The math of sending 4 townreads
(Disclaimer: I suck at math, Volxen proof checked this, if anyone finds a gaping mistake let me know)
Let's say we send 4
random
slots to the party today, and play the rest of the game as usual with no further additions. We also enforce the rule that we lynch only from the pool that had a Night Kill in the previous night; which is obvious.
We either end up sending (1) All four town; (2) 3 town and 1 scum; (3) 2 town and 2 scum; (4) 1 town and 3 scum.
The pools end up being [7-3 vs 4-1]; [8-2 vs 3-1]; [9-1 vs 2-2]; [10-0 vs 3-1].
Lemma 1: In the second and third cases, it is always negative EV for scum to perform a NK in the smaller pool (the Party), therefore scum always Night Kills in the House. This implies that both cases are equivalent to a mountainous game in just the house (assuming we don't use the mechanic again).
Lemma 2: When played according to above, exterminating all scum in the House (i.e. the win-con of the mountainous equivalents) almost always wins the game. The worst case occurs only in (2) with a final distribution of 1-0 vs 1-1 in the pools which affects the overall EV little.
By virtue of above lemmas, we can approximate the winning EV to the equivalent mountainous EV for House. The EVs in (1) and (4) are 100% obviously. Therefore, the EVs for each case are (1) 100%, (2) 30%, (3) 60%, (4) 100%.
At random, the chance for each case to happen is (1) 11C4/14C4, (2) (11C3*3C1)/14C4, (3) (11C2*3C2)/14C4, (4) 3C3/14C4 = (1) 33%, (2) 49.5%, (3) 16.5%, (4) 1% respectively.
We multiply the chances for each happening with the corresponding winning EVs, and sum them up to get
Code: Select all
0.33*1 + 0.495*0.3 + 0.165*0.6 + 0.01*1 = 58.75%
Even considering the mild EV drop from the worst case in (2), this implies the winning EV for the strategy
at random
is still
greater than half
, making this a strong strategy. Now, the fact that strong townreads are usually >rand accurate strengthens the case for this strategy.
In conclusion, this is the strategy we should absolutely follow.