When should the cop come forward?

[Zorblag]

Yosarian2 actually needs 1 more confirmed town (to get to the more than half him said were needed) for that example to work with 12 players (5 straight mislynches still be possible and loses for the town) but otherwise the idea be right.

-Zorblag R`Lyeh

[mykonian]

It's also worth remembering that if town ever gets to the point when more then 50% of the town is confirmed innocent, then if there's only 1 scum kill a night, town should always win (unless something stupid happens).

So, if there's 12 people left alive, there are 3 known masons, and you are a cop with 2 confirmed innocents, then claim. With 1 claimed cop in the open (soon to be night-killed most likely), 2 cop-cleared innocents, and 3 masons, that's half the town confirmed innocent; all town has to do is to lynch one person in the pool of "unconfirmeds" every day, and town wins.

this is if you have no risk at being killed. When that comes in to play, you are also happy with an increased chance, since waiting for the sure win is a bigger gamble. So ideally, you claim before this situation, to avoid being killed before you can claim.

[Elmo]

I actually think there is a close-to-optimal analytic solution to this (if you can accurately estimate a few things), but I'm just too lazy right now. I'm pretty sure you can find an exact solution (or at least an exact higher bound) for closed California using the random lynching EV vs. random nightkills if you assume that the cop is never lynched outside of LyLo and the cop is always nightkilled after claiming.

Of course, accurately estimating the "few things" is where you have to fudge it hugely, and is where it just becomes "it depends" outside of something like Califonia, imo.

[Mr. Flay]

So, if there's 12 people left alive, there are 3 known masons, and you are a cop with 2 confirmed innocents, then claim.

Has anyone put a 3-man Confirmed Mason group in a game in 4 years, though?

[Yosarian2]

So, if there's 12 people left alive, there are 3 known masons, and you are a cop with 2 confirmed innocents, then claim.

Has anyone put a 3-man Confirmed Mason group in a game in 4 years, though?

Sure, 3 man mason groups are pretty common in large games. .

Of course, there's other ways to get confirmed innocents (or mostly confirmed innocents) as well. Also, if there's a town vig, that can help as well, since it means the town can go through the pool of unconfirmeds faster.

[Yosarian2]

It's also worth remembering that if town ever gets to the point when more then 50% of the town is confirmed innocent, then if there's only 1 scum kill a night, town should always win (unless something stupid happens).

So, if there's 12 people left alive, there are 3 known masons, and you are a cop with 2 confirmed innocents, then claim. With 1 claimed cop in the open (soon to be night-killed most likely), 2 cop-cleared innocents, and 3 masons, that's half the town confirmed innocent; all town has to do is to lynch one person in the pool of "unconfirmeds" every day, and town wins.

this is if you have no risk at being killed. When that comes in to play, you are also happy with an increased chance, since waiting for the sure win is a bigger gamble. So ideally, you claim before this situation, to avoid being killed before you can claim.

Well, I'm saying you should *always* claim if it means the town is then going to have +50% of the people in the game as confirmed innocents (if there's only one killing scum group, at least). If not, then there are still times you might want to, it's situational obviously.

[petroleumjelly]

So, if there's 12 people left alive, there are 3 known masons, and you are a cop with 2 confirmed innocents, then claim.

Has anyone put a 3-man Confirmed Mason group in a game in 4 years, though?

In Back to Gambits 1 & 2, the town was outright told at the beginning of the game that there were 3 Confirmed Masons (in other words, you never really had to question them ever). I think there have also been those crazy open games with like 4 mafia v 4 masons v 4 townies, or somesuch. Though I guess in the open games there probably weren't Cops that would make this comment in any way relevant to the thread. >.>

[ortolan]

a game/series called "back to gambits" sounds inherently awesome.

[Yosarian2]

Yosarian2 actually needs 1 more confirmed town (to get to the more than half him said were needed) for that example to work with 12 players (5 straight mislynches still be possible and loses for the town) but otherwise the idea be right.

-Zorblag R`Lyeh

And yes, you are right. You actually need more then 50% confirmed town to have an autowin, so 6 town out of 11 here.

It happens more often later in the game; it's not unusual to end up with 4 confirmed town out of 7 after a cop claim, or something like that.

[YamiJoey]

Assuming that the Cop is confirmed, and that any given Townie can count themselves into it, you really only need 4/11 to justify coming forward.

If a game starts with 10 Town Vs 2 Scum, mislynching every turn, and Cop scanning a Town that doesn't get lynched or killed, assuming Cop is the only power role: (Toown:Scum [Confirmed by Cop])

D1: 10:2
D2: 8:2 [1]
D3: 6:2 [2]
D4: 4:2 [3]

At D3 the Cop could come forward confirming two Town and themselves. As an unconfirmed Town, you now have two-Town and two-Scum remaining in the game to identify. The lynch for D3 is then much more informed, and the Cop will die that night.

If the Cop comes forward on D4, then that confirms themselves and everyone else. However; they are at a point where Scum could easily claim the same to take the game, so you can't trust them there, as it'll probably end up either being Scum, or getting Counterclaimed. I think a Counterclaim could easily work here, as you could claim you've scanned dead people alongside one other. Decide yourself if you select Scumbuddy or a Town. Scumbuddy would be quite obvious, but if they suspect you of that, it'll be safer to just go for you and risk losing Cop, IMO.

IMO Cop should come forward D3 in that situation, confirming a large majority of the Town. In a larger game:

16 Town Vs 5 Scum (Same as above)

D1: 16:5
D2: 14:5 [1]
D3: 12:5 [2]
D4: 10:5 [3]
D5: 8:5 [4]
D6: 6:5 [5]

There you have an obvious answer of D5, IMO. Whilst D6 would confirm everyone, the above applies. Scum could come forward as Cop and take the game too easily there, so no Cop-claim can be trusted. On D5 you'll be making 5 Scum Vs 3 Town. From thereon: (Confirmed:Unconfirmed:Scum)

D5: 5:3:5
D6: 4:3:4
D7: 3:3:3

I believe that's a much better position than anything else, simply going off probability of hitting your desired target. There are obviously many other things to take into account, but when it comes to the theory, you can often take your amount of confirmed, plus yourself, plus 1 when deciding on how far towards the 50% you are. Staying later might help the Town more, but at the same time, you could lose a lot more by not doing so. (Being NK'd, for a kick-off.)

YJ