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July 3, 2017 01:43
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{ | |
"cells": [ | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# 538 Riddler: Town Full of Thieves" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"> A town of 1,000 households has a strange law intended to prevent wealth-hoarding. On January 1 of every year, each household robs one other household, selected at random, moving all of that house’s money into their own house. The order in which the robberies take place is also random and is determined by a lottery. (Note that if House A robs House B first, and then C robs A, the houses of A and B would each be empty and C would have acquired the resources of both A and B.)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 144, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [], | |
"source": [ | |
"%matplotlib inline\n", | |
"import numpy as np\n", | |
"import matplotlib.pyplot as plt" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 151, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"num_households = 1000\n", | |
"cash_start = 100" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Probabilistic Results" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"**What is the probability that a house is not robbed over the course of the day?**\n", | |
"\n", | |
"Each household chooses one of the other 999 houses to rob at random (they can't rob themselves). If a house isn't robbed, that means one of the remaining 998 are.\n", | |
"\n", | |
"Robberies are independent events, so we can multiply across all 999 potential robberies of the house." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 166, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"36.769524049349926" | |
] | |
}, | |
"execution_count": 166, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"((num_households - 2) / (num_households - 1)) ** (num_households - 1) * 100" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"**Suppose that every house has the same amount of cash to begin with — say $100. Which position in the lottery has the most expected cash at the end of the day, and what is that amount?**\n", | |
"\n", | |
"Every house has the same likelihood of being robbed at some point in the day. But only the last house to go has 100% certainty they will keep whatever amount they have after their turn robbing.\n", | |
"\n", | |
"You can iteratively determine a house's end-of-day expected amount based on their lottery order:\n", | |
"\n", | |
"1. Find the probability they haven't already been robbed.\n", | |
"2. Multiply that value by the amount they were given at the start of the day (\\$100).\n", | |
"3. Because the total amount across all the households doesn't change ($100 * 1000 households), we can find the expected amount they would get by robbing another house this turn (the total amount less whatever they're expected to have, divided by the number of houses they can rob).\n", | |
"4. Add the two values above and multiply by the probability they won't get robbed at some point later in the day to get the end-of-day expected amount." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 167, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"result_expected = []\n", | |
"\n", | |
"for num_turn in range(num_households):\n", | |
" p_not_yet_robbed = ((num_households - 2) / (num_households - 1)) ** num_turn\n", | |
" expected_assets_start = p_not_yet_robbed * cash_start\n", | |
" expected_assets_others = (num_households * cash_start - expected_assets_start) / (num_households - 1)\n", | |
" p_wont_be_robbed_later = ((num_households - 2) / (num_households - 1)) ** (num_households - num_turn - 1)\n", | |
" expected_value_at_end = p_wont_be_robbed_later * (expected_assets_start + expected_assets_others)\n", | |
" \n", | |
" result_expected.append(expected_value_at_end)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 163, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"999" | |
] | |
}, | |
"execution_count": 163, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"np.argmax(result_expected)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Which is the last house to go." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 164, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"136.8328178190703" | |
] | |
}, | |
"execution_count": 164, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"np.max(result_expected)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Simulations" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 145, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"def simulate(num_households, cash_start):\n", | |
" cash = [cash_start] * num_households\n", | |
" status = [0] * num_households\n", | |
" households = np.arange(num_households)\n", | |
" np.random.shuffle(households)\n", | |
"\n", | |
" def rob(robber, victim):\n", | |
" cash[robber] += cash[victim]\n", | |
" cash[victim] = 0\n", | |
" status[victim] = 1\n", | |
"\n", | |
" for robber in households:\n", | |
" other_households = np.arange(num_households)\n", | |
" np.delete(other_households, robber)\n", | |
" victim = np.random.choice(other_households)\n", | |
" rob(robber, victim)\n", | |
"\n", | |
" return households, cash, status" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 152, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [], | |
"source": [ | |
"num_sims = 1000\n", | |
"num_robbed = 0\n", | |
"result_sim = np.zeros(num_households)\n", | |
"\n", | |
"for i in range(num_sims):\n", | |
" households, cash, status = simulate(num_households, cash_start)\n", | |
" num_robbed += np.sum(status)\n", | |
" for num_turn in range(num_households):\n", | |
" result_sim[num_turn] += cash[households[num_turn]]\n", | |
"\n", | |
"result_sim /= num_sims" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 158, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"On average, 36.7536% of households are not robbed on January 1\n" | |
] | |
} | |
], | |
"source": [ | |
"pct_robbed = num_robbed / (num_sims * num_households) * 100\n", | |
"print('On average, {}% of households are not robbed on January 1'.format(100 - pct_robbed))" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Comparing the Expected and Simulated Results" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 137, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
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bHFqLy82ZE1xQzuEZF33/PYsWLQo6r7q6Oty3FVeajLKitT6EEWD7GbBOKbUF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\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x10d407a20>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"fig = plt.figure()\n", | |
"ax = fig.add_subplot(111)\n", | |
"\n", | |
"ax.plot(list(np.arange(num_households)), result_sim, 'o', color='r', markersize=3, mew=0.0, label='Simulated')\n", | |
"ax.plot(np.arange(num_households), result_expected, 'o', color='c', markersize=3, mew=0.0, label='Expected')\n", | |
"\n", | |
"ax.set_ylabel('Day-End Assets')\n", | |
"ax.set_xlabel('Lottery Order')\n", | |
"plt.legend(loc='upper left')\n", | |
"\n", | |
"plt.show()" | |
] | |
} | |
], | |
"metadata": { | |
"anaconda-cloud": {}, | |
"kernelspec": { | |
"display_name": "Python [default]", | |
"language": "python", | |
"name": "python3" | |
}, | |
"language_info": { | |
"codemirror_mode": { | |
"name": "ipython", | |
"version": 3 | |
}, | |
"file_extension": ".py", | |
"mimetype": "text/x-python", | |
"name": "python", | |
"nbconvert_exporter": "python", | |
"pygments_lexer": "ipython3", | |
"version": "3.5.2" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 1 | |
} |
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