Dice Probability Magic.ipynb

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   "source": [
    "## Würfeldesaster \n",
    "\n",
    "Spielregel: N Würfel werden gewürfelt mit gleichen under Unterschiedlichen würfelseiten. Es gibt ein Goldstück für jedes Würfelergebnis, wo für den würfel der TopScore erreicht wird. Alternativ: jeweils bei einer 1.   \n",
    "\n",
    "Problem: Aufaddierung von einzelprobabilities vs. Einzelberechnungen  \n",
    "Aussage: man kann die einzelwahrscheinlichkeiten pro würfel Aufaddieren um eine Gesamtwahrscheinlichkeit zu bekommen. Wo funktioniert das? wo funktioniert das nicht."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Same value dices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import itertools\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 1]\n",
      " [1 2]\n",
      " [1 3]\n",
      " [2 1]\n",
      " [2 2]\n",
      " [2 3]\n",
      " [3 1]\n",
      " [3 2]\n",
      " [3 3]]\n",
      "Actual ratio: 0.6666666666666666\n",
      "Estimated ratio: 0.6666666666666666\n"
     ]
    }
   ],
   "source": [
    "\n",
    "n_dices = 2\n",
    "n_sides = 3\n",
    "\n",
    "# create matrix with possibilities of outcome\n",
    "dice_results =  np.array(list(itertools.product(range(1,n_sides+1), repeat=n_dices)))\n",
    "print(dice_results)\n",
    "\n",
    "# count number of ones\n",
    "n_ones = sum(dice_results.flatten() == 1)\n",
    "\n",
    "# calculate actual ratio\n",
    "actual_ratio = n_ones / (dice_results.size / n_dices)\n",
    "print(f'Actual ratio: {actual_ratio}')\n",
    "\n",
    "# calculate estimated probabilities of \n",
    "estimated_ratio = 1/n_sides * n_dices\n",
    "print(f\"Estimated ratio: {estimated_ratio}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Different value dices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[((1, 1),),\n",
       " ((1, 2),),\n",
       " ((1, 3),),\n",
       " ((1, 4),),\n",
       " ((1, 5),),\n",
       " ((2, 1),),\n",
       " ((2, 2),),\n",
       " ((2, 3),),\n",
       " ((2, 4),),\n",
       " ((2, 5),),\n",
       " ((3, 1),),\n",
       " ((3, 2),),\n",
       " ((3, 3),),\n",
       " ((3, 4),),\n",
       " ((3, 5),),\n",
       " ((4, 1),),\n",
       " ((4, 2),),\n",
       " ((4, 3),),\n",
       " ((4, 4),),\n",
       " ((4, 5),)]"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dice_list = eval(\"((x,y) for x in range(1,4+1) for y in range(1,5+1))\")\n",
    "list(itertools.product(dice_list))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[array([[list([1, 2, 3])],\n",
      "       [list([1, 2, 3, 4])]], dtype=object)]\n"
     ]
    },
    {
     "ename": "TypeError",
     "evalue": "'bool' object is not iterable",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-77-c715b1632d23>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      9\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     10\u001b[0m \u001b[1;31m# count number of ones\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 11\u001b[1;33m \u001b[0mn_ones\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0msum\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdice_results\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     12\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     13\u001b[0m \u001b[1;31m# calculate actual ratio\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mTypeError\u001b[0m: 'bool' object is not iterable"
     ]
    }
   ],
   "source": [
    "\n",
    "dices = [4,5]\n",
    "dice_list = ((x,y) for x in range(1,5) for y in range(1,6))\n",
    "\n",
    "# create matrix with possibilities of outcome\n",
    "dice_results = []\n",
    "dice_results.append(np.array(list(itertools.product(dice_list))))\n",
    "print(dice_results)\n",
    "\n",
    "# count number of ones\n",
    "n_ones = sum(dice_results == 1)\n",
    "\n",
    "# calculate actual ratio\n",
    "actual_ratio = n_ones / (dice_results.size / n_dices)\n",
    "print(f'Actual ratio: {actual_ratio}')\n",
    "\n",
    "# calculate estimated probabilities of \n",
    "estimated_ratio = 1/n_sides * n_dices\n",
    "print(f\"Estimated ratio: {estimated_ratio}\")"
   ]
  }
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