Why does switching doors in the Monty Hall Problem increase odds: 2 doors, 50-50

Question

I have read through around 10 articles and webpages on this problem, and still don’t understand. I’ve run simulations and yes, switching does get you better odds, but why?

In: Mathematics

Answer 1

Lots of good ways of thinking here.  Here’s a way of visualising it.

You’ve a dartboard split into three equal sections.  Two sections lose, one section wins.

You’re blindfold and the board is spun, then you throw darts until you hit the board, completely randomly.

Then you are given the choice – do you want the outcome you landed on, or the other one?

You’re still blindfolded, but you know you were twice as likely to land in a losing segment than a winning one even though *now* you are being offered the 50/50 of ‘the one you chose, or the one that’s left’