So to answer our original question: choosing the proper subset matters because Monty reveals a goat from the subset such that the subset retains its probability of having the car. To be more precise, picking the subset alone isn’t very meaningful, but Monty’s reveal gives that subset meaning by introducing asymmetry. If we don’t consider this asymmetry when making decisions, then we’re discarding important knowledge and weighing probabilities based on incomplete information, leading to suboptimal choices.
and the host, who knows what's behind the doors, opens another door
acemuzzy wrote:The key point is, if you're first guess was a goat (which is more likely than not), then the host has no choice but to reveal the other goat, and hence switching gives you the car. So in the likely case of being wrong initially, your guaranteed being right after "round 2". In the less likely case you were right to start with, then yeah you fucked it and are switching to a first. But that's only 1/3 vs 2/3. But yes it's counterintuitive cos what Tiger said. But, as it's normally the case, he's wrong.
acemuzzy wrote:The key point is, if you're first guess was a goat (which is more likely than not), then the host has no choice but to reveal the other goat, and hence switching gives you the car. So in the likely case of being wrong initially, your guaranteed being right after "round 2". In the less likely case you were right to start with, then yeah you fucked it and are switching to a first. But that's only 1/3 vs 2/3. But yes it's counterintuitive cos what Tiger said. But, as it's normally the case, he's wrong.
GurtTractor wrote:That would be a fun experimet actually as the drag from the flow of the water is probably quite a lot more than with wheels on hard surface, so you could figure out how fast a river would have to be to prevent takeoff. Not sure if that flow speed exists on the planet but it may do. If I was proper clever like I would do the maths on it.
SpaceGazelle wrote:Monty Hall is fairly easy. If you don't swap you're not taking advantage of the fact a goat door has been revealed (eliminated) and your odds are what they always were, 1/3.
Alan Kay
Founding member of Xerox PARC; President of Viewpoints Research Institute, Inc
A Big Mind Change At Age 10: Vacuums Don't Suck!
At age 10 in 1950, one of the department stores had a pneumatic tube system for moving receipts and money from counters to the cashier's office. I loved this and tried to figure out how it worked The clerks in the store knew all about it. "Vacuum", they said, "Vacuum sucks the canisters, just like your mom's vacuum cleaner". But how does it work, I asked? "Vacuum", they said, "Vacuum, does it all". This was what adults called "an explanation"!
So I took apart my mom's Hoover vacuum cleaner to find out how it worked. There was an electric motor in there, which I had expected, but the only other thing in there was a fan! How could a fan produce a vacuum, and how could it suck?
We had a room fan and I looked at it more closely. I knew that it worked like the propeller of an airplane, but I'd never thought about how those worked. I picked up a board and moved it. This moved air just fine. So the blades of the propeller and the fan were just boards that the motor kept on moving to push air.
But what about the vacuum? I found that a sheet of paper would stick to the back of the fan. But why? I "knew" that air was supposed to be made up of particles too small to be seen. So it was clear why you got a gust of breeze by moving a board — you were knocking little particles one way and not another. But where did the sucking of the paper on the fan and in the vacuum cleaner come from?
Suddenly it occurred to me that the air particles must be already moving very quickly and bumping into each other. When the board or fan blades moved air particles away from the fan there were less near the fan and the already moving particles would have less to bump into and would thus move towards the fan. They didn't know about the fan, but they appeared to.
The "suck" of the vacuum cleaner was not a suck at all. What was happening is that things went into the vacuum cleaner because they were being "blown in" by the air particles' normal movement, which were not being opposed by the usual pressure of air particles inside the fan!
When my physiologist father came home that evening I exclaimed "Dad, the air particles must be moving at least a hundred miles an hour!". I told him what I'd found out and he looked in his physics book. In there was a formula to compute the speed of various air molecules at various temperatures. It turned out that at room temperature ordinary air molecules were moving much faster than I had guessed: more like 1500 miles an hour! This completely blew my mind!
Then I got worried because even small things were clearly not moving that fast going into the vacuum cleaner (nor in the pneumatic tubes). By putting my hand out the window of the car I could feel that the air was probably going into the vacuum cleaner closer to 50 or 60 miles an hour. Another conversation with my Dad led to two ideas (a) the fan was probably not very efficient at moving particles away, and (b) the particles themselves were going in every direction and bumping into each other (this is why it takes a while for perfume from an open bottle to be smelled across a room.
This experience was a big deal for me because I had thought one way using a metaphor and a story about "sucking", and then I suddenly thought just the opposite because of an experiment and non-story thinking. The world was not as it seemed! Or as most adults thought and claimed! I never trusted "just a story" again.
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