[SETUP] Capture the Flag

[mith]

Huh. Wouldn't have expected that.

The "decide each night" version (starting N0) of this is balanced linearly - for M Mafia you want about 3M+1 Townies. (1:4 is 46.67%, same as Vanilla, of course; 2:7 is 48.25%; 3:10 is 49.10%; 4:13 is 49.59%; 5:16 is 49.90%; and after that it actually creeps above 50%, maxing out at 14:43, 50.46%, before apparently approaching 50% from above while M:3M-1 approaches 50% from below). For comparison, Nightless is balanced at exactly M:3M. I suspect the EV approaches Nightless EV for sufficiently large M, regardless of M:T ratio (e.g. M:5M+1 approaches M:5M Nightless, EV 2/3 - 200:1001 in this setup is 66.61% for example).

Note that this is always a bit better than the fixed day assignment version (even the 1/4, 2/5, 3/6 type), since town might lynch the wrong Mafia at some point and lose out on a potential flag bearer lynch on a future day.

If you start N1 (which is probably a better way to go, so the first flag bearer choice isn't information-less), EV is 45.55%.

[mith]

I like that flavor-wise, too.

[mith]

Right. (And as mentioned above, I prefer no D1 flagbearer. It's not like Mafia is totally screwed if they have one - they just have incentive to protect that player - but it feels a little less swingy without.)

Some more EVs for this version:

2:7 - 43.17%
2:9 - 50.27%
3:10 - 45.55%
3:12 - 50.92%
4:13 - 46.87%
5:14 - 43.22%
5:16 - 47.68%
6:17 - 44.47%
6:19 - 48.23%

(3:10 is probably the most interesting, but 2:7 isn't bad for a Micro, if you don't want the Nightless version at 3:6.)