Vengeful Mafia- Analysis of the MoS Plan

[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].

[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.

[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.

[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.