from random import randint

N = 6
n = 10000

def nxt(x, N):
    sgn = randint(0, 1) * 2 - 1
    y = (x + sgn) % N
    return y if y != 0 else N

def game(N):
    rem_to_see = set(range(1, N))
    x = N
    while len(rem_to_see) > 1:
        x = nxt(x, N)
        rem_to_see.discard(x)
    return rem_to_see.pop()


def sim(N, n):
    cnt = {k : 0 for k in range(1, N + 1)}
    for _ in range(n):
        g = game(N)
        cnt[g] += 1
    for g in cnt:
        cnt[g] /= n
    return cnt
    
print(sim(N, n))