markov.py

from __future__ import division


def P(n, x, y, z):
    if n == 0:
        return int(x == 12 and y == 2 and z == 2)
    elif n > 0:
        if y == 0 and z == 0:
            return P(n - 1, x + 1, 0, 0) + 1 / 2 * (P(n - 1, x, 1, 0) + P(n - 1, x, 0, 1))
        elif x == 0 and z == 0:
            return P(n - 1, 0, y + 1, 0) + 1 / 2 * (P(n - 1, 1, y, 0) + P(n - 1, 0, y, 1))
        elif x == 0 and y == 0:
            return P(n - 1, 0, 0, z + 1) + 1 / 2 * (P(n - 1, 1, 0, z) + P(n - 1, 0, 1, z))
        elif z == 0:
            return 1 / 2 * (P(n - 1, x + 1, y, 0) + P(n - 1, x, y + 1, 0)) + 1 / 3 * P(n - 1, x, y, 1)
        elif y == 0:
            return 1 / 2 * (P(n - 1, x + 1, 0, z) + P(n - 1, x, 0, z + 1)) + 1 / 3 * P(n - 1, x, 1, z)
        elif x == 0:
            return 1 / 2 * (P(n - 1, 0, y + 1, z) + P(n - 1, 0, y + 1, z)) + 1 / 3 * P(n - 1, 1, y, z)
        elif x > 0 and y > 0 and z > 0:
            return 1 / 3 * (P(n - 1, x + 1, y, z) + P(n - 1, x, y + 1, z) + P(n - 1, x, y, z + 1))


print(P(15, 0, 1, 0) + P(15, 0, 0, 1))