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Isaac Lee
Isaac Lee

Posted on • Updated on • Originally published at crunchingnumbers.live

4 Full Examples of Monte Carlo Simulation

People land (stumble) on my blog the most to learn Monte Carlo simulation. It's a numerical method for solving real-world problems, especially those for which we don't know the exact solution. It's also a great way to learn coding and use math to further understand a problem.

Let me show you 4 examples, best to be read in sequence. The codes on my blog are in Matlab, but you can also find them in Python and R on GitHub.

1. Craps

Skills covered:

  • Random number generation
  • If-else statement
  • While and for loops
  • Conditional probability

Dice being rolled

2. Penney's Game

Skills covered:

  • Arrays
  • String operations
  • User-defined function
  • Conway's algorithm

Probability distribution of winning Penney's game

3. Buffon's Needle

Skills covered:

  • Ceiling and floor functions
  • Min and max functions
  • Trigonometry & calculus
  • Affine transformation
  • Vectorization (parallelization)
  • Polymorphism

Needles intersecting lines

4. How Big Is Your Heart?

Skills covered:

  • Dimensional analysis
  • Boundary value analysis
  • Size-dependent simulation

Hearts of various sizes

Discussion (2)

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Maria Boldyreva

Thank you for the articles, they are very informative, yet simple.
The second link leads to the first post, btw.

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Isaac Lee Author

Hi, Maria. I'm glad that you found them helpful. Thanks for letting me know about the incorrect link, it's fixed now. :)