# There are 85 town roles (counting Judas and 1-shot townie)
# There is 1 alien sympathizer (alien if there are aliens)
# There are 8 alien roles
# There are 145 - 85 - 1 - 8 = 51 other scum roles, excluding wild card

players = 13
bins = [85, 1, 8, 51]
num_scum = [0] * (players // 2)

def make_role_list(picked, multiplier):
    symp = 0
    if picked[2]:
        symp = 1
    scum = sum(picked[2:]) + symp
    if scum > 6:
        return
    if sum(picked) == players:
        if scum == 0:
            return
        num_scum[scum-1] += multiplier
        return

    unpicked = [a - b for a, b in zip(bins, picked)]
    for i, alignment in enumerate(unpicked):
        if not alignment:
            continue
        picked[i] += 1
        make_role_list(picked, multiplier * alignment)
        picked[i] -= 1

make_role_list([0] * 4, 1)
total = sum(num_scum)
print([e / total for e in num_scum])
# [0.010570822660374658, 0.04394145890194956, 0.11441840993186787,
# 0.21186328591767783, 0.29689402004896487, 0.3223120025391652]