Solution to 538 Riddler 8-24-18

538_Riddler_8_24_18.md

538 Classic Riddler for 8-24-2018

The code included is a simulated answer to a classic riddler challenge from 538:

Let’s call this game rock-paper-scissors-hop. Here is an idealized list of its rules:

• Kids stand at either end of N hoops.
• At the start of the game, one kid from each end starts hopping at a speed of one hoop per second until they run into each other, either in adjacent hoops or in the same hoop.
• At that point, they play rock-paper-scissors at a rate of one game per second until one of the kids wins.
• The loser goes back to their end of the hoops, a new kid immediately steps up at that end, and the winner and the new player hop until they run into each other.
• This process continues until someone reaches the opposing end. That player’s team wins!
• You’ve just been hired as the gym teacher at Riddler Elementary. You’re having a bad day, and you want to make sure the kids stay occupied for the entire class. If you put down eight hoops, how long on average will the game last? How many hoops should you put down if you want the game to last for the entire 30-minute period, on average?

The Python simulation asks the user to choose the length of time they'd like the game to last (the default is 30 minutes), and set the number of simulations. There are two questions to answer here:

How long will the game last with 8 hoops?

This comes out to a little over 5 minutes (approximately 5 minutes and 15 seconds). Here is the average length of time as we increase the number of hoops:

{8: 5.25, 9: 10.60, 10: 21.38, 11: 42.66, 12: 85.90, 13: 171.04, 14: 345.51, 15: 688.96}

The time essentially doubles with each added hoop. The run time to simulate past 15 hoops gets very long - a game with 15 hoops would already take pretty much the whole school day. We can also include the 95% confidence intervals, which show just how much variation there is as the number of hoops goes up. The upper range with 15 hoops starts to look like a classic 3-4 day game of cricket.

How many hoops are needed to exceed 30 minutes in a particular game?

If we set the threshold at 50%, the cut-off is just over 11 hoops

{8: 0.004, 9: 0.06, 10: 0.208, 11: 0.479, 12: 0.686, 13: 0.837, 14: 0.923, 15: 0.964}

so if we're really feeling lazy we might put out 12 hoops just to be safe. At 15 hoops you could pretty much take a nap 19 out of 20 class periods (although it sounds like this is a pretty loud game).

538_Riddler_8_24_18.py

# import necessary packages
import random
import numpy

# define function to simulate game of rock-paper-scissors-hop
# min = start position for one team
# max = start position for other team / total number of hoops
# default number of hoops is 8 as defined by 538 question
# play continues until one team reaches the other end
def rock_paper_scissor_hop(min = 1, max = 8):
    player1 = min
    player2 = max
    count = 0
    while player1 != max and player2 != min:
        player1 += 1
        player2 -= 1
        count += 1
        winner = False
        while winner == False:
            p1_throw = random.choice(['rock','paper','scissor'])
            p2_throw = random.choice(['rock','paper','scissor'])
            count +=1
            if p1_throw == p2_throw:
                winner = False
            elif (p1_throw == 'rock' and p2_throw == 'scissor') or (p1_throw == 'scissor' and p2_throw == 'paper') or (p1_throw == 'paper' and p2_throw == 'rock'):
                winner = True
                player2 = max
            else:
                winner = True
                player1 = min
    return(count)
    
# simulates games, calculates based on number of iterations input by user    
# identifies expected values, 95% confidence interval, and likelihood of exceeding a particular time period (time_goal)
# baseline time_goal is 30 minutes based on 538 question - can adapt to determine likelihood of exceeding alternate period of time
sim_num = False
goal_time = False
while goal_time == False:
    goal_answer = input("Would you like to stick with the probability of the game lasting at least 30 minutes (y/n): ")
    if goal_answer.lower()[0] == 'y':
        goal_time = 30
    else:
        while goal_time == False:
            goal_answer = input("How long would you like the game to last? ")
            if not goal_answer.isnumeric():
                print("please enter an integer (whole number)")
            else:
                goal_time = int(goal_answer)
while sim_num == False:
    sim_num = input("How many simulations would you like to run? ")
    if not sim_num.isnumeric():
        print("please enter an integer (whole number)")
        sim_num = False
    else:
        sim_num = int(sim_num)
if (sim_num) < 100:
    print("Less than 100 might be good for a quick check, but at least 1,000 is probably better for accuracy.")
elif (sim_num) >= 10000: 
    print(sim_num,"simulations each...you may want to go for a walk. I hope you get paid for compile time.")

simulations = range(int(sim_num))
minutes_list = []
minutes_average = []
probability = []
lower_95 = []
upper_95 = []
# this sets the maximum number of hoops for the simulations - currently 8-15
for max in range(8,16):
    minutes = []
    count = 0
    total = 0
    for sim in simulations:
        minute = rock_paper_scissor_hop(max = max)/60
        minutes.append(minute)
        if minute > goal_time:
            count +=1
        total +=1
    probability.append(count/total)
    minutes_list.append(minutes)
    minutes_average.append(sum(minutes)/len(minutes))
    lower_95.append(round(numpy.percentile(numpy.array(minutes), 2.5),2))
    upper_95.append(round(numpy.percentile(numpy.array(minutes), 97.5),2))
    print("That's",max,"hoops !")
    
# view average minutes, upper and lower 95% CI for each number of hoops
print(minutes_average)
print(lower_95)
print(upper_95)

# average times per number of hoops
hoops_average_times = dict(zip(list(range(8,15)), minutes_average))
hoops_average_times

# probability of exceeding goal_time per number of hoops
hoops_probability = dict(zip(list(range(8,15)), probability))
hoops_probability

# plot results of expected game time
import matplotlib.pyplot as plt

lines = plt.plot(list(range(8,16)),minutes_average)
plt.xlabel("Number of hoops")
plt.ylabel("Minutes")
plt.title("Average minutes per game based on number of hoops")
plt.setp(lines,'linewidth', 4, 'color','r')
plt.show()

# plot results of expected game time with 95% confidence intervals
lines = plt.plot(list(range(8,16)),minutes_average)
upper = plt.plot(list(range(8,16)),upper_95)
lower = plt.plot(list(range(8,16)),lower_95)
plt.xlabel("Number of hoops")
plt.ylabel("Minutes")
plt.title("Average minutes per game based on number of hoops\nwith 95% confidence intervals")
plt.setp(lines,'linewidth', 4, 'color','r')
plt.setp(upper,'linewidth', .5, 'color','b','ls','--')
plt.setp(lower,'linewidth', .5, 'color','b','ls','--')
plt.show()

# plot probability of exceeding goal_time
prob_lines = plt.plot(list(range(8,16)),probability)
plt.xlabel("Number of hoops")
plt.ylabel("Probability")
plt.title("Probability of game lasting at least", goal_time,"\nbased on number of hoops")
plt.setp(prob_lines,'linewidth', 4, 'color','r')
plt.show()

Riddler_8_24_18.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import random\n",
    "import numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def rock_paper_scissor_hop(min = 1, max = 8):\n",
    "    player1 = min\n",
    "    player2 = max\n",
    "    count = 0\n",
    "    while player1 != max and player2 != min:\n",
    "        player1 += 1\n",
    "        player2 -= 1\n",
    "        count += 1\n",
    "        winner = False\n",
    "        while winner == False:\n",
    "            p1_throw = random.choice(['rock','paper','scissor'])\n",
    "            p2_throw = random.choice(['rock','paper','scissor'])\n",
    "            count +=1\n",
    "            if p1_throw == p2_throw:\n",
    "                winner = False\n",
    "            elif (p1_throw == 'rock' and p2_throw == 'scissor') or (p1_throw == 'scissor' and p2_throw == 'paper') or (p1_throw == 'paper' and p2_throw == 'rock'):\n",
    "                winner = True\n",
    "                player2 = max\n",
    "            else:\n",
    "                winner = True\n",
    "                player1 = min\n",
    "    return(count)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Would you like to stick with the probability of the game lasting at least 30 minutes (y/n): y\n",
      "How many simulations would you like to run? 1000\n",
      "That's 8 hoops !\n",
      "That's 9 hoops !\n",
      "That's 10 hoops !\n",
      "That's 11 hoops !\n",
      "That's 12 hoops !\n",
      "That's 13 hoops !\n",
      "That's 14 hoops !\n",
      "That's 15 hoops !\n"
     ]
    }
   ],
   "source": [
    "sim_num = False\n",
    "goal_time = False\n",
    "while goal_time == False:\n",
    "    goal_answer = input(\"Would you like to stick with the probability of the game lasting at least 30 minutes (y/n): \")\n",
    "    if goal_answer.lower()[0] == 'y':\n",
    "        goal_time = 30\n",
    "    else:\n",
    "        while goal_time == False:\n",
    "            goal_answer = input(\"How long would you like the game to last? \")\n",
    "            if not goal_answer.isnumeric():\n",
    "                print(\"please enter an integer (whole number)\")\n",
    "            else:\n",
    "                goal_time = int(goal_answer)\n",
    "while sim_num == False:\n",
    "    sim_num = input(\"How many simulations would you like to run? \")\n",
    "    if not sim_num.isnumeric():\n",
    "        print(\"please enter an integer (whole number)\")\n",
    "        sim_num = False\n",
    "    else:\n",
    "        sim_num = int(sim_num)\n",
    "if (sim_num) < 100:\n",
    "    print(\"Less than 100 might be good for a quick check, but at least 1,000 is probably better for accuracy.\")\n",
    "elif (sim_num) >= 10000: \n",
    "    print(sim_num,\"simulations each...you may want to go for a walk. I hope you get paid for compile time.\")\n",
    "\n",
    "simulations = range(int(sim_num))\n",
    "minutes_list = []\n",
    "minutes_average = []\n",
    "probability = []\n",
    "lower_95 = []\n",
    "upper_95 = []\n",
    "# this sets the maximum number of hoops for the simulations - currently 8-15\n",
    "for max in range(8,16):\n",
    "    minutes = []\n",
    "    count = 0\n",
    "    total = 0\n",
    "    for sim in simulations:\n",
    "        minute = rock_paper_scissor_hop(max = max)/60\n",
    "        minutes.append(minute)\n",
    "        if minute > goal_time:\n",
    "            count +=1\n",
    "        total +=1\n",
    "    probability.append(count/total)\n",
    "    minutes_list.append(minutes)\n",
    "    minutes_average.append(sum(minutes)/len(minutes))\n",
    "    lower_95.append(round(numpy.percentile(numpy.array(minutes), 2.5),2))\n",
    "    upper_95.append(round(numpy.percentile(numpy.array(minutes), 97.5),2))\n",
    "    print(\"That's\",max,\"hoops !\")\n",
    "print(\"Done !\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5.468516666666667, 10.20828333333333, 20.664766666666697, 42.506383333333396, 81.3800166666666, 172.04560000000012, 330.42843333333303, 683.0073166666668]\n",
      "[0.38, 0.56999999999999995, 0.84999999999999998, 1.7, 2.5499999999999998, 5.8200000000000003, 9.7200000000000006, 18.149999999999999]\n",
      "[19.100000000000001, 36.969999999999999, 75.299999999999997, 147.31, 304.39999999999998, 614.50999999999999, 1198.6199999999999, 2593.5599999999999]\n"
     ]
    }
   ],
   "source": [
    "print(minutes_average)\n",
    "print(lower_95)\n",
    "print(upper_95)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{8: 5.251470000000011, 9: 10.6000066666667, 10: 21.37872666666669, 11: 42.66154833333358, 12: 85.90134333333363, 13: 171.04060500000034, 14: 345.51273333333444, 15: 688.9630099999999}\n"
     ]
    }
   ],
   "source": [
    "hoops_average_times = dict(zip(list(range(8,16)), minutes_average))\n",
    "print(hoops_average_times)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{8: 0.004,\n",
       " 9: 0.06,\n",
       " 10: 0.208,\n",
       " 11: 0.479,\n",
       " 12: 0.686,\n",
       " 13: 0.837,\n",
       " 14: 0.923,\n",
       " 15: 0.964}"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hoops_probability = dict(zip(list(range(8,16)), probability))\n",
    "hoops_probability"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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8996+48ePdys3SSx5GGNCo+q6VR8+3CUPE6fJk+GQQ1w5X1nZ3uNyclw2fvfd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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0a5415c940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "lines = plt.plot(list(range(8,16)),minutes_average)\n",
    "upper = plt.plot(list(range(8,16)),upper_95)\n",
    "lower = plt.plot(list(range(8,16)),lower_95)\n",
    "plt.xlabel(\"Number of hoops\")\n",
    "plt.ylabel(\"Minutes\")\n",
    "plt.title(\"Average minutes per game based on number of hoops\\nwith 95% confidence intervals\")\n",
    "plt.title(\"Average minutes per game based on number of hoops\")\n",
    "plt.setp(lines,'linewidth', 4, 'color','r')\n",
    "plt.setp(upper,'linewidth', .5, 'color','b','ls','--')\n",
    "plt.setp(lower,'linewidth', .5, 'color','b','ls','--')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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o0KMH3HADbLddcXGZtaPmuo/+L/v76/YJx6wgt90G3/9+upxmgx490p7DjjsW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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0a5477ee10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "prob_lines = plt.plot(list(range(8,16)),probability)\n",
    "plt.xlabel(\"Number of hoops\")\n",
    "plt.ylabel(\"Probability\")\n",
    "plt.title(\"Probability of game lasting at least 30 minutes \\nbased on number of hoops\")\n",
    "plt.setp(prob_lines,'linewidth', 4, 'color','r')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}