3 ms·

> The thing that is often de-emphasised in the presentation of the problem, in order to make it seem more mysteriously paradoxical, is that the presenter knows

by Metus 4y ago

> The thing that is often de-emphasised in the presentation of the problem, in order to make it seem more mysteriously paradoxical, is that the presenter knows where the car is and this knowledge is always used perfectly. If the question always ended with "remember: Monty knows where the car is and will use this information", it would be more obvious. The associated line of reasoning resolved the paradox for me. If I stick with my original choice, it is as if I ignored the new information. If I switch the choice, I react to the new information. The extreme of this is to pick among countably infinite doors, having the presenter open countably infinite doors and leaving just yours and another closed. Who could reasonable suggest that the chance is still 50/50, assuming you don't flip a coin and base your choice on that?

Jensson 4y ago
> If I switch the choice, I react to the new information This assumes that him opening a door is new information. It isn't unless you make an assumption about the game masters intentions. If the host doesn't want you to win then you will lose 100% of the time if you switch, if the host wants you to win then you could win 100% of the time by switching etc. But people think that these assumptions are "obvious" so of course you must make them, but that makes the riddle bad. If the riddle doesn't say that the host always opens an empty door after you pick a door, then the typical solution isn't correct. People does the typical "X happened once" and assumes it means "X always happens", that is a typical naive assumption but no, just because it happened once doesn't mean it always happens, you can't make that assumption here unless stated in the riddle.
- basch 4y ago
  >if the host wants you to win then you could win 100% of the time by switching etc. 66% of the time. 33% of the time you picked right first time and lost it by switching. The host never conveys "dont switch."

by Metus 4y ago

Jensson 4y ago

> If I switch the choice, I react to the new information This assumes that him opening a door is new information. It isn't unless you make an assumption about the game masters intentions. If the host doesn't want you to win then you will lose 100% of the time if you switch, if the host wants you to win then you could win 100% of the time by switching etc. But people think that these assumptions are "obvious" so of course you must make them, but that makes the riddle bad. If the riddle doesn't say that the host always opens an empty door after you pick a door, then the typical solution isn't correct. People does the typical "X happened once" and assumes it means "X always happens", that is a typical naive assumption but no, just because it happened once doesn't mean it always happens, you can't make that assumption here unless stated in the riddle.

basch 4y ago
>if the host wants you to win then you could win 100% of the time by switching etc. 66% of the time. 33% of the time you picked right first time and lost it by switching. The host never conveys "dont switch."