3 ms·

The presentation of the problem included the phrase "the host, who knows what's behind the doors, opens another door", so I think in that case the interpretatio

The presentation of the problem included the phrase "the host, who knows what's behind the doors, opens another door", so I think in that case the interpretation that Monty deliberately reveals a goat is more appropriate (in addition, obviously, to being what was intended), although I agree there is wiggle room enough to admit both possibilities and clarity about which case you are discussing is important as it changes the answer.

jVinc 5y ago
> as it changes the answer. It doesn't. If the host randomly reveals a car, then you have 0% chance to win. If he doesn't you have 66% chance to win by switching.
- dllthomas 5y ago
  I once thought that had to be the case. I wrote the simulation to demonstrate that I was correct. I learned that I wasn't. I encourage you to do likewise. I think I now have an understanding of why the right answer is the right answer, but I thought I had that before; I am more confident in the answer than my reasoning.
  - deleted 5y ago
    [deleted]
  - jVinc 5y ago
    I owe you an apology, you're correct, I was wrong. I can't pinpoint where my reasoning failed me exactly, but my confidence certainly was misplaced, and that's from someone who did do the simulation originally to understand the outcomes, but not to understand the distinction between the host deliberately or randomly revealing the door. I'm sorry, but thank you for you persistence in correcting me. It was a fruitful learning experience to dig into this problem again.
jml7c5 5y ago
It does, but it doesn't emphasize it enough to allay confusion, particularly for those unfamiliar with the "gotcha" in the problem. It's easy to overlook in that description unless you know that it is the important clue to understanding. Kind of like the classic riddle "John's mother has four children. They are named March, April, and May. What's the last child's name?" which uses underemphasis for almost comedic effect.

jVinc 5y ago

> as it changes the answer. It doesn't. If the host randomly reveals a car, then you have 0% chance to win. If he doesn't you have 66% chance to win by switching.

dllthomas 5y ago
I once thought that had to be the case. I wrote the simulation to demonstrate that I was correct. I learned that I wasn't. I encourage you to do likewise. I think I now have an understanding of why the right answer is the right answer, but I thought I had that before; I am more confident in the answer than my reasoning.
- deleted 5y ago
  [deleted]
- jVinc 5y ago
  I owe you an apology, you're correct, I was wrong. I can't pinpoint where my reasoning failed me exactly, but my confidence certainly was misplaced, and that's from someone who did do the simulation originally to understand the outcomes, but not to understand the distinction between the host deliberately or randomly revealing the door. I'm sorry, but thank you for you persistence in correcting me. It was a fruitful learning experience to dig into this problem again.

jml7c5 5y ago

It does, but it doesn't emphasize it enough to allay confusion, particularly for those unfamiliar with the "gotcha" in the problem. It's easy to overlook in that description unless you know that it is the important clue to understanding. Kind of like the classic riddle "John's mother has four children. They are named March, April, and May. What's the last child's name?" which uses underemphasis for almost comedic effect.