There is one single game. It's my version and I make the rules! Rules2: "One player picks a door, the second picks a door (maybe the same), the host opens a

There is one single game. It's my version and I make the rules! Rules2: "One player picks a door, the second picks a door (maybe the same), the host opens a door that has not been picked (if there are two he picks at random). Then the players can either keep their choice or switch to the other closed door." Scenario2: "Player #1 picked one door, player #2 picked another door, the third door was opened and there was a goat behind it." In that scenario, what are the probabilities? I agree it's different from the original problem, that's the point! Rules0: "The player picks a door, the host opens a door that has not been picked with full knowledge that there will be a goat behind it. Then the player can either keep his choice or switch to the other closed door." Scenario0: "The player picked one door, the host opened another door and there was a goat behind it." But the game I proposed is equivalent to the version of the problem that some people, including you apparently [0], insist in this thread that is equivalent to the original problem. Rules1: "The player picks a door, the host opens another door selected at random. Then the player can either keep his choice or switch to the other closed door." Scenario1: "The player picked one door, the host opened another door and there was a goat behind it." The latter is not equivalent to the original problem. The situation is similar but the rules are different. The solution is different. However the solution of Problems 1 and 2 is the same. In both cases the rules allow for the car being unveiled when the host opens the door (it happens with probability 1/3). In both cases under the scenarios proposed there is no point in switching doors. They are both different to the original problem where everybody knows beforehand that the door opened will hide a goat. [0] The problem I proposed at https://news.ycombinator.com/item?id=24707305 https://news.ycombinator.com/item?id=24707305 is also equivalent: Rules1': "The player picks a door, and opens another door selected at random. Then he can either keep his choice or switch to the other closed door." Scenario1': "The player picked one door, then opened another door and there was a goat behind it."