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> The problem is not about the game overall > The Monty Hall problem is not about "the whole game". The Monty Hall problem is about the whole game. That's the

> The problem is not about the game overall > The Monty Hall problem is not about "the whole game". The Monty Hall problem is about the whole game. That's the difference, and that's why the 50/50 claim doesn't make much sense here. > The Monty Hall problem is quite explicitely about what would you do in the following situation: [...] After all those things have happened you're being offered to switch from your initial pick to the remaining door. Steps (3) and (4) in the Monty Hall problem are a bit more nuanced - the host opens a door guaranteed to be a goat, because the host knows where the goat is. At this point, when you choose to switch or stay with your door, you have a 1/3 chance of winning if you stay, and a 2/3 chance of winning if you switch. But the key point that you are missing is that this is the same for every single time you play the entire game. It doesn't matter where the car is in step (1), or which door you choose in step (2), or which door the host opens is step (3) - if you always switch doors, no matter what, every single game you double your odds. And in the 50/50 scenario posed, that just doesn't hold. It isn't analogous.

kgwgk 3y ago
> But the key point that you are missing is that this is the same for every single time you play the entire game. It doesn't matter where the car is in step (1), or which door you choose in step (2), or which door the host opens is step (3) - if you always switch doors, no matter what, every single game you double your odds. The key point that you are missing is that it doesn't need to be "the same for every single time you play the entire game" to have a well-defined solution for the particular realization of the game described in the problem statement. And the solution for the problem where (1),(2),(3),(4) happen with the host picking a door at random is 50/50. That's what cman1444 said. You're asked a question conditional on (1),(2),(3),(4) happening and the things that didn't happen are irrelevant. Just like if you're asked if you want to switch the envelopes when you got $1 you will say "yes" and it's completely irrelevant that you could have got $10 and you would have said "no" in that case - because you didn't. In conclusion, some people find the problem where (1),(2),(3),(4) have happened and the host was picking a door at random (and its 50/50 solution) interesting and you don't. De gustibus non est disputandum.
- jjnoakes 3y ago
  I addressed this above. See the coin flipping example.
  - kgwgk 3y ago
    > I addressed this above. I'm not sure what is "this". > See the coin flipping example. "I claim the odds of flipping a fair coin 100 times in a row and getting heads every time is 50/50, but only in the situation where you happened to flip 99 heads in a row already". If I'm told that I'm in a coin flipping contest and (1) in my first flip I got heads, (2) in my second flip I got heads, ..., (n) in my n-th flip I got heads, ..., (99) in my 99-th flip I got heads and then I'm asked what's the probability that I get to 100 heads in a row there are different answers that I could give. I could assume that the probability of every single flip is 50/50 and then my answer will by 50%. Or I could give an answer higher than 50% if I'm able to control the outcome - or if by now I suspect that the coin has two heads. Or I could give an answer lower than 50% if I suspect the game is rigged and they are going to make me lose now. Whetever my assumptions about the upcoming flip, my answer will be conditional on (1),(2),...,(99) having happened already. There is no point in thinking about the "whole game" at this point in time. I already got heads 99 times - just like in the Monty Hall problem I already picked a door and he already picked another door with a goat.

kgwgk 3y ago

> But the key point that you are missing is that this is the same for every single time you play the entire game. It doesn't matter where the car is in step (1), or which door you choose in step (2), or which door the host opens is step (3) - if you always switch doors, no matter what, every single game you double your odds. The key point that you are missing is that it doesn't need to be "the same for every single time you play the entire game" to have a well-defined solution for the particular realization of the game described in the problem statement. And the solution for the problem where (1),(2),(3),(4) happen with the host picking a door at random is 50/50. That's what cman1444 said. You're asked a question conditional on (1),(2),(3),(4) happening and the things that didn't happen are irrelevant. Just like if you're asked if you want to switch the envelopes when you got $1 you will say "yes" and it's completely irrelevant that you could have got $10 and you would have said "no" in that case - because you didn't. In conclusion, some people find the problem where (1),(2),(3),(4) have happened and the host was picking a door at random (and its 50/50 solution) interesting and you don't. De gustibus non est disputandum.

jjnoakes 3y ago
I addressed this above. See the coin flipping example.
- kgwgk 3y ago
  > I addressed this above. I'm not sure what is "this". > See the coin flipping example. "I claim the odds of flipping a fair coin 100 times in a row and getting heads every time is 50/50, but only in the situation where you happened to flip 99 heads in a row already". If I'm told that I'm in a coin flipping contest and (1) in my first flip I got heads, (2) in my second flip I got heads, ..., (n) in my n-th flip I got heads, ..., (99) in my 99-th flip I got heads and then I'm asked what's the probability that I get to 100 heads in a row there are different answers that I could give. I could assume that the probability of every single flip is 50/50 and then my answer will by 50%. Or I could give an answer higher than 50% if I'm able to control the outcome - or if by now I suspect that the coin has two heads. Or I could give an answer lower than 50% if I suspect the game is rigged and they are going to make me lose now. Whetever my assumptions about the upcoming flip, my answer will be conditional on (1),(2),...,(99) having happened already. There is no point in thinking about the "whole game" at this point in time. I already got heads 99 times - just like in the Monty Hall problem I already picked a door and he already picked another door with a goat.