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

Pretend there are 100 doors with only one prize. You pick a door at random. Chances are 1:100 you picked the right door. Next, 98 doors are removed from the game (guaranteed to be without a prize).

The odds you picked the correct door are still 1%. The odds the other door has the prize is 100%-1%=99%.