import matplotlib.pyplot as plt

n = 0.5 # number of smoke lovers

# some initial values
k = 1 # ratio between smoke lovers and non-smoke lovers probabiltiies
q = 0.01 # probability non smoke lovers smoke
p = k*q  # probability smoke lovers smoke

pHist = []
qHist = []
kHist = []

for i in range(10000):
    # calculate conditional probabilities
    pKilledIfSmokes = p*n / (p*n + q*(1-n))
    pKilledIfNoSmokes = (1-p)*n / (1 - p*n + q*(1-n))

    # make decision according to EDT
    # if smoking is desirable, slightly increase the probability of smoking
    # otherwise, decrease it
    if -101*pKilledIfSmokes - 1*(1-pKilledIfSmokes) > -100*pKilledIfNoSmokes:
        q *= 1.01
    else:
        q /= 1.01

    if -90*pKilledIfSmokes + 10*(1-pKilledIfSmokes) > -100*pKilledIfNoSmokes:
        k *= 1.01
    else:
        k /= 1.01

    p = k*q

    # record the histories of p, q and k
    pHist.append(p)
    qHist.append(q)
    kHist.append(k)

# plot either one
# plotting p, q is best when n > 0.9
# plotting k is best when n < 0.9

""" plt.plot(pHist)
plt.plot(qHist)"""

plt.plot(kHist)
plt.show()