4 ms·

Hang on, I think you've missed something. They are not completely independent, because if they pick different doors, that forces the host to pick the last door

Hang on, I think you've missed something. They are not completely independent, because if they pick different doors, that forces the host to pick the last door. Removing the host's freedom to choose a non-winning door (and effectively help the player) changes the math. Having two players with the ability to choose different doors (but still 3 doors and the host must choose the third) makes it a different game with different dynamics. It doesn't work the same because it's not the same game.

basch 6y ago
Or, because they are two independent games, the host can flip different goats for different people. You would have to add an element of "no screen peaking" where the contestants cant see which door opened for the other person. So you have Player A who chose door 1. The host flips the goat in door 3. You have Player B who chooses door 2. For them the host flips open the goat in door 1. Player A should switch, and wins the car. Player B should switch, but had the car and loses it. The right move in both their cases was to switch. Really, its no different than playing two separate games. Unless, like you said, you somehow change the rules and limit someones choices, in which case Im not sure why its a part of the conversation, other than being introduced through confusion.
- kgwgk 6y ago
  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.
the_af 6y ago
Well, you're right: in fact, in some cases Monty cannot open any door! That is, if players A & B both chose goats, then the remaining door is the car, and Monty cannot open it without ruining the game. For this reason, both players should be playing "blind", without seeing the other's choices or the door Monty opens for the other player. Anything else doesn't make sense for the game.
deleted 6y ago
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kgwgk 6y ago
> Removing the host's freedom to choose a non-winning door (and effectively help the player) changes the math. As it does removing the host's ability to choose a non-winning door in the variant where "the host had just picked at random from the two doors, and it happened to show a goat". That doesn't work the same either because it's not the same game.

basch 6y ago

Or, because they are two independent games, the host can flip different goats for different people. You would have to add an element of "no screen peaking" where the contestants cant see which door opened for the other person. So you have Player A who chose door 1. The host flips the goat in door 3. You have Player B who chooses door 2. For them the host flips open the goat in door 1. Player A should switch, and wins the car. Player B should switch, but had the car and loses it. The right move in both their cases was to switch. Really, its no different than playing two separate games. Unless, like you said, you somehow change the rules and limit someones choices, in which case Im not sure why its a part of the conversation, other than being introduced through confusion.

kgwgk 6y ago
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.

the_af 6y ago

Well, you're right: in fact, in some cases Monty cannot open any door! That is, if players A & B both chose goats, then the remaining door is the car, and Monty cannot open it without ruining the game. For this reason, both players should be playing "blind", without seeing the other's choices or the door Monty opens for the other player. Anything else doesn't make sense for the game.

deleted 6y ago

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kgwgk 6y ago

> Removing the host's freedom to choose a non-winning door (and effectively help the player) changes the math. As it does removing the host's ability to choose a non-winning door in the variant where "the host had just picked at random from the two doors, and it happened to show a goat". That doesn't work the same either because it's not the same game.