Fall 2019 Project 1: Martingale - Revision history

Jfox44: /* Required, Allowed & Prohibited */

2019-08-16T22:37:01Z

Required, Allowed & Prohibited

Jfox44: /* Tasks */

2019-08-15T16:08:43Z

Tasks

Jfox44: /* Tasks */

2019-08-15T16:08:24Z

Tasks

Jfox44: /* Rubric */

2019-08-15T16:02:48Z

Rubric

Jfox44: /* Rubric */

2019-08-15T16:01:47Z

Rubric

Jfox44: /* Contents of the report */

2019-08-15T16:01:09Z

Contents of the report

Jfox44: /* Tasks */

2019-08-15T15:57:31Z

Tasks

Jfox44: /* Tasks */

2019-08-15T15:52:15Z

Tasks

Jfox44: /* Required, Allowed & Prohibited */

2019-08-15T14:50:09Z

Required, Allowed & Prohibited

David.joyner: Python 2.7 -> 3.6

2019-08-04T17:02:19Z

Python 2.7 -> 3.6

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 * Any libraries not listed in the "allowed" section above.
 * Use of Python's os module.
-* Any code you did not write yourself (except for the 5 line rule in the "allowed" section).
+* Any code you did not write yourself (except for provided/allowed by the instructor).
 * Knights who say "neeee."
 ==Legacy versions==

← Older revision		Revision as of 16:08, 15 August 2019
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	Now we want you to run some experiments to determine how well the betting strategy works. The approach we're going to take is called Monte Carlo simulation where the idea is to run a simulator over and over again with randomized inputs and to assess the results in aggregate. Skip to the "report" section below to which specific properties of the strategy we want you to evaluate.		Now we want you to run some experiments to determine how well the betting strategy works. The approach we're going to take is called Monte Carlo simulation where the idea is to run a simulator over and over again with randomized inputs and to assess the results in aggregate. Skip to the "report" section below to which specific properties of the strategy we want you to evaluate.
−

	* Figure 1: Run your simple simulator 10 times and track the winnings, starting from 0 each time. Plot all 10 runs on one chart using <tt>matplotlib</tt> functions. The horizontal (X) axis should range from 0 to 300, the vertical (Y) axis should range from -256 to +100. Note that we will not be surprised if some of the plot lines are not visible because they exceed the vertical or horizontal scales.		* Figure 1: Run your simple simulator 10 times and track the winnings, starting from 0 each time. Plot all 10 runs on one chart using <tt>matplotlib</tt> functions. The horizontal (X) axis should range from 0 to 300, the vertical (Y) axis should range from -256 to +100. Note that we will not be surprised if some of the plot lines are not visible because they exceed the vertical or horizontal scales.

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 Track your winnings by storing them in a numpy array. You might call that array <tt>winnings</tt> where <tt>winnings[0]</tt> should be set to 0 (just before the first spin).  <tt>winnings[1]</tt> should reflect the total winnings after the first spin and so on. For a particular episode if you ever hit $80 in winnings, stop betting and just fill the data forward with the value 80.
 '''Experiment 1: Explore the strategy and make some charts'''
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 Now we want you to run some experiments to determine how well the betting strategy works.  The approach we're going to take is called Monte Carlo simulation where the idea is to run a simulator over and over again with randomized inputs and to assess the results in aggregate.  Skip to the "report" section below to which specific properties of the strategy we want you to evaluate.
 * Figure 1: Run your simple simulator 10 times and track the winnings, starting from 0 each time.  Plot all 10 runs on one chart using <tt>matplotlib</tt> functions.  The horizontal (X) axis should range from 0 to 300, the vertical (Y) axis should range from -256 to +100.  Note that we will not be surprised if some of the plot lines are not visible because they exceed the vertical or horizontal scales.

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 '''Code'''
 * Does the code run without crashing? (-10 points if not)
-* Does the code generate appropriate charts written to png files? (-10 points each up to a max of -20 if not)
+* Does the code generate appropriate charts written to png files? <b> DO NOT use plt.show() and manually save your figures. The figures should be created and saved using Python code</b> (-10 points each up to a max of -20 if not)
 * Does the implemented code reflect the project requirements? (Up to -10 points if not)

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 '''Report'''
 * Are the questions answered correctly? (Up to -5 points for each incorrect answer)
-* Is the reasoning for each question correct and supported by the evidence? (Up to -5 points for each if incorrect)
+* Is the reasoning for each question correct and supported by the evidence thoroughly? (Up to -5 points for each if incorrect)
 * Are each of the charts provided and correct and include labeled axis and legend? (Up to -8 points for each if incorrect)

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 Please address each of these points/questions in your report, to be submitted as <tt>report.pdf</tt>
-# In Experiment 1, estimate the probability of winning $80 within 1000 sequential bets.  Explain your reasoning.
+# In Experiment 1, estimate the probability of winning $80 within 1000 sequential bets.  Explain your reasoning thoroughly.
-# In Experiment 1, what is the estimated expected value of our winnings after 1000 sequential bets? Explain your reasoning. Go here to learn about expected value: https://en.wikipedia.org/wiki/Expected_value
+# In Experiment 1, what is the estimated expected value of our winnings after 1000 sequential bets? Explain your reasoning thoroughly. Go here to learn about expected value: https://en.wikipedia.org/wiki/Expected_value
-# In Experiment 1, does the standard deviation reach a maximum value then stabilize or converge as the number of sequential bets increases?  Explain why it does (or does not).
+# In Experiment 1, does the standard deviation reach a maximum value then stabilize or converge as the number of sequential bets increases?  Explain why it does (or does not) thoroughly.
-# In Experiment 2, estimate the probability of winning $80 within 1000 sequential bets.  Explain your reasoning using the experiment. (not based on plots)
+# In Experiment 2, estimate the probability of winning $80 within 1000 sequential bets.  Explain your reasoning using the experiment thoroughly. (not based on plots)
-# In Experiment 2, what is the estimated expected value of our winnings after 1000 sequential bets? Explain your reasoning. (not based on plots)
+# In Experiment 2, what is the estimated expected value of our winnings after 1000 sequential bets? Explain your reasoning thoroughly. (not based on plots)
-# In Experiment 2, does the standard deviation reach a maximum value then stabilize or converge as the number of sequential bets increases?  Explain why it does (or does not).
+# In Experiment 2, does the standard deviation reach a maximum value then stabilize or converge as the number of sequential bets increases?  Explain why it does (or does not) thoroughly.
 # Include figures 1 through 5.

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 * Figure 1: Run your simple simulator 10 times and track the winnings, starting from 0 each time.  Plot all 10 runs on one chart using <tt>matplotlib</tt> functions.  The horizontal (X) axis should range from 0 to 300, the vertical (Y) axis should range from -256 to +100.  Note that we will not be surprised if some of the plot lines are not visible because they exceed the vertical or horizontal scales.
-* Figure 2: Run your simple simulator 1000 times.  Plot the mean value of winnings for each spin using the same axis bounds as Figure 1.  Add an additional line above and below the mean at mean+standard deviation, and mean-standard deviation of the winnings at each point.
+* Figure 2: Run your simple simulator 1000 times.  Plot the mean value of winnings for each spin using the same axis bounds as Figure 1.  Add an additional line above and below the mean at mean (+) standard deviation, and mean (-) standard deviation of the winnings at each point.
-* Figure 3: Use the same data you used for Figure 2, but plot the median instead of the mean.  Be sure to include the standard deviation lines above and below the median as well.
+* Figure 3: Use the same data you used for Figure 2, but plot the median instead of the mean.  Add an additional line above and below the median at median (+) standard deviation, and median (-) standard deviation of the winnings at each point.
 For all of the above charts and experiments, if and when the target $80 winnings is reached, stop betting and allow the $80 value to persist from spin to spin.
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 You may have noticed that the strategy actually works pretty well, maybe better than you expected.  One reason for this is that we were allowing the gambler to use an unlimited bank roll.  In this experiment we're going to make things more realistic by giving the gambler a $256 bank roll.  If he or she runs out of money, bzzt, that's it.  Repeat the experiments above with this new condition.  Note that once the player has lost all of their money (i.e., episode_winnings reaches -256) stop betting and fill that number (-256) forward.  An important corner case to be sure you handle is the situation where the next bet should be $N, but you only have $M (where M<N).  Make sure you only bet $M.  Here are the two charts to create:
-* Figure 4: Run your realistic simulator 1000 times.  Plot the mean value of winnings for each spin using the same axis bounds as Figure 1.  Add an additional line above and below the mean at mean+standard deviation, and mean-standard deviation of the winnings at each point.
+* Figure 4: Run your realistic simulator 1000 times.  Plot the mean value of winnings for each spin using the same axis bounds as Figure 1.  Add an additional line above and below the mean at mean (+) standard deviation, and mean (-) standard deviation of the winnings at each point.
-* Figure 5: Use the same data you used for Figure 4, but plot the median instead of the mean.  Be sure to include the standard deviation lines above and below the median as well.
+* Figure 5: Use the same data you used for Figure 4, but plot the median instead of the mean.  Add an additional line above and below the median at median (+) standard deviation, and median (-) standard deviation of the winnings at each point.
 ==Contents of the report==

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 Required:
 * Your project must be coded in Python 3.6.x.
-* This requirement is not enforced for this first project, but will be for future projects. <s>Your code must run on one of the university-provided computers (e.g. buffet02.cc.gatech.edu).</s>
+* <s>Your code must run on one of the university-provided computers (e.g. buffet01.cc.gatech.edu).</s> This requirement is not enforced for this first project, but will be for future projects.
 Allowed: