It wasn't presented as a paradox, though. Just a problem whose solution runs counter to much intuition.
Inara: I think she looks adorable. Mal: Yeah, but I never said it.
'Shindig'
What Happens in Natter 35 Stays in Natter 35
Off-topic discussion. Wanna talk about corsets, duct tape, or physics? This is the place. Detailed discussion of any current-season TV must be whitefonted.
§ ita § - May 14, 2005 7:42:32 am PDT #4157 of 10001
Well not canonically, no, but this is transformative fiction.
Hil R. - May 14, 2005 7:45:51 am PDT #4158 of 10001
Sometimes I think I might just move up to Vermont, open a bookstore or a vegan restaurant. Adam Schlesinger, z''l
When you pick yours the first time, you've got a 1/3 chance of being right. Him telling you that one of the other two isn't the car gives you no new information about the one you picked to begin with -- you already knew that at least one of those other two wasn't a car. You've still got a 1/3 chance of being right with the one you picked. But that leaves a 2/3 chance of being wrong, and that 2/3 chance is now entirely on the still hidden unpicked one.
(I really can't figure out a good way to explain this entirely. The way I was able to totally convince myself was just to set up all the different possible situations and look at the results.)
§ ita § - May 14, 2005 7:48:07 am PDT #4159 of 10001
Well not canonically, no, but this is transformative fiction.
If you can't explain it to me, Hil, I don't feel so bad about not getting it.
Hil R. - May 14, 2005 7:51:03 am PDT #4160 of 10001
Sometimes I think I might just move up to Vermont, open a bookstore or a vegan restaurant. Adam Schlesinger, z''l
Let's say that the car is in door 1. If you picked door 1, then you'll get it if you stay. If you picked door 2 or door 3, then you'll get the car if you switch. There's a 1/3 chance you picked right on that first try, but a 2/3 chance you picked wrong, so in 1/3 of the cases you'll get the car if you stay, but in 2/3 you'll get it if you switch.
Stephanie - May 14, 2005 7:53:58 am PDT #4161 of 10001
Trust my rage
I'm glad others are confused because I din't get it last night.
§ ita § - May 14, 2005 7:56:04 am PDT #4162 of 10001
Well not canonically, no, but this is transformative fiction.
What's at the core of the problem? Being given the chance to switch to a card that has a 1/2 chance of being the right one? I mean, 1/2 if you started from step 2?
You know, this might be one I just accept, or run the numbers on. My big issue is that I want there to be some calculation that gets you from the odds on the first pass to the new odds, and I just can't see it.
Hil R. - May 14, 2005 8:00:33 am PDT #4163 of 10001
Sometimes I think I might just move up to Vermont, open a bookstore or a vegan restaurant. Adam Schlesinger, z''l
What's at the core of the problem? Being given the chance to switch to a card that has a 1/2 chance of being the right one? I mean, 1/2 if you started from step 2?
I think the core of the problem is that the odds don't change. You've got a 1/3 chance of being right, 2/3 chance of being wrong. Suppose they don't tell you "door 2 is not a car." They just say, "You can stay where you are, or you can switch to doors 2 and 3. If either of those is a car, you get it; if neither of them is, you don't." That's an equivalent problem -- knowing which door of 2 and 3 is the one without a car doesn't change anything.
§ ita § - May 14, 2005 8:03:59 am PDT #4164 of 10001
Well not canonically, no, but this is transformative fiction.
Aha! All the potential lives in the one card. I'd still rather see some multiplication, but I can live with that.
dcp - May 14, 2005 8:15:44 am PDT #4165 of 10001
The more I learn, the more I realize how little I know.
Think of it from Charlie's point of view. You pick one card from three. That leaves Charlie with three possible combinations of two cards:
goat/goat
car/goat
goat/car
Charlie reveals a goat card. The three possibilities for his hidden card are reduced to:
goat
car
car
If you switch with Charlie you go from one chance in three to win, to two chances in three.
Aims - May 14, 2005 8:26:01 am PDT #4166 of 10001
Shit's all sorts of different now.
I also need to start working on the Miracleborns. What, 6 hours in the car with a baby could be fun!
Specially now that we have the Miracleborn Stealth MiniVan.