A Random Walk & Monte Carlo Simulation || Python Tutorial || Learn Python Programming

𝙎𝙩𝙖𝙮 𝙞𝙣 𝙩𝙝𝙚 𝙡𝙤𝙤𝙥 𝙄𝙉𝙁𝙄𝙉𝙄𝙏𝙀𝙇𝙔: snu.socratica.com/python A random walk is a process where each step is chosen randomly. This technique has many applications. In this video we solve a random walk puzzle using Monte Carlo simulations and the random module in Python.
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Python instructor: Ulka Simone Mohanty (@ulkam on Twitter)
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[@ChumX100]

As for the "even numbers get you closer" thing: Since the direction of the steps is evenly distributed, in the even case, we can expect the number of steps going up to be the same to those going down. But in the odd case, we can expect the number of steps in one direction to be one larger than the other, leading us further away from the origin. The same is true for the left/right dimension. This phenomenon should be less and less noticeable, as we increase the number of steps.

[@saraperestrelo8377]

Yes, but this is only because it was considered the result "distance = abs(x) + abs(y)", removing the influence of the sign of x and y, which can influence your distance in each direction. Interesting.

[@chukypedro818]

Yes., Also this is dependent on the number of blocks chosen, take for instance 5 blocks away from home, We expect the even number to be further aways..

[@sebastiandonickler.6715]

I think it is because I’m the second step you have a only a 25% chance to be 2 blocks away and 75% to be one block away or back to the starting point. For example if your first step is W only if the second step is W you will be 2 blocks away, if it is S or N you will be 1 block away and if it is E you will be back at the starting point. So this tendency will impact the subsequent results as more steps are added.

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Is it safe to say that with an even number of blocks, there are more chances of backtracking compared to an odd number of blocks?

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Thank you for this explanation of Monte Carlo simulations.

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Wow! That's the best monte Carlo simulation tutorial I've ever seen.

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This lady is not just a programmer, but she is actually a real scientist I have been searching for more than ten years for an efficient and logical way to implement Monte Carlo simulation

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Where's Monte Carlo ?

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[@tanmay094]

Why range of walk length is (1,31)

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@@tanmay094 Assume that with a length greater than 30 random steps it is impossible to stay close to the origin.

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I walked randomly and found Socratica ...just 0 block from my house

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Wow, this blew my mind. When I increased it to 5 blocks or less, the odd walk has a higher chance of being closer to home.

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To answer @Benjamin Voll, my initial guess is that the odd distances (numbers) are not perfectly divisible by two like even distance(numbers). P.S. Great videos. I like the emphasis on computer science and not just "learning python." Also, great videos on mathematics, too.

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I wish I watched this video like 5 years ago, the Monte Carlo method is a cornerstone of many important fields of research, but I had felt locked out of it for the longest time because classrooms simply dismissed it as an abstract idea from which we derive a single average value. Whelp, time to jump back into polymer science!

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Gosh that was fascinating! Great video style, good content! (Now I no longer feel guilty for being a Monte Carlo type dude 😉)

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