[gechr]

It's far easier to grasp when you consider that Monty opening one of the other 2 doors makes no difference to his offer (since he'll always open a door with a goat behind it anyway), i.e. he could also say "Do you want to stick with your door, or switch to both these other 2 doors?" without the unnecessary misdirection of opening the goat door beforehand.

[tomalpha]

Thanks, I hadn’t thought of it quite that way. I hesitate to say “eureka!” but maybe, just maybe that might get me there :)

[girvo]

Wow that made this finally click for me. Instead of two actions with the host in between, it’s just two actions. Thanks!

[yarg]

Damn, that's way more intuitive than what I came up with.