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"input": [
"import random\n",
"import seaborn as sns\n",
"sns.set(context=\"poster\", style=\"dark\")\n",
"import mpld3\n",
"\n",
"def monty_hall():\n",
" doors = list(range(3))\n",
"\n",
" car = randint(0,2)\n",
" old_choice = randint(0,2)\n",
"\n",
" # reveal a door that is neither the car nor the choice and remove it from doors\n",
"\n",
" for i in range(3):\n",
" if i != car and i != old_choice:\n",
" reveal = i\n",
"\n",
" [ doors.remove(i) for i in [reveal, old_choice] ]\n",
" \n",
" bayes_choice = doors[0] # can change to randomly selecting a member of the list for len(doors)>3\n",
" \n",
" return car, old_choice, bayes_choice\n",
"\n",
"def mass_monty(num_trials):\n",
" stubborn_wins = 0\n",
" bayes_wins = 0\n",
" stubborn_rate = zeros(num_trials)\n",
" bayes_rate = zeros(num_trials)\n",
"\n",
" for i in range(num_trials):\n",
" car, old_choice, bayes_choice = monty_hall()\n",
" \n",
" if old_choice == car:\n",
" stubborn_wins += 1\n",
" else:\n",
" bayes_wins += 1\n",
" \n",
" stubborn_rate[i] = stubborn_wins / (i+1)\n",
"# print(\"\\n\", i+1, \" st \", stubborn_wins, \" \", stubborn_rate[i])\n",
"\n",
" bayes_rate[i] = bayes_wins / (i+1)\n",
"# print(i+1, \" bayes \", bayes_wins, \" \", bayes_rate[i])\n",
" \n",
" return stubborn_rate, bayes_rate\n",
"\n",
"stubborn_rate, bayes_rate = mass_monty(100)\n",
"\n",
"plot(stubborn_rate, '-', label=\"stubborn choice\")\n",
"plot(bayes_rate, '-r', label=\"bayes choice\")\n",
"legend(loc=\"best\")\n",
"xlabel(\"trial\")\n",
"ylabel(\"success rate\")\n",
"mpld3.display()"
],
"language": "python",
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"input": [
"stubborn_rate, bayes_rate = mass_monty(1000)\n",
"\n",
"plot(stubborn_rate, '-', label=\"stubborn choice\")\n",
"plot(bayes_rate, '-r', label=\"bayes choice\")\n",
"legend(loc=\"best\")\n",
"print(\"final stubborn rate: {s}; final bayes rate: {b}\".format(s=stubborn_rate[-1], b=bayes_rate[-1]))\n",
"xlabel(\"trial\")\n",
"ylabel(\"success rate\")\n",
"mpld3.display()"
],
"language": "python",
"metadata": {},
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"output_type": "stream",
"stream": "stdout",
"text": [
"final stubborn rate: 0.339; final bayes rate: 0.661\n"
]
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