Kelly Chen wrote: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.
fos: empking
