When I first heard about the problem, I struggled with the seemingly 50/50 chances. either you picked the right door and now switch and lose, or you picked a w

When I first heard about the problem, I struggled with the seemingly 50/50 chances. either you picked the right door and now switch and lose, or you picked a wrong door and switch and win. Switching seemed a zero sum game. The explanation that works best for me is that you were more likely to have picked a wrong door in the first place, so while the impacts are opposite equals, the likelihoods are not equivalent.