This tool was written by Mark Peterson, an Assistant Professor at Viterbo University in La Crosse, Wisconsin. It is built using Shiny for R (shiny.rstudio.com); if you would like to see the code or have suggestions, please contact me. If you use any of the outputs, ideas, etc, from this tool, please include a reference to this site and me by name.
The Monty Hall problem is a classic example of counter-intuitive probablity. Loosely based on the game show Let's Make A Deal, the problem is as follows.
You, as a contentestant, are offered a choice of three doors (A, B, and C). Behind one is the Grand Prize (lots of money, a car, your wildest dreams come true, etc.). Behind the other two are goats. You select a door, and then the host opens one of the remaining doors, always revealing one of the goats.
Now, you are offered a choice: Would you like to switch to the remaining (closed door)?
The question is if switching will make a difference, and if so, what your odds of winning the game are if you switch (and if you don't).
Before proceeding, take a moment to think through the logic of the game and decide what you think the odds are under each condition. Then, click over to the 'Current Game' tab and play a few rounds. The data will be saved and available for download when you are done (in the 'All Data' tab). Finally, you can run many, many simulations all at once if you prefer on the 'Simulate Many' tab.
When you are done, consider whether your intuition was correct, and if not, why not? For more information, including a thorough description of the solution, visit Wikipedia's description.