Also, I got sick of debating this in-game when it should be more for discussion.
http://www.sc2mafia.com/forum/showthread.php/36913-Day-1-Lynch-Policy-Analysed
(It stands to reason that these same statistics provided would be similar to CC's, but for the sake of the argument, I'll take 20 games with a lynch and a no lynch (40 games in total) to validate the claim. I'm at work at the time of this post so my time is limited, getting all this info every other hour has been hard enough. Give me time. ).
https://mybroadband.co.za/vb/showthread.php/526350-NO-Lynch-Strategy
A post on the statistical considerations of first-day lynchings:
(TL;DR version: Don't lynch on day 1 if you can avoid it.)
The exact numbers involved in this will vary highly depending on the number of players and the number of mafia members. However, in general, it is a benefit to the village to not lynch on the first day (if the rules make it possible), as I will try to show here.
First of all, in almost all cases, the first day lynch will be completely random; there simply is not anything solid to go by in the first day. This means that first-day lynches can therefore be looked at from a purely statistical perspective. One important consideration to keep in mind which stems from this: There will almost always be one less villager the second day (because of the mafia's kill) than the first day, and this improves your chances of randomly guessing a mafia member. For example, in a game featuring 6 players with 1 mafia member, each villager's chance of guessing the mafia correctly on the first night is only 1-in-5, or 20% (remember, any villager guessing would be discounting themselves), whereas waiting a night and letting the mafia kill someone improves that chance to 1-in-4, or 25%.
Secondly, if there are an even number of players, then it is possible for the village to gain an extra day in a worst-case scenario (repeatedly lynching villagers) if they refrain from lynching on the first day. As an example, using a game starting off with 10 players, two of whom are mafia members:
Day Lynch on Day 1 No lynch on Day 1
1 10 10
2 8 9
3 6 7
4 4 5
5 2 (loss) 3
6 --- 1 (loss)
Keep in mind that, so long as the village is able to control the lynch vote, there is a chance of victory... so, that extra day means that there is still a hope of victory after the point when the first-day lynch would have led to a village loss.
Putting off a first-day lynch improves the chances of the village winning (though with closer victories) in almost all cases, but delaying past that tends to hurt the village. To illustrate how large of an effect this can have, I'll provide some probabilities from three hypothetical games. While the actual math is a bit too space-consuming to put here, the odds of victory (given purely random lynching each day) for these games are as follows:
In a 6-person match with one mafia member:
First lynch on day 1: 38% chance of village win, 63% chance of mafia win. Average of 3.89 villagers left if the village wins.
First lynch on day 2: 47% chance of village win, 53% chance of mafia win. Average of 2.86 villagers left if the village wins.
First lynch on day 3: 50% chance of village win, 50% chance of mafia win. Average of 3.0 villagers left if the village wins.
In a 10-person match with two mafia members:
First lynch on day 1: 22% chance of village win, 78% chance of mafia win. Average of 4.04 villagers left if village wins.
First lynch on day 2: 30% chance of village win, 70% chance of mafia win. Average of 2.98 villagers left if village wins.
First lynch on day 3: 16% chance of village win, 84% chance of mafia win. Average of 3.53 villagers left if village wins.
In a 12-person match with three mafia members:
First lynch on day 1: 11% chance of a village win, 89% chance of a mafia win. Average of 3.71 villagers left if the village wins.
First lynch on day 2: 16% chance of a village win, 84% chance of a mafia win. Average of 2.65 villagers left if the village wins.
First lynch on day 3: 7% chance of a village win, 93% chance of a mafia win. Average of 3.36 villagers left if the village wins.
Appendix: Chances of you randomly guessing a mafia member, by number of remaining players (chances are per remaining mafia member; multiply by the number of mafia members left to get actual chances)
Players (including you) Chance
3 50%
4 33.3%
5 25%
6 20%
7 16.7%
8 14.3%
9 12.5%
10 11.1%
11 10
12 9.1%
13 8.3%
14 7.7%
15 7.1%
17 6.7%
18 6.3%
19 5.6%
20 5.3%
Mainly used this one to help support the no lynch in statistical terms.
As for my own brief stance, that I'm sure, by now, everyone is well aware of, I don't agree with the lynch policy on Days 1.
1. You have a joke phase that lasts for several pages and then it becomes an awkward accusations phase afterwards. I tend to look at it as if it's a meet and greet.
2. Accusations are mostly baseless. Nothing concrete to follow up on, no roles to confirm or deny claims. The argument of "feeling" for a players reaction to bandwagons or pressure from others is, while a decent tool, I don't believe it serves any purpose later. It's almost as if it's like town hunting instead of scum hunting. You may have someone reveal as cop or doc and that just hurts.
3. "Its for the benefit of the town!". I disagree. Look at it strategically. Is 2 dead town better than 1 dead town? In some cases I believe luck plays a bigger part of it than anything. For example, the game currently running at the time of this post (Lion King) a Vig killed a scum. While I applaud a job well done, I whole heartedly believe that it was 100% luck with no other factual evidence being in play.
4. Lynching is the towns most powerful tool. I agree with this statement to a fault. There's been many a time when the town simply gets lynch happy and just suicides to death. It's a minor double edged sword, by minor I mean that it can sway in scum's favor if there is enough misinformation or abuse of the vote. Remember, scum can also vote and with enough persuasion, can get others lynched. I think Day 1 can apply to this more heavily than the others when there are no roles to oust a scum.
5. Town can take the hit over scum. I agree and disagree. On one hand, if the lynchee turns out to be a useless role such as a miller or something similar with no night ability, on another, people can't seem to grasp the concept that losing a jail, doc, cop or another power role is simply devastating. Even backing people into a corner may have them be revealed and killed outright. However, I realize that scum are way more pressured if they were to lose one, and therefor, have to be careful. This is why I notice a lot of lurkers/submariners during the Day 1 phase after the joking subsides. No one wants to be a target and no one wants to be killed Day 1, regardless if it's for "The Greater Good".
6. Cons. Con's are pretty obvious but I believe it wouldn't have any impact on the outcome of the game. No one will feel pressure during the Day 1 phase if everyone plays the "No Lynch" card. There wouldn't be much of a day phase outside of just the typical "whats up lolz". Some argue that scum get a free pass. I'd like to think that it's Town erring on the side of caution rather than risking ousting power roles and or lynching them by accident. Statics are honestly a horrible reference to use in a game where gathering information is key, however, it stands to reason that even a game such as this, patterns do develop in a grander scale, basically, I can see both sides of the spectrum but I'm choosing one over the other, which is apparently wrong.
I am by no means saying "HEY CC! CHANGE YOUR PLAYSTYLE AND POLICY!" I am merely advocating my stance and what others (Apparently across the web as well) the pro's and con's to a no lynch. I'm also, again, making this post so we don't have to have another debate the merits of lynching vs not lynching on Days 1.
I whole heartedly respect people's playstyles and approach on their game. Chu, Ragian (You poor f*ck lol), Mandy, and Hotshot to name a few. If it suits your style, it suits your style.
Let's try and keep this discussion here rather than in-game from now on, I feel like it'll be one of those that would be re-occurring.
Disclaimer: I am by no means attempting to take an in-game topic outside to here, nor am I attempting to relieve myself of pressure inside of Lion King. I simply wanted to avoid a 3rd or 4th or infinite amount of discussion of the pros and cons of a no lynch.