re: Let's discuss the Monty Hall problem (probabilities, odds)

Ok

There are 3 doors and 2 goats... you have a 2/3 chance from the beginning of being wrong... when he opens one door revealing a goat, he is essentially telling you what door the car is behind in 2/3 of the game... and it isn't the one you picked, and clearly isn't the goat... by showing you the goat, he adds value to the last door, boosting your chances of you switch

You now have a 2/3 advantage if you switch, and only a 1/3 chance of you stay

Another way to see it:

The player has a 1/3 chance of being right the first time, and the other two doors combined have a 2/3 chance... when he shows you the goat, those odds remain, except the full 2/3 odds shift from two doors to the one remaining door you didn't pick and a goat wasn't shown