not much at all (<5%)

4. How many scum are needed to balance a Nightless game with 20 players total?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

5. How balanced is the Lovers Mafia setup - a Nightless setup with 4 Townies and 2 Mafia Lovers?
(A) Extremely Town-sided (>75% Town win)
(B) Leaning Town-sided (60-75% Town win)
(C) Balanced (40-60% Town win)
(D) Leaning Scum-sided (25-40% Town win)
(E) Extremely Scum-sided (<25% Town win)

6. If you only wanted to include a single scum in a Mountainous game, you are a bad person. But how many Townies should you include to make the game balanced? Assume that at even numbers the Town will No Lynch to get on odds, so only even numbers of Townies are available as answers.
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10

7. Let's say you are a Serial Killer in a game that has a player ratio of 5:2:1. How likely are you to win?
(A) At least as much as anyone else (>33%)
(B) It's still manageable (25-33%)
(C) This could get interesting (17-25%)
(D) I'm screeeeeeeeeeeewed (10-17%)
(E) I expect a Scummy after this (<10%)

8. Let's say that you have found yourself as the sole survivor of the second scumgroup in a game with a 2:2:1, and the game is presently in Night. How likely are you to win?
(A) I wouldn't count it out (>20%)
(B) Not so likely (15-20%)
(C) One can only hope (10-15%)
(D) This is gonna suck (5-10%)
(E) CHALLENGE ACCEPTED (<5%)

9. You are playing Friends and Enemies, and you are the last Mason alive. You have not yet claimed. Right now there are five Townies alive (including yourself) and two scum alive. You know that the scum will fakeclaim Mason to draw you out if it looks like they're going to get lynched.

Ceteris paribus

(that's economics-speak for "making the unrealistic assumption that there are no other factors"), what are your odds of winning?
(A) I like these odds (>45%)
(B) Not all that bad (35-45%)
(C) Not all that good (25-35%)
(D) I REALLY miss my Mason partners (15-25%)
(E) This is what should

really

be named White Flag (<15%)

Spoiler: Answers

1. (D) 10:2 Mountainous has historically been called "balanced" by people who haven't known better. The chance of Town winning a 10:2 Mountainous game is 35.2%, pretty much the same as if you just cut to the chase and started the game at 2:1 LyLo.

2. (C) 11:2 Mountainous has a win rate of 39.5%, a bit over 4% up from 10:2 Mountainous. So don't call that balanced either. The major boost from going to 13 players is that power roles have an extra Night to get results before LyLo.

3. (A) 10:3 Mountainous has a 20.8% Town win rate (ew). 10:3 White Flag ups this to 47.8%, an increase of 27%. See also the White Flag Gambit, though.

4. (C) The Nightless Expectation Rule allows you to calculate the theoretical win rate of a Nightless game for any number of players. The short version of it is that if scum make up a quarter of the players in the game, the win rate is balanced. Not that anyone would ever play a 20-player Nightless game - that's just me abusing theory.

5. (B) and (C) Trick question; the theoretical win rate is exactly 60%. What's interesting about this setup is that without starting the game in LyLo, there is no way to bring the game as it is closer to balanced. (It's also interesting because without bussing, it requires all of the Townies to unanimously vote to lynch scum.) Two caveats - studying what happens when only two of the three scum are Lovers hasn't been done yet, and this is another game that scum have loved to win via White Flag Gambit.

6. (D) 8:1 is closest to balanced (assuming random lynches, of course) with a 48.3% Town win rate. It wouldn't be held against you if you chose (E) for a 53.0% Town win rate, though.

7. (D) With a 11.1% chance of winning on your own, it's no surprise why people give immunities to Serial Killers.

8. (E) In a field filled with huge fractions and ugly decimals, it must come of some comfort to know that your chance of winning in this scenario is precisely 0. Multiball is not forgiving to scumteams who start losing members. You have a really nice chance of a draw (38.9%) based on Dilemma Yomi Layer 3 though.

9. (C) This is just barely at (C) level, with a 25.9% Town win rate. Contrast 5:2 Mountainous, which has a 22.9% Town win rate. Also contrast 5:2 with Innocent Child, which has a 24.4% Town win rate. One confirmed innocent suddenly doesn't look like much... If one of the other Townies was a dead Mason partner, though, things would look noticeably better.

I should probably include this too, for the curious - The EV Project

[zoraster]

I get different numbers than you, Vi. For example, 11v2 mountainous gives a 39.49% EV and 10v2 is only 26.43%, assuming day starts of course.

[Vi]

I get different numbers than you, Vi. For example, 11v2 mountainous gives a 39.49% EV and 10v2 is only 26.43%, assuming day starts of course.

Take a look at the page and tell me where your numbers start diverging.

[zoraster]

hold on. actually calculating now. I'm using the program. http://games-net.de/hosted/tggc/trash/m ... 0&do=Go%21

[Empking]

D
C
B
E is the right answer.
Unforgibably town-favoured: B
B
B
E
D

Also: Am I the only one of the view that anything over 50% is unbalanced? (To my mind that makes games like vanilla mountainious where the best play is to lynch randomly impossible to balance.)

[Vi]

Also: Am I the only one of the view that anything over 50% is unbalanced? (To my mind that makes games like vanilla mountainious where the best play is to lynch randomly impossible to balance.)

The major reason why they pass for balanced is because nobody actually lynches randomly.

zorro - I just tried a different method and got the 39.something. Let me look at things again.

This might cause a domino effect. :\

[Empking]

6. (D) 8:1 is closest to balanced with a 48.3% Town win rate. It wouldn't be held against you if you chose (E) for a 53.0% Town win rate, though.D) 8:1 is closest to balanced with a 48.3% Town win rate. It wouldn't be held against you if you chose (E) for a 53.0% Town win rate, though.

Are you high?

[zoraster]

Yeah, I'm fairly confident there was a screw up somewhere. 6v1 is the closest to a 50% town win rate at 54.29%, 8v1 gets me 59.37%

[Vi]

I found it. It's fairly high up on the chain so it shouldn't completely destroy everything, but I will need to do some fixing.

Empking - Perhaps I should say

balanced by random lynching

?

Actually, that would be a good follow-up topic to make - what would be considered "balanced" and some examples of each. ...Once I do the requisite readjusting.

[zoraster]

As for Empking: I think the closer you are to true mountainous, the more important it is to have an EV of close to 50%. If it's mountainous with a 55% town win rate, I think that's more balanced than a 40% town rate.

[Gammagooey]

Spoiler: Guesses

1)C
2)B
3)A
4)E (its either that or D)
5)1/3+((2/3)*(2/5))=60% town? B I guess
6)B
7)C (assuming killable)
8)B
9)D

edit: I seem to be fairly bad at this. I'm confused on how

8 is zero though, shouldn't it go to 1:1:1 some of the time and then sometimes you win by lynching the other scum?

[zoraster]

So for balanced I'd say

Powerless setups:
6v1 (7v1 with no lynching not allowed also works)
15v2
22v3 or 24v3 (though god knows why you'd want to run this)
10v3 White Flag or 8v3 White Flag

[Empking]

As for Empking: I think the closer you are to true mountainous, the more important it is to have an EV of close to 50%. If it's mountainous with a 55% town win rate, I think that's more balanced than a 40% town rate.

I'd say that other than 1:4, its impossible to acceptably balance a mountainious game. "More" balanced simply doesn't come into it.

[zoraster]

As for Empking: I think the closer you are to true mountainous, the more important it is to have an EV of close to 50%. If it's mountainous with a 55% town win rate, I think that's more balanced than a 40% town rate.

I'd say that other than 1:4, its impossible to acceptably balance a mountainious game. "More" balanced simply doesn't come into it.

I don't understand the point you're trying to make here. I'd say balance is easiest in a mountainous.

[Empking]

As for Empking: I think the closer you are to true mountainous, the more important it is to have an EV of close to 50%. If it's mountainous with a 55% town win rate, I think that's more balanced than a 40% town rate.

I'd say that other than 1:4, its impossible to acceptably balance a mountainious game. "More" balanced simply doesn't come into it.

I don't understand the point you're trying to make here. I'd say balance is easiest in a mountainous.

I don't understand the point you're saying either? How is it easiest to balance a mountainous?

[zoraster]

As for Empking: I think the closer you are to true mountainous, the more important it is to have an EV of close to 50%. If it's mountainous with a 55% town win rate, I think that's more balanced than a 40% town rate.

I'd say that other than 1:4, its impossible to acceptably balance a mountainious game. "More" balanced simply doesn't come into it.

I don't understand the point you're trying to make here. I'd say balance is easiest in a mountainous.

I don't understand the point you're saying either? How is it easiest to balance a mountainous?

In a game with only two sides, balance is giving both sides an even chance of winning in the abstract. It's basically a problem of math to balance a mountainous game, then. But once you start introducing power roles into the equation, those can be used in a multitude of ways and it's far harder to figure out how to simply calculate the use if done randomly. There are just a lot more variables in the equation and a lot more assumptions to be made. The more assumptions that must be made, the harder it is to truly balance a game.

[Empking]

As for Empking: I think the closer you are to true mountainous, the more important it is to have an EV of close to 50%. If it's mountainous with a 55% town win rate, I think that's more balanced than a 40% town rate.

I'd say that other than 1:4, its impossible to acceptably balance a mountainious game. "More" balanced simply doesn't come into it.

I don't understand the point you're trying to make here. I'd say balance is easiest in a mountainous.

I don't understand the point you're saying either? How is it easiest to balance a mountainous?

In a game with only two sides, balance is giving both sides an even chance of winning in the abstract.

That's simply not true.

[zoraster]

Say what? Why not?

[Vi]

Woo. That didn't change nearly as much as I feared. Okay, the party can resume now.

@Gammagooey: Remember that we're talking about Open setups. It will be known that the situation is 1:1:1. The scum can only draw.

@zoraster: I believe Empking is trying not to say that Town should lynch better than average.

[Gammagooey]

but if it's 1:1:1 then shouldn't they no lynch and then have one possibly kill the town while the other kills the other scum?

[zoraster]

I'd love to see some sort of data that confirms town lynches better than average over a large number of games without the assistance of power roles, but our sample size is fairly small.

Still, my argument isn't that balance means average randomly. If we can establish town lynches 10% better than average OVERALL, then balance would take that into account. My point is that a perfectly balanced game if run a thousand times to people who were unfamiliar with it, it'd end up with close to 500 victories for town and 500 for scum.

[Vi]

but if it's 1:1:1 then shouldn't they no lynch and then have one possibly kill the town while the other kills the other scum?

Which naive soul is playing the other scum role, that you actually expect them to kill the Townie?

[Zachrulez]

This page should be of great help to people like myself who are too lazy to figure out how to calculate EV themselves...

[zoraster]

This page should be of great help to people like myself who are too lazy to figure out how to calculate EV themselves...

Have you tried out this tool, Zach?

http://games-net.de/hosted/tggc/trash/m ... 0&do=Go%21

[Gammagooey]

If neither scum have claimed scum like idiots then they should have a 50/50 shot of hitting town in the final night.