>>13888150Think of it in terms of finding both goats, since that is equivalent to determining where the car is.
You have to find the goats, I'll give you two offers:
I will reveal one goat and then you can pick a door at random.
or
You can pick a door at random then after I will reveal one goat.
What are your odds of picking a goat at random in either of these scenarios? Well its kind of like having to clear a minefield of two invisible poison gas mines, and if you can't clear both you can't cross. You have a bomb sniffing rat who will always find one and die, and you have a rock which will set one off if it lands on it. Are you going to send the rat out and then throw the rock? Of course not, you'll throw the rock first when it has twice the chance of landing on a mine, then send the rat out second since it has a 100% chance of finding a mine, even if there is only one.
In the case of finding goats you don't want to clear the field before you have to take a chance with your first pick, you want to take your chance with as many targets as possible, then allow the rat, or the host, to reliably find one even if you did hit the first one. Since when you took your initial chance you had a 2/3 shot of picking a goat, if you assume because of your good odds you did find a goat, and the host just revealed another one to you then you actually have a 2/3 shot of knowing where both goats are in that moment.