Little typo in 4:13, the denominators should be 36 unless I'm misunderstanding that part (in the code I believe this is fixed). As a side note, in theory for the doubles it would be more precise to have three states per square, one for zero previous doubles, one previous double and a last one for two previous doubles. The reason being that in your model you could end up in jail after three odd dice results (like advancing 5 each round) while in the real game this is impossible because doubles always end up with an even number of steps. Obviously this makes three times the number of states slowing the process, makes the model much harder to code and the precision you're losing is negligible. Just a thought that is worth pointing out. Another side note, I don't know if you got the inspiration from there but this is a Project Euler problem, number 84. Also, fun video!, it's always nice to see people doing fun problems like this with math.
I really appreciate the feedback. Just checked and you are correct. That was a typo when I put it on screen but correct in the code. I was just looking for a board game to solve. I will take a look at other Project Euler problems though. Thanks again for taking the time and giving this feedback!
Dude, I'm a French CS student, I have my exams on Markov Chains next monday, you saved my ass (well, actually your video alone is not enough but it's a very cool example of markov chains being used)
Hey fam, nice video you got there, I'm definitely subscribing ! Just to be clear, you said that we can multiply the transition matrix with itself a few thousand times to get the steady state, but how can we be sure that a steady state exists in the first place ? I mean, when you compute it there doesn't seem to be any issues, but is that sufficient ?
That’s true. There are cases where there isn’t a steady state probability and you can see that after a few multiplications. If you are getting radically different numbers from on multiplication to the next after you’ve already done a few then there isn’t a steady state most likely. Good observation though. Thanks for the comment
hey man great video. I loved it, really gave off code bullet vibes. However I didn't understand one thing. When you are getting the steady state probabilities, why do you divide it by the sum of the steady state vector?
The only complaint I have is that, as someone who isn't from America, the places have a different name and I can't understand them as a result. Edit: Also, the fractions are supposed to be divided by 36, not 12.
Hey, I am currently working on the same topic on my Math assignment in school. Can you please share the python code for all the three conditions? I'm having a little problem understanding what exactly is being done here and I also need to use that code for my own assignment. Thanks a lot btw, I still understood a lot!!
can somebody explain why multiplying all these matrix give the "final transition matrix" ? And I don't understand the code line : steadyStateVec= steadyStateVec/sum(steadyStateVec) . Is there a theorem behind it ?
In the Python code, I'm not sure if the matrix multiplication is done in the right order! It makes a huge difference to the final matrix depending on the order of the matrix multiplication!!!
Would have been nice to see like a colormap of the monopoly board colored by most visited to least visited, anything visual would have been awesome. Just saying "those are the most visited" after talking about it for 7 minutes is just underwhealming and disapointing.
