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.

[Iammars]

Care to enlighten people who don't know about the MoS plan? Or at least link to it?

[Glork]

Care to enlighten people who don't know about the MoS plan? Or at least link to it?

I'm MoS in a lyncher game.

I pair the other four players off. We'll call them Player A1, A2, B1, and B2.

If we lynch A1 as town, then A1 vigges A2, and vice versa.

If we lynch B1 as town, then B1 vigges B2, and vice versa.

We don't lynch MoS.





I'm not sure what the numbers are for the average non-MoS townie. Yeah, using "The MoS plan" increases MoS's chances of winning, but does it increase the

town's

overall chances of winning? (The answer to this may very well be yes; I just haven't bothered to run the numbers, and I am too intoxicated to do so.)

[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.

[Xdaamno]

I modded this particular game. It's hardly relevant, but the MoS player (who was actually MoS) didn't look at his role. He obviously ended up being the godfather.

[Adel]

I modded this particular game. It's hardly relevant, but the MoS player (who was actually MoS) didn't look at his role. He obviously ended up being the godfather.

MoS somehow manages to not read or not remember his role is every recent game where he was a powerrole or scum? interesting.

[Kelly Chen]

Assuming scum have to kill back if they are lynched:

Assuming they don't have to kill back:

Jeeeesus. Neither of these is the correct rule. Did you really have six people playing a game where the scum had at least the option of making a venge kill?

Town win odds are 40% under the official rule.

In any case, I'd still love to hear why the MoS strategy helps town (even if effected randomly), no matter what game you were playing.

[Kelly Chen]

Also, I would like to hear how it is possible that giving scum the option (vs requirement) to make a venge kill could possibly hurt the town. If the lynched scum doesn't exercise the option then he does nothing but increase the odds that the next death will be scum, from 0% to 25%. After this death the game would be in the same state (final 3) no matter what [well, unless the last scum was lynched].

[Mastermind of Sin]

I modded this particular game. It's hardly relevant, but the MoS player (who was actually MoS) didn't look at his role. He obviously ended up being the godfather.

MoS somehow manages to not read or not remember his role is every recent game where he was a powerrole or scum? interesting.

To be fair, this is a somewhat misleading (and even incorrect) statement.

I do not refuse to read my role pm in forum games. I did it for that particular scumchat game BECAUSE it was vengeful, and my strategy would remain the same regardless of if I was scum or not. Knowing I was scum would not change my reactions in the slightest. I even hammered knowing full well that the person being lynched would probably not listen to me and vig me instead of following the plan. True to form, he did vig me, and the town lost anyways. Just goes to show, people who don't follow the plan lose the game for the town.

Anyway, I got sidetracked. As I was saying, I always read my role at the start of a game. On top of that, Lost Boys mafia is a "recent" game where I was "scum", and I was very aware of my alignment and scumpartners throughout the entire game. So your statement isn't really relevant. =P

[Mr. Flay]

So your statement isn't really relevant. =P

Since when has that ever stopped Adel?

[Adel]

So your statement isn't really relevant. =P

Since when has that ever stopped Adel?

qft

[Kelly Chen]

Hi guys.

Here are mafia's win odds given random play (as given already on the wiki page). The 33s and 67s are rounded, as you might expect.

(20% chance of godfather lynch D1 * 0% chance of mafia win ) +
(20% chance of goon lynch D1 * 75% chance to survive final four * 67% chance to survive final three) +
(60% chance of townie lynch D1 *
(50% chance of vig kill targeting a townie +
(50% chance of vig kill targeting mafia * 67% chance to survive final three)) )

= 60%.

Now instead we will arbitrarily select one player, MoS, as an arbitrary pair-maker. MoS of course is either GF, goon, or town, so we must take into consideration what happens in each of these situations:

20% MoS is GF * [
(25% chance of goon lynch D1 * 75% chance to survive final four * 67% chance to survive final three) +
(75% chance of townie lynch D1 *
(67% chance of vig kill targeting a townie +
(33% chance of vig kill targeting mafia * 67% chance to survive final three)) )
] +
20% MoS is goon * [
(25% chance of godfather lynch D1 * 0% chance of mafia win in this case ) +
(0% chance of goon lynch D1 ) +
(75% chance of townie lynch D1 *
(67% chance of vig kill targeting a townie +
(33% chance of vig kill targeting mafia * 67% chance to survive final three)) )
] +
60% MoS is town * [
(25% chance of godfather lynch D1 * 0% chance of mafia win in this case) +
(25% chance of goon lynch D1 * 75% chance to survive final four * 67% chance to survive final three) +
(50% chance of townie lynch D1 *
(33% chance of vig kill targeting a townie +
(67% chance of vig kill targeting mafia * 67% chance to survive final three)) )
]

= 60%.

So, mathematically it doesn't help to use pairs strategy.

I can't argue with armlx beyond that, because he never showed his work. 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.

Breaking it down a little:
If MoS is the godfather, mafia will win 79.1667% of the time.
If MoS is the goon, they'll win 66.667% of the time.
If MoS is town, mafia will win 51.333% of the time (and town and MoS, 48.667%).
When there is no pairmaker, a random player will win 48% of the time.
When there is, MoS will win 58.3667% of the time.

Because any given player has the ability to be MoS, if this decision is made randomly and not simply seized by someone unilaterally deciding to be the pairmaker, there's mathematically no reason to support or oppose the use of the pairs strategy.

If a random player (but not you) were to unilaterally choose to be the pairmaker, and you are a townie, I would oppose this move, because it increases scum's win odds slightly from 60% to 62.153%.

Of course, there could be other less tangible benefits to pairs strategy (or "vengekill in a cycle" strategy, etc etc) which aid the town but can't be reflected in the math.

[OhGodMyLife]

Holy shit its Kelly Chen

[Xdaamno]

I modded this particular game. It's hardly relevant, but the MoS player (who was actually MoS) didn't look at his role. He obviously ended up being the godfather.

Hell, did I really post this? I can't even remember what a MoS strategy is, even after reading the first post.

What's up,

d-

Kelly?

[mith]

Kelly's math probably already shot it down as a viable strategy anyway, but another thing worth pointing out is that even if having a pairmaker increases the town's chances of winning, it does not necessary increase a given townie's chances of winning. When the town wins, the pairmaker will be part of that a disproportionate percentage of the time.

[Kelly Chen]

I modded this particular game. It's hardly relevant, but the MoS player (who was actually MoS) didn't look at his role. He obviously ended up being the godfather.

Hell, did I really post this? I can't even remember what a MoS strategy is, even after reading the first post.

What's up,

d-

Kelly?

Not too much, I couldn't face doing my work so I came here instead.

[Lord Gurgi]

Gasp!

[Yosarian2]

I agree with Kelly

Also, Hi Kelly!

[Vel-Rahn Koon]

I modded this particular game. It's hardly relevant, but the MoS player (who was actually MoS) didn't look at his role. He obviously ended up being the godfather.

Hell, did I really post this? I can't even remember what a MoS strategy is, even after reading the first post.

What's up,

d-

Kelly?

Not too much, I couldn't face doing my work so I came here instead.

Wow, this sounds familiar...

Hi Kelly!

[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.

[Thok]

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.

[Kelly Chen]

Hi Yos, VRK.

Thok, I meant randomly, and mentioned a case where it isn't random. I can't imagine for what else there could be any math.


armlx, presumably you're saying you had my result first but then decided it was wrong.

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.

If you agree that the pairs don't matter, then it seems to me all you would be saying is that randomly granting one player lynch immunity for a day, will help the town on average (because that player is more likely to be town than scum). If so then one would wonder why this strategy isn't used in all games.

[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.