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Industrial Engineering
Date
Feb 20, 2024
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7
Uploaded by ElderJaguarPerson412
Machine Learning for Trading : Project 1 Report
Odera Okafor
ookafor8@gatech.edu
Abstract-
In this project, we will implement a Simple Gambling Simulator. Using
the below pseudocode, we will run 1000 successive bets/spins per episode.Our
goal
is
to analyze/simulate the strategy with two experiment.One includes
unlimited bankroll and another set at $256. The multiple runs/episodes are used
to evaluate expectation.Expectation essentially means, given a distribution,X,the
expectation is the value x multiplied by its probability of finding x in distribution
for all possible x values.
Pseudocode of strategy:
episode_winnings = $0
while episode_winnings < $80:
won = False
bet_amount = $1
while not won
wager bet_amount on black
won = result of roulette wheel spin
if won == True:
episode_winnings = episode_winnings + bet_amount
else:
episode_winnings = episode_winnings - bet_amount
bet_amount = bet_amount * 2
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Question 1
:
In Experiment 1, based on the experiment results calculate and
provide the estimated probability of winning $80 within 1000 sequential bets.
Thoroughly explain your reasoning for the answer using the experiment output.
In theory, the probability is very high.With 1000 runs and unlimited bankroll,
it's almost inevitable.No ma±er how much loss we accumulate, we have a
chance to make it back.In Fig 1 you can see all episodes hit the $80 price point
within 150 to 200 bets/spins.
Question 2
: In Experiment 1, what is the estimated expected value of winnings
after 1000 sequential bets? Thoroughly explain your reasoning for the answer.
First we need to update the win_prob parameters according to the correct
probability of winning in American roule±e.The wheel has 38 pockets including
1 through 36 ,and a single zero and double zero.For placing bets on red /black or
odd/even the probability is 18/38 (47%).Based on our strategy the expected value
for 1000 bets is 1000 * $0.474 = $474
Question 3:
In Experiment 1, do the upper standard deviation line (mean +
stdev) and lower standard deviation line (mean – stdev) reach a maximum (or
minimum) value and then stabilize? Do the standard deviation lines converge
with one another as the number of sequential bets increases? Thoroughly explain
why it does or does not.
2
In Fig 2 you can clearly see that the plot does not stabilize when reaching
maximum or minimum,but does when it reaches the $80 price point.This happens
because the simulation is designed to keep the remaining values at 80 once
met.The standard deviation lines do seem to be converging because throughout
the simulation they are relatively close. The lines seem to converge because they
are trending towards a certain value.
Question 4
:
In Experiment 2, based on the experiment results calculate and
provide the estimated probability of winning $80 within 1000 sequential bets.
Thoroughly explain your reasoning for the answer using the experiment output.
Your explanation should NOT be based on estimates from visually inspecting
your plots, but from analyzing any output from your simulation.
Based on my simulation,the chances of you winning(reach $80) is about 661 out
of 1000 bets/spins.That is roughly 66% of the time.The chances of losing(reaching
-256) is about 160 out of 1000. That is about 16% of the time. The lower chance of
winning is probably due to the bankroll limit.
Question 5
:
In Experiment 2, what is the estimated expected value of winnings
after 1000 sequential bets? Thoroughly explain your reasoning for the answer.
Using the calculations from question 4,For 1000 bets/spins with bankroll you
can use this equation for my simulation .
66.0839% * 80 + 16.1938%*(-256) = $11.41
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Question 6
: In Experiment 2, do the upper standard deviation line (mean +
stdev) and lower standard deviation line (mean – stdev) reach a maximum (or
minimum) value and then stabilize? Do the standard deviation lines converge
with one another as the number of sequential bets increases? Thoroughly explain
why it does or does not
.
In experiment 2,they do stabilize once the simulation reaches around 15
bets/spins. I think it's directly correlated to the winning/losing limits at
$80/$-256.The lines do converge briefly before the stabilized point.
Question 7
:What are some of the benefits of using expected values when
conducting experiments instead of simply using the result of one specific random
episode?
Using expected values offer many benefits over simply using the results of one
episode.Expected values provide a more stable and reliable measure.Expected
values reduce sensitivity to outliers than one episode .Expected values show a
be±er representation of long term values and involve probability of different
outcomes .
4
Figure 1 : Experiment 1
Figure 2 : Experiment 1
5
Figure 3 : Experiment 1
Figure 4 : Experiment 2
6
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Figure 5: Experiment 2
References:
h±ps://en.wikipedia.org/wiki/Roule±e
h±ps://cs.nyu.edu/~mohri/mlbook/
h±ps://probml.github.io/pml-book/book1.html
h±ps://en.wikipedia.org/wiki/Expected_value
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