README.ipynb

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    "# Slots\n",
    "\n",
    "Modelling of slot- game.\n",
    "\n",
    "There is an output matrix $N \\times M$.\n",
    "\n",
    "There are $P$ items(symbols) corresponding for each column.\n",
    "The probability of the $i$-th item to be on the any row on the $j$-th\n",
    "column is equal $p_{i,j}$.\n",
    "\n",
    "The column is formed by the next rule:\n",
    "at first the bottom row is formed, then another symbol is generated\n",
    "on the upper row - this symbol cannot be the same that is on bottom row:\n",
    "so the probability of $i_1$-th item to be there is $p_{i_1}/(1-p_{i})$, where\n",
    "$i \\neq i_1$.\n",
    "\n",
    "The same way, the next symbol cannot equal to any of the previous\n",
    "ones, therefore, the probability of the $i2$-th item to be on the column is\n",
    "$p_{i_2}/(1-p_{i}-p_{i_1}))$.\n",
    "\n",
    "By continuing so on, the last probability is\n",
    "$p_{i_N}/(1-p_{i}-p_{i_1} -p_{i_{N-1}}))$.\n",
    "\n",
    "If there are same $l$ symbols in the first $K$ columns then the output result\n",
    "is $S_{l,K}$.\n"
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