Eskildsen has been publishing napkin math problems for a while. The latest one, Napkin Problem #16, has tried to grow a new leaf, and instead has exposed some prior assumptions.

The crux of the post is when should we write a simulation?

From an epistemology perspective, this is like the problem of clocks at sea. If you bring one clock on a 17th century sea voyage , how do you know it is still correct? If you bring two clocks, what happens when they differ? If three clocks, ...

Estimations and simulations should be the last things done. The bulk of the work should be researching and trying to find ways to validate results. ie. are there multiple models or ways to think about this problem? how sensitive are each model's results to changes in inputs?

For example, the Monty Hall problem referenced in the post can be counted out on a napkin, but how do you know your result is correct?

If you cannot see conceptually different approaches, then it's time to hit the books and get familiar with the problem space.