tanutarou

import numpy as np

N = 10000
winfreq = np.array([0, 0])
playerA = "111"
playerB = "011"

for i in xrange(N):
    res = [2, 2, 2]
    while True:

tanutarou

import numpy as np
import operator

def rec(idx, nums, digit):
    if idx == 9:
        if sum(nums) == digit:
            cand = reduce(operator.add, [cnt * (power[9-i][digit]) for i, cnt in enumerate(nums)])
            bin_cand = [0 for i in xrange(10)]
            for i in str(cand):
                bin_cand[9-int(i)] += 1

tanutarou

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tanutarou

\begin{eqnarray}
\sum_i \sum_{k=1}^K q_i(z_k)\ln \left[\frac{p(x_i, z_k|\theta)}{q_i(z_k)} \right] &=& \sum_i \sum_{k=1}^K q_i(z_k)\ln \left[ \frac{p(z_k|x_i,\theta)p(x_i|\theta)}{q_i(z_k)} \right] \\
&=&\sum_i \sum_{k=1}^K q_i(z_k)\ln \left[ p(x_i|\theta) \right] + \sum_i \sum_{k=1}^K q_i(z_k)  \ln\left[ \frac{p(z_k|x_i, \theta)}{q_i(z_k)} \right] \\
&=& \sum_i \ln \left[ p(x_i|\theta) \right] +\sum_i \sum_{k=1}^K q_i(z_k) \ln \left[ \frac{p(z_k|x_i, \theta)}{q_i(z_k)} \right]
\end{eqnarray}

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tanutarou