[SETUP] Target Practice

[mith]

2 Mafia
5 Townies

One of the Townies is randomly chosen to be the Target, known only to the Mafia during Day 1.

If the Target is lynched Day 1, the game becomes a normal Vanilla game. (EV 2/15 for town, who are in 2:3 Vanilla, LyLo)

If there is No Lynch Day 1, the Mafia get a one-shot kill which cannot target the Target, and the Target finds out they were the Target, but otherwise have no ability. (EV 1/2 for town, 2:3:1 Nightless with Named Townie)

If there is No Lynch Day 1, the Target dies and the Mafia do not get a kill. (EV 1/3, 2:4 Nightless)
If a non-Target Townie is lynched Day 1, the Mafia do not get a kill, and the Target gets a one-shot kill instead (finding out they are the target). (EV 1/2 for town, this is either 2:2:1 Nightless with Named Townie or 1:3:1 Nightless with Named Townie)
If Mafia is lynched Day 1, no one gets a kill but the Target finds out they were the Target. (EV 4/5 for town, 1:4:1 Nightless with Named Townie)

(Total EV for town is 8/15, assuming a random lynch Day 1 - a bit better than No Lynch, and of course with No Lynch there is less/no information generated.)

In some ways this is an inverted version of Lynchpin (though they were developed independently; I have actually run this setup already in SEKKRIT PLACE with Mafia winning from a non-Target Townie lynch and Target hitting Mafia). I list specific numbers for this one because I haven't calculated EVs for any variations on the counts (and also because I may want to tweak some of the cases). Should be easy to throw in a spreadsheet, since all the cases lead to either Vanilla or Nightless with Named Townie.

The goal of course is to make Day 1 more meaningful and force information to be generated (since with 7 players, the game isn't lasting long). The Mafia have a significant incentive both to avoid being lynched and to lynch the Target, with most games likely going to the middle ground of a non-Target Townie lynch. Looking town to the Target is also very important for the Mafia's chances.

One other interesting aspect of this setup is that in the most likely scenario (non-Target Townie lynch and Target misses), Mafia have the same EV if they counterclaim the Target and if they don't. Would be interesting to see whether they chose to go that route. (And if they do counterclaim, the EV remains the same whether the group chooses to lynch among the Target claims or among the other three.)

[mith]

And to help with EV calculation for the general case:

EV of Nightless+Named M:T:1 is (P-2M)/(P-M) = (T+1-M)/(T+1).

(50% EV at 1:1:1, 2:3:1, 3:5:1, etc. Too much power in a single player slot to be worth running I think... though it might be interesting to play just making it Innocent Child - same EV, just ruling out counterclaim - and a rotating player in that slot.)

[mith]

After crunching some numbers, 2M+1 Townies seems to give the EV closest to 50%, and possibly converges to 50%.

1:3 = 50% exactly (town wins if they lynch Mafia, and lose if they hit Target, and in the non-Target case the Target has a 50-50 shot)
2:5 = 53.3%
3:7 = 52%
4:9 = 51.7%
5:11 = 51.3%
6:13 = 51.2%

The problem here is that No Lynch for these counts is exactly 50%, so the larger the game the less incentive there is to lynch. So that's the first place to start with tweaking these rules. (No Lynch could just be an auto-loss for Town, don't really care if it's worse than lynching the Target, as long as it's worse than the Lynch Randomly EV.)

Fixed above.

[Sukima]

If you No Lynch, I'm assuming Mafia's one shot kill can't target the Target? Otherwise I'd imagine they'd shoot them to reduce to a 2v4.

[mith]

Yes, just missed that in copying over the rules.

[mith]

Though really just going to 2:4 Nightless would solve the No Lynch problem, since it would reduce EV to 1/3. (Edited the rules above to reflect this.)

[callforjudgement]

I'd make it even simpler by just banning No Lynch (and using plurality as a tiebreak if the game goes to deadline). Nowadays, I normally do that anyway in smaller setups, as it's too hard to balance around that possibility on top of all the others.

[mith]

I personally dislike plurality lynches in games that aren't designed around them. I'd rather force the town to make a bad deadline decision (by No Lynch = loss) than give them an ambivalent lynch, and having a reasonable (but inferior) No Lynch alternative is better still; with the new rule, No Lynch EV is always 1/3 for the EV ~ 1/2 setups, which is bad enough to discourage towns from going that route but not so bad that it's totally out of the question if (for some reason) they think the Mafia's chance of hitting the Target are much better than random.

[Mathdino]

This seems pretty runnable, even if somewhat lacking in simplicity (given the 4 possible pathways D1 could take).

[mith]

It is (and already has been). And in some ways, it is a distillation of the endgame for the final game in the California Trilogy (different vanilla variant endgames depending on what has already happened). With 7, there's not a lot of room to vary the "endgames" of course, there's only so many ways day 1 can go.

[mith]

(A larger version of this concept should be called "Vanilla Variance"...)