from random import randint
import math
import matplotlib.pyplot as plt
import matplotlib.animation
from IPython.display import HTML



def jeu(mise):
    lancer1 = randint(1,8)
    if lancer1 == 1:
        gain = mise
    else:
        lancer2 = randint(1,8)
        if lancer2 <= 4:
            gain = 6
        else:
            gain = -mise
    return gain


def gainMoyen(mise, n):
    gainTotal = 0
    for i in range(n):
        gainTotal = gainTotal + jeu(mise)
    return gainTotal/n

def cumul(n):
    F = []
    gainTotal = 0
    for i in range(n): 
        gainTotal = gainTotal + jeu(mise)
        F.append(gainTotal/(i+1))
    return F

def esperance(X,P):
    E = 0
    for i in range(len(X)):
        E = E + X[i]*P[i]
    return E

def ecartType(X,P):
    E = esperance(X,P)
    V = 0
    for i in range(len(X)):
        V = V + P[i]*(X[i]-E)**2
    return math.sqrt(V)



# Création de la liste des gainsmoyens pour N échantillons de taille n
def echantillonGains(mise, N, n):
    echantillon = []
    for i in range(N):
        echantillon.append(gainMoyen(mise, n))
    return echantillon
# Borne de l'intervalle 
def bornes(E, sigma, n):
    return E-2*sigma/math.sqrt(n),E+2*sigma/math.sqrt(n)
#Calcul de la proportion des cas où l’écart entre le gain moyen et l'espérance est inférieur ou égal à 2𝜎/√𝑛
def propPoint(echantillon, i, s):
    filtre = [x for x in echantillon if x <= s and x >= i]
    return len(filtre)/len(echantillon)



#Constantes
mise = 8.4
N = 100
n = 100
X = [mise, 6, -mise]
P = [1/8, 7/16, 7/16]

#Espérance et écart-type
E = esperance(X, P)
sigma = ecartType(X, P)

#Bornes de l'intervalle
i, s = bornes(E, sigma, n)

#Echantillon
echantillon = echantillonGains(mise, N, n)

#paramètres figure
fig, ax1 = plt.subplots(1, 1,figsize=(20, 6))

ax1.plot([0,N],[i,i],'r--',label='$\mu-2\sigma/\sqrt {n}$;$\mu+2\sigma/\sqrt {n}$')
ax1.plot([0,N],[E,E],'g--',label='$\mu$')
ax1.plot([0,N],[s,s],'r--')

points, = ax1.plot([],[],'bo')
ax1.legend(bbox_to_anchor=(1.01, 1), loc=2, borderaxespad=0.)



def init():
    points.set_data([], [])
    return (points,)


def animate(i):
    global echantillon
    points.set_data([range(i+1),echantillon[:i+1]])
    return (points,)

plt.close ()
ani = matplotlib.animation.FuncAnimation(fig, animate, frames=N,init_func=init,blit=True)
# l'un ou l'autre
HTML(ani.to_jshtml())
#HTML(ani.to_html5_video())

Once Loop Reflect