Update
So... here's what I did:
- Finished the P4E specialization
I would go on to do the Python Data Science Specialization, but it turns out the auto-grader is really weird ( and thus I am getting errors that I honestly cannot test ), so I want to figure out what the errors are and find the patience necessary to bug test (Which honestly sucks in comparison to actually working on the course materials)
On another note, I have decided the next endeavor will be to work on a book entitled "Vector Calculus, Linear Algebra, and Differential Manifolds", which I am very excited to read and do as it combines my LA knowledge to teach me some multivariable calculus. After working through some of the definitions and the like, I became inspired to figure out some probabilities for Monopoly distribution of places after 10,20,30,40,50, and 100 moves. So, without any context whatsoever, here is are some of the graphs of the most and least likely locations (removing the jail space to preserve spacing, as Go to Jail messes a lot of stuff up ):
In order to do this, I applied what is known as a Markov Chain by doing the following:
1. I created a transition matrix giving the probability of landing in a certain spot after rolling the two dice in monopoly from a given spot. In it, I assumed that the Community Chest and Chance cards did not move anyone ( An assumption that I will end up changing later if I decide to change up this analysis ) and that rolling doubles does nothing ( Another assumption I will need to change later ).
2. I then started the player at GO by creating a 1x40 vector with 1 in the first place and 0s everywhere else, detailing where the player is supposed to be at the beginning ( i.e. at GO )
3. Then I multiplied the vector by the transition matrix the required number of times to see how the distribution changed.
While the analysis was relatively simple, I am not entirely sure of the efficacy, as I had to re-normalize the probabilities so they summed to one ( A fact which probably comes up because of the nature of the game's "Go To Jail" option and my implementation). Overall, while not entirely accurate, I might do another one of these again, as it was relatively simple yet shows some interesting data. ( I think Chutes and Ladders might be a better test case )
- Finished the P4E specialization
I would go on to do the Python Data Science Specialization, but it turns out the auto-grader is really weird ( and thus I am getting errors that I honestly cannot test ), so I want to figure out what the errors are and find the patience necessary to bug test (Which honestly sucks in comparison to actually working on the course materials)
On another note, I have decided the next endeavor will be to work on a book entitled "Vector Calculus, Linear Algebra, and Differential Manifolds", which I am very excited to read and do as it combines my LA knowledge to teach me some multivariable calculus. After working through some of the definitions and the like, I became inspired to figure out some probabilities for Monopoly distribution of places after 10,20,30,40,50, and 100 moves. So, without any context whatsoever, here is are some of the graphs of the most and least likely locations (removing the jail space to preserve spacing, as Go to Jail messes a lot of stuff up ):
In order to do this, I applied what is known as a Markov Chain by doing the following:
1. I created a transition matrix giving the probability of landing in a certain spot after rolling the two dice in monopoly from a given spot. In it, I assumed that the Community Chest and Chance cards did not move anyone ( An assumption that I will end up changing later if I decide to change up this analysis ) and that rolling doubles does nothing ( Another assumption I will need to change later ).
2. I then started the player at GO by creating a 1x40 vector with 1 in the first place and 0s everywhere else, detailing where the player is supposed to be at the beginning ( i.e. at GO )
3. Then I multiplied the vector by the transition matrix the required number of times to see how the distribution changed.
While the analysis was relatively simple, I am not entirely sure of the efficacy, as I had to re-normalize the probabilities so they summed to one ( A fact which probably comes up because of the nature of the game's "Go To Jail" option and my implementation). Overall, while not entirely accurate, I might do another one of these again, as it was relatively simple yet shows some interesting data. ( I think Chutes and Ladders might be a better test case )
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