Back to Epicmafia

Optimal strategy discussion

Irreverent
over 8 years

https://epicmafia.com/game/5284523/review

In the d3 of this game, town has an ml with 2 clears. Cop has a guilty on an unclear.

SheepPotato's opinion: The optimal strategy is to lynch outside of the guilty for a 50% chance at an autowin. I brushed off his strategy at first, but on second thought, he might have had a point.

My opinion (as an unclear): It didn't matter to me, mainly because I scumread the guilty over the other unclear. I thought if no one hard townread the unclear, there was no reason to lynch outside of him and potentially lose the ml for strategy's sake.

So what would you have done if you were in my shoes? Pls give onions.

deletedover 8 years
probabilistic analysis makes me hot n sweaty
Tatami
over 8 years

blank says

Nerds everywhere


I'm glad that the first thing you did after presumably waking up was go on nerd patrol.
deletedover 8 years
Nerds everywhere
Irreverent
over 8 years
ty Tatami & Cody for the breakdowns
Cody
over 8 years
Cop, 2 blues, miller, nilla alive. Cop and 1 blue are clear.

Lynching outside of the guilty first day (2 cases):

1. Guilty is nilla 1/2 of the time (conditioning on the fact that you see a miller in the GY). Lynching outside of guilty has a 50% chance of autowin. Chance of winning on first day: 50%. Chance of winning on second day: 50% (didn't win the first day) * 50% (second clear hammers between miller CCs). Total chance of winning = 1/2 + 1/4 = 3/4.

2. Guilty is miller 1/2 of the time. Lynching outside of guilty has a 50% chance of winning that day. Chance of winning first day: 1/2. Chance of winning the second day: 1/2 (failed to win first day) * 1/2 (chance of hammering right in miller CCs) = 1/4. Total chance of winning = 3/4.

In both cases, lynching outside of the guilty gives you a 3/4 chance of winning the game overall. Chance of winning by lynching outside of the guilty is exactly (1/2)(3/4) + (1/2)(3/4) [law of total probability] = 3/4.

Now let's look at lynching the guilty.

1. Guilty is nilla 1/2 of the time. Lynching the guilty wins. Game is won with probability 1.

2. Guilty is miller 1/2 of the time. Lynching the guilty does not win and gives the second clear a 50/50 (1/2) hammer between a blue and the nilla next day. Chance of winning is exactly 1/2 (0 on the first day, 1/2 second day).

Law of total probability in this case: (1/2)(1) + (1/2)(1/2) = 3/4.

They're equivalent.
Tatami
over 8 years
My bad I messed up the setup a little bit and forgot that blue lynch reset the chance to 50/50 because I'm dumb (as compared to weighting in favor of lynching the initial guilty)

It's equivalent no matter when/where you lynch the guilty if at all, 75% chance of a win.

Scenarios:

Lynching outside:

-Guilty is town (50% chance), lynch outside and get a 50% chance of win (75% total chance of a win)
-Guilty is mafia (50% chance), lynch outside and get a 50% chance of autowin followed by a 50/50 if no autowin (75% chance)

.5 * .75 + .5 x .75, obviously 75% win

Instalynching guilty:

-Guilty is town (50% chance), is lynched and goes to three way w/ one clear (50% chance).
-Guilty is scum (50% chance), 100% win.

.5 x .5 + .5 x 1 = .75, 75% chance of win

I think the odds are pretty obvious but I just wanted to demonstrate the math fully just in case you had any questions about it rather than just taking my word for it.
Tatami
over 8 years
Statistically equivalent as long as the guilty is lynched in either 5 way or 3 way.

Edit: Numbers are slightly off, hold on and I'll post again with the accurate.