[SETUP] COUNTERCLAIM

[Flower]

Day 2 onwards is just 50/50's so the EV's pretty simple to calculate with a binomial distribution

In the d1 town lim case scum winrate is just the probability of having 0/1/2 scum limmed over 5 trials, in the d1 scum lim case scum winrate is the probability of having 0/1 scum limmed over 4 trials so

Spoiler: d1 town lim

P(0 scum limmed after d1) = 5 choose 0 * 0.5⁰ * 0.5⁵ = 1 * 1 * 0.5⁵ = 0.5⁵
P(1 scum limmed after d1) = 5 choose 1 * 0.5¹ * 0.5⁴ = 5 * 0.5 * 0.5⁴ = 2.5 * 0.5⁴
P(2 scum limmed after d1) = 5 choose 2 * 0.5² * 0.5³ = 10 * 0.25 * 0.5³ = 2.5 * 0.5³

P(scum win after d1 town lim) = 0.5⁵ + (2.5 * 0.5⁴) + (2.5 * 0.5³) = 0.5 = 1/2

Spoiler: d1 scum lim

P(0 scum limmed after d1) = 4 choose 0 * 0.5⁰ * 0.5⁴ = 1 * 1 * 0.5⁴ = 0.5⁴
P(1 scum limmed after d1) = 4 choose 1 * 0.5¹ * 0.5³ = 4 * 0.5 * 0.5³ = 2 * 0.5³

P(scum win after d1 scum lim) = 0.5⁴ + (2 * 0.5³) = 0.3125 = 5/16

Scum winrate = (8/13 * 1/2) + (5/13 * 5/16) = 89/208 ~= 0.428
Town winrate = 119/208 ~= 0.572