Comment by arnvald

The most intuitive and simple explanation that worked for me is:

* if on the 1st try you choose the correct box (33% chance), then the one you can switch to will be wrong

* if on the 1st try you choose the wrong box (66% chance), then the one you can switch to will be correct one

therefore your goal is to pick the wrong box on the 1st try and then switch, and you have 66% chance to do it