Решение 1

def moves(h):
    a, b = h
    return (a + 4, b), (a * 2, b), (a, b + 4), (a, b * 2)


def game_over(h):
    return sum(h) >= 165


def win1(h):
    return not game_over(h) and any(game_over(m) for m in moves(h))


def lose1(h):
    return not win1(h) and all(win1(m) for m in moves(h))


def win2(h):
    return not win1(h) and any(lose1(m) for m in moves(h))


def lose2(h):
    return (
        not win1(h)
        and not win2(h)
        and all(win1(m) or win2(m) for m in moves(h))
        and any(win2(m) for m in moves(h))
    )


def win3(h):
    return not win1(h) and not win2(h) and any(lose2(m) for m in moves(h))


def lose3(h):
    return (
        not win1(h)
        and not win2(h)
        and not win3(h)
        and all(win1(m) or win2(m) or win3(m) for m in moves(h))
        and any(win3(m) for m in moves(h))
    )


for s in range(1, 151):
    if (lose2((14, s)) or lose3((14, s))) and not win2((14, s)):
        print(s)
        break