[et_pb_section fb_built=”1″ _builder_version=”4.4.5″][et_pb_row _builder_version=”4.4.5″][et_pb_column type=”4_4″ _builder_version=”4.4.5″][et_pb_text _builder_version=”4.5.6″ header_font=”|700||on|||||”]<\/p>\n
[\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row _builder_version=”4.4.5″][et_pb_column type=”4_4″ _builder_version=”4.4.5″][et_pb_text _builder_version=”4.5.6″ header_2_font=”|||on|on||||”]<\/p>\n
08\/30\/2020 11:59PM <\/span>Anywhere on Earth time<\/a><\/p>\n [\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row _builder_version=”4.4.5″][et_pb_column type=”4_4″ _builder_version=”4.4.5″][et_pb_text _builder_version=”4.5.6″ header_2_font=”|||on|on||||” hover_enabled=”0″]<\/p>\n This assignment is subject to change up until 3 weeks prior to the due date. We do not anticipate changes; any changes will be logged in this section.<\/span><\/p>\n [\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row _builder_version=”4.4.5″][et_pb_column type=”4_4″ _builder_version=”4.4.5″][et_pb_text _builder_version=”4.5.6″ header_2_font=”|||on|on||||”]<\/p>\n The purpose of this assignment is to get you started programming in Python right away and to help provide you some initial feel for risk, probability, and \u201cbetting.\u201d Purchasing a stock is, after all, a bet that the stock will increase in value.<\/p>\n In this project you will evaluate the actual betting strategy that Professor Balch uses at roulette when he goes to Las Vegas. Here it is:<\/p>\n [\/et_pb_text][et_pb_dmb_code_snippet title=”Pseudocode ” code=”ZXBpc29kZV93aW5uaW5ncyA9ICQwCndoaWxlIGVwaXNvZGVfd2lubmluZ3MgPCAkODA6Cgl3b24gPSBGYWxzZQoJYmV0X2Ftb3VudCA9ICQxCgl3aGlsZSBub3Qgd29uCgkJd2FnZXIgYmV0X2Ftb3VudCBvbiBibGFjawoJCXdvbiA9IHJlc3VsdCBvZiByb3VsZXR0ZSB3aGVlbCBzcGluCgkJaWYgd29uID09IFRydWU6CgkJCWVwaXNvZGVfd2lubmluZ3MgPSBlcGlzb2RlX3dpbm5pbmdzICsgYmV0X2Ftb3VudAoJCWVsc2U6CgkJCWVwaXNvZGVfd2lubmluZ3MgPSBlcGlzb2RlX3dpbm5pbmdzIC0gYmV0X2Ftb3VudAoJCQliZXRfYW1vdW50ID0gYmV0X2Ftb3VudCAqIDI=” usetabwidth=”on” tabwidth=”4″ _builder_version=”4.4.6″]ZXBpc29kZV93aW5uaW5ncyA9ICQwCndoaWxlIGVwaXNvZGVfd2lubmluZ3MgPCAkODA6Cgl3b24gPSBGYWxzZQoJYmV0X2Ftb3VudCA9ICQxCgl3aGlsZSBub3Qgd29uCgkJd2FnZXIgYmV0X2Ftb3VudCBvbiBibGFjawoJCXdvbiA9IHJlc3VsdCBvZiByb3VsZXR0ZSB3aGVlbCBzcGluCgkJaWYgd29uID09IFRydWU6CgkJCWVwaXNvZGVfd2lubmluZ3MgPSBlcGlzb2RlX3dpbm5pbmdzICsgYmV0X2Ftb3VudAoJCWVsc2U6CgkJCWVwaXNvZGVfd2lubmluZ3MgPSBlcGlzb2RlX3dpbm5pbmdzIC0gYmV0X2Ftb3VudAoJCQliZXRfYW1vdW50ID0gYmV0X2Ftb3VudCAqIDI=[\/et_pb_dmb_code_snippet][et_pb_text _builder_version=”4.5.6″]<\/p>\n Here are some details regarding how roulette betting works: Betting on black (or red) is considered an “even money” bet. That means that if you bet N chips and win, you keep your N chips and you win another N chips. If you bet N chips and you lose then those N chips are lost. The odds of winning or losing depend on whether you’re betting at an American wheel or a European wheel. For this project we will be assuming an <\/span>American wheel<\/b>. You can learn more about roulette and betting here: <\/span>https:\/\/en.wikipedia.org\/wiki\/Roulette<\/a><\/p>\n [\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row _builder_version=”4.4.5″][et_pb_column type=”4_4″ _builder_version=”4.4.5″][et_pb_text _builder_version=”4.5.6″ header_2_font=”|||on|on||||”]<\/p>\n First, if you haven’t yet set up your software environment, follow the instructions here: ML4T_Software_Setup<\/a>. This is the base directory structure used for all projects in the class, including supporting data and software will be set up correctly when you follow those instructions.<\/p>\n Then:<\/p>\n You should change only martingale.py<\/tt>. All of your code should be in that one file. Do not create additional files. It should always remain in and run from the directory ML4T_2020Fall\/martingale\/<\/tt>. Leave the copyright information at the top intact.<\/p>\n To test your code, we will be calling __main__()<\/tt> function only. Doing so should run all aspects of the program and output the desired charts.<\/p>\n [\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row _builder_version=”4.4.5″][et_pb_column type=”4_4″ _builder_version=”4.4.5″][et_pb_text _builder_version=”4.5.6″ header_2_font=”|||on|on||||”]<\/p>\n Revise the code functions author()<\/tt> and gtid()<\/tt> to correctly include your GT Username and 9 digit GT ID respectively. Your GT Username should be something like tbalch78<\/tt> and your GTID is a 9 digit number. You should also update this information the comments section at the top.<\/p>\n Revise the code in martingale.py<\/tt> to simulate 1000 successive bets on spins of the roulette wheel using the betting scheme outlined above. You should test for the results of the betting events by making successive calls to the get_spin_result(win_prob)<\/tt> function. Note that you’ll have to update the win_prob<\/tt> parameter according to the correct probability of winning. You can figure that out by thinking about how roulette works (see wikipedia link above).<\/p>\n Track your winnings by storing them in a numpy array. You might call that array winnings<\/tt> where winnings[0]<\/tt> should be set to 0 (just before the first spin). Winnings[1]<\/tt> should reflect the total winnings after the first spin and so on.\u00a0<\/p>\n For the following charts, and for all charts in this class you should use python’s matplotlib library. Your submitted project should include all of the code necessary to generate the charts listed in your report. You should configure your code to write the figures to .png files. Do not allow your code to create a window that displays images (DO NOT use plt.show() and manually save as .png files). If it does you will receive a penalty.<\/p>\n 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. Review the “report” section below for specific properties of the strategy we want you to evaluate.<\/p>\n 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 (e.g., fill the data forward with a value of $80<\/span>)<\/span><\/span><\/span>.<\/p>\n You may have noticed that the strategy 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:<\/p>\n [\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row _builder_version=”4.4.5″][et_pb_column type=”4_4″ _builder_version=”4.4.5″][et_pb_text _builder_version=”4.5.6″ header_2_font=”|||on|on||||”]<\/p>\n Answer the following prompt in a maximum of 7 pages (excluding references) in JDF format<\/a>. Any content beyond 7 pages will not be considered for a grade. Seven pages is a maximum, not a target; our recommended per-section lengths intentionally add to less than seven pages to leave you room to decide where to delve into more detail. This length is intentionally set expecting that your submission will include diagrams, drawings, pictures, etc. These should be incorporated into the body of the paper unless specifically required to be included in an appendix.<\/p>\n The JDF format<\/a> specifies font sizes and margins, which should not be altered. Charts should be generated by the code and saved to files. Charts should be properly annotated with legible and appropriately named <\/span>labels, titles, and legends.<\/p>\n Please address each of these points \/ questions in your report. The report is to be submitted as report.pdf<\/strong>.<\/p>\n Question 1<\/strong>: In Experiment 1, based off the experiment results<\/em> calculate the estimated probability of winning $80 within 1000 sequential bets. Explain your reasoning<\/em> for the answer<\/em> using the experiment thoroughly (not based on plots).<\/p>\nRevisions<\/h2>\n
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Overview<\/h2>\n
This assigment counts towards 3% of your overall grade.<\/span><\/h3>\n
Template<\/h2>\n
Set up your development environment<\/span><\/h3>\n
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Tasks<\/h2>\n
author() and gtid() function<\/span><\/h3>\n
Build a simple gambling simulator<\/span><\/h3>\n
Chart Creation<\/span><\/h3>\n
Experiment 1: Explore the strategy and make some charts<\/span><\/h3>\n
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Experiment 2: A more realistic gambling simulator<\/span><\/h3>\n
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Contents of Report<\/h2>\n
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Experiment 1: ~ 1 page<\/span><\/h3>\n