Who says they are two independent games? https://news.ycombinator.com/item?id=24713352 https://news.ycombinator.com/item?id=24713352 If the players pick diffe

Who says they are two independent games? https://news.ycombinator.com/item?id=24713352 https://news.ycombinator.com/item?id=24713352 If the players pick different doors, the host will open the third door. That prevents him from being sure to get a goat, in the same way that opening a door at random in the single-player case prevents him from being sure to get a goat.