Vengeful Mafia- Analysis of the MoS Plan

[armlx]

If this has been discussed before in detail in this forum, feel free to berate me.

On scumchat we ran a Vengeful game, and we started with the MoS strategy. I wanted to run the numbers on it, so here they are. MoS is a randomly chosen player who, if the plan is run, creates the brackets.

Edit: For those who don't know.

Vengeful Mafia


Has all the details.

Assuming scum have to kill back if they are lynched:

No MoS strategy:

Scum wins 19/30 (63.333...%)
Town wins 11/30 (36.666...%)

MoS wins 40% of the time.

MoS Strategy:

Town wins 23/60 times (38.333....%).
Scum wins 37/60 (61.666....%)

MoS wins 33/60 (55%)

Assuming they don't have to kill back:

No MoS

:

Town wins 21/60 (35%)
Scum wins 39/60 (65%)

MoS wins 40% of the time

MoS Strategy

:

Scum wins 152/240 (63.3333%)
Town wins 88/240 (36.666.....%)

MoS wins 130/240 (54.166...%)


Notable things:

The KC "fix" of not making scum night kill decreases town odds by about a percent.

MoS plan increases odds of a town win by 1.666....%

MoS plan increases the odds of a MoS win by 15% in the standard variant (!).


What this means: The first stage of any 5 man lyncher game should be determining who should play the role of MoS. Then brackets and lynch occur.

More to follow on odds of the non-MoS people winning and what not.

[armlx]

Yes, it increases the overall town chance of winning by 5/3rds of a percent.

Not sure if it increases the odds of a random other player winning though.

[armlx]

Presumably one would try to argue that the pairs need to be worked into the math, and that it isn't sufficient to note the probabilities of the first lynch's partner's alignment. But I've never heard a good reason why it should make any difference, whether you determine the random moves in advance of them happening, or at the time when the moves are made.

The fact that the pairs exist is relevant IIRC. I lost the work I did on this, but my first result was what you got.

[armlx]

The way MOS is chosen has to play a part in analyzing this scenario, for example one would presume that scum would try to manipulate it so that the godfather is MOS (and specifically, that the GF rather than the Goon is the MOS). I guess using RNG avoids this problem, but then it leads to a game that's played in a mechanical fashion.

The last 2 sentences are 100% correct.

All I'd like to see is how you arrive at 35% win odds for the town given random moves. You've claimed that pairs strategy increased those odds to 36.667%. If you had already found my result that it's 40% in any case, you must have wondered what was mistaken about it.

IIRC, when I laid it out, the odds of the pairs being S-S and T-T in the scenario of MoS being town was low to the point it increased the odds of the kill over random, but I could be very wrong.