[9.Sept.2020] To switch or not to switch, that is the question

With a “staycation” being almost the only option on how to spend a holiday we decided to re-watch some classical movies and stumbled on a 2008 American heist drama “21”. The movie is inspired by a true story of the MIT Blackjack Team as told in the book “Bringing down the House”.
What triggered our curiosity in the Alfasoft Mathcad team, was the Monty Hall Problem, and the name of one team member, Jon Hirschtick.

Monty hall problem

With money, this MIT blackjack team generated Jon Hirschtick started SolidWorks, a well-known CAD software that was sold to Dassault Systemes. He then created another CAD software, that has just been acquired by PTC. Both companies are currently our valued partners who make it possible for us to provide you with Mathcad and simulation software, Simulia Abaqus, and SimuliaWorks that we are launching this month!

Now back to the Monty Hall problem, and how we can use Mathcad to satisfy our curiosity.
The riddle in the movie goes like this: Imagine that you are on an American game show (hosted by Monty Hall, that's why the problem is called that) and you've been presented with three doors. Behind one door is a brand-new car, behind the other two doors are goats. After you select a door, Monty opens another of the doors and reveals a goat. He then asks you if you want to change your choice to the other door, or stick with the one you picked in the first place.
So does switching the doors help your chances to win the car?

Let’s analyse the answer. For those of you who are not keen on reading long texts, you can have a look at the movie scene. But make sure you look at the solution in Mathcad.

By picking door no. 1 you have 1/3 chance to get it right. The 2/3 chance lies with the two other doors. Once the show host revealed what's behind door no. 3, then the 2/3 chance now sorely lies with door no 2. So, you have 1/3 chance that door no 1 is right and 2/3 chance that door no 2 is right. Switching would be mathematically the right choice.

So the calculation needed is only:

mh0 the normal wy

But let's make something simple more complicated.

We were curious to simulate in Mathcad what the chances would be if you did and did not switch the doors. We therefore used our programming options in Mathcad. So first a program that use the strategy to not switch door. And as a test run a million times:

mh1 simulating keep

 With a few modifications we can turn it into the other strategy:

mh2 simulating switch

Clearly Mathcad has proven that the probability to win the car is greater if you choose to switch the door.
Maybe you can use the programming function in Mathcad for some other problems, or even work-related issues. We are always happy to hear your great ideas. And if you need help with the programming in Mathcad, we are only an email away.