[SETUP] Draft Lottery Mafia

[mith]

3 Mafia Goons
10 Vanilla Town

Before the game, each player is randomly assigned a lottery position. (These are public.) Each position has a certain chance of being drawn as Mafia:

A: 135/1001
B: 132/1001
C: 128/1001
D: 123/1001
E: 116/1001
F: 103/1001
G: 77/1001
H: 51/1001
I: 38/1001
J: 31/1001
K: 26/1001
L: 22/1001
M: 19/1001

Virtual ping pong balls* are then used to select the Mafia (with repeats being redrawn).

I haven't done much math** on the specific numbers - they aren't arbitrary, but the spread may well be too big. The EV should be *roughly* how likely it is all three Mafia are in A-F, I think, which is (again roughly) 33%. There are other considerations though, like one of the unlikely players not being nightkilled. Anyway, the basic idea is that town has a lot of probabilistic information day 1, but nothing that solves the game for them.

*This is based on the NBA draft lottery, which uses 14 ping pong balls and assigns each team some number of combinations of 4 of those balls - 1001 = 14 choose 4. It doesn't have to actually be drawn this way, and the denominator could be any sufficiently large number.
**The spread of probabilities is based on a logistic function. Gold star to anyone who can figure out exactly what I did...

[northsidegal]

Finally found what this reminded me of, The Odds.

[RadiantCowbells]

I think this would be a horrible setup to actually play. Roll A and then get autolynched.

At least the Ether verseion there's some level of negotiation in the role that you get.

[mith]

Yes, this sort of thing has been suggested and done before (there was a "Quantum Mafia" game run a long time ago which had probabilities adjusting in game as the "waveform" collapsed, for another example).

I very much disagree that A should be autolynched. The distribution is deliberately designed such that the differences between the first few (and last few) are very small - the likelihood of A being scum ~1% greater than the likelihood of B being scum (vs. ~5% in the Ether setup - not exactly, due to redraws). Even between A and D should be less than 5%. (At some point I'll run a simulation to actually calculate these.)

Now, obviously the town should focus on the top few letters day 1 (just as they should focus on the top two or four in The Odds). But focusing entirely on the top 6 for the game will get them to an EV around 1/3, which is not great. The key to playing a setup like this is adjusting those probabilities based on what the players are doing, flips, etc. - and that, coupled with the closely packed probabilities at the top, gives each of those players a chance to demonstrate their townieness in the first few days. (FWIW, when The Odds was run, town ended up lynching a 15% slot day 1, in the bottom half of probabilities. A little different there since there was a PR and the 35% slot happened to draw it, but still.)

[northsidegal]

Do you think the probabilities serve as enough of a benefit to town to move it enough away from essentially 3:10 Vanilla?

[mith]

As I mentioned, the EV should be around 33%, vs. ~21% for 3:10 Vanilla. Aside from getting the random lynch EV up to a more reasonable range, I think it would focus town on day 1 and get them generating information faster, and additional information in who the scum choose to nightkill.

It just occurred to me that you could also mess with the pairing probabilities (in addition to individual players, or even keeping everyone's individual probabilities the same). That might be interesting, seeing how players react to other players who they are most likely to be scum with.