21 - I am confused

[denver2k]

oracleSlave - Check this out....It would save time and energy

http://www.mste.uiuc.edu/reese/monty/MontyGame5.html

My results are :
Stick --> W 6 L 9 --> Total attempts 15
Change --> W 9 L 6 --> Total attempts 15

TimberWolf. Iv got a confusion.

Before any selection, probability of each door is 1/3. I select Door 1 and host opens Door 2. Now, Door 1 and Door 3 left. How come we can definitely say that only Door 3 will have probability of 2/3. Why cant Door 1 (which i selected first) have 2/3 probability and Door 3 with 1/3.

[TimberWolf]

oracleSlave - Check this out....It would save time and energy

http://www.mste.uiuc.edu/reese/monty/MontyGame5.html

My results are :
Stick --> W 6 L 9 --> Total attempts 15
Change --> W 9 L 6 --> Total attempts 15

TimberWolf. Iv got a confusion.

Before any selection, probability of each door is 1/3. I select Door 1 and host opens Door 2. Now, Door 1 and Door 3 left. How come we can definitely say that only Door 3 will have probability of 2/3. Why cant Door 1 (which i selected first) have 2/3 probability and Door 3 with 1/3.

After door 2 is revealed to be a goat, either door 1 or door 3 must have the car. So they each have a probability of 1/2 of a car (or goat).

[Doggy Styles]

FFS. Just kill the goat and make some mutton curry. FFS.

What are the chances of finding mutton in a dead goat?

[The Lone Gunman]

After door 2 is revealed to be a goat, either door 1 or door 3 must have the car. So they each have a probability of 1/2 of a car (or goat).

Now I am really confused! Is that not the 50 50 case I said it was?

[expat]

After door 2 is revealed to be a goat, either door 1 or door 3 must have the car. So they each have a probability of 1/2 of a car (or goat).

Why so?

That is using probability as a best guess while in the dark, but the guess you are making is not the best guess, because you are failing to use all the information that is now available.

Yes indeed, if you have only 2 choices and you know nothing more about them, then 1/2 is the best probability to assign to each. It is equivalent to saying that each outcome is equally likely, or at any rate you know of no reason why it should be otherwise.

But that is not this case. You do know of a reason why it should be otherwise. That reason is that the door that you first picked will have the car in 1/3 of cases. That is still true. Showing you a door with a goat behind it does nothing to change that: so your best estimate is still that there is 1/3 of a chance that your door has the car.



To see the fallacy, imagine this game: there are 100 doors: 1 car and 99 goats. You have to pick 1 door. Then you are offered the choice of opening your 1 door, or opening all 99 other doors. Will you still maintain that "either door 1 or doors 2-100 must have the car" so each of those 2 choices has 1/2 a chance? I'd take the 99 doors myself.

[TimberWolf]

Now I am really confused! Is that not the 50 50 case I said it was?

Only after one door is eliminated.

[TimberWolf]

Why so?

That is using probability as a best guess while in the dark, but the guess you are making is not the best guess, because you are failing to use all the information that is now available.

Yes indeed, if you have only 2 choices and you know nothing more about them, then 1/2 is the best probability to assign to each. It is equivalent to saying that each outcome is equally likely, or at any rate you know of no reason why it should be otherwise.

But that is not this case. You do know of a reason why it should be otherwise. That reason is that the door that you first picked will have the car in 1/3 of cases. That is still true. Showing you a door with a goat behind it does nothing to change that: so your best estimate is still that there is 1/3 of a chance that your door has the car.



To see the fallacy, imagine this game: there are 100 doors: 1 car and 99 goats. You have to pick 1 door. Then you are offered the choice of opening your 1 door, or opening all 99 other doors. Will you still maintain that "either door 1 or doors 2-100 must have the car" so each of those 2 choices has 1/2 a chance? I'd take the 99 doors myself.

Sorry, I should have said only the remaining door has a 1 in 2 chance of being the car.

[expat]

Sorry, I should have said only the remaining door has a 1 in 2 chance of being the car.

No. That doesn't change anything. Your door has 1 chance in 3, the other choices all together have 2 chances in 3. Open 1 door that doesn't have the car, nothing has changed, it's still 1/3 vs 2/3.

If you were to open 1 door that doesn't have the car, and then re-allocate the car and the remaining goat randomly between the 2 doors that remain, then the chances would be 1/2 vs 1/2. That way you have changed the chances to match the visible possibilities, but if you do not re-allocate the prizes after opening 1 door, you have not changed the chances away from the original 1/3 vs 2/3.

What you are doing is looking at the changed door-count, and implicitly imagining this re-allocation; but it is not happening.

[TimberWolf]

No. That doesn't change anything. Your door has 1 chance in 3, the other choices all together have 2 chances in 3. Open 1 door that doesn't have the car, nothing has changed, it's still 1/3 vs 2/3.

If you were to open 1 door that doesn't have the car, and then re-allocate the car and the remaining goat randomly between the 2 doors that remain, then the chances would be 1/2 vs 1/2. That way you have changed the chances to match the visible possibilities, but if you do not re-allocate the prizes after opening 1 door, you have not changed the chances away from the original 1/3 vs 2/3.

What you are doing is looking at the changed door-count, and implicitly imagining this re-allocation; but it is not happening.

Aaargh, you're right. I once looked at this in horrible detail, which have now forgotten . I think I must have picked up the 1/2 on here somewhere. The important thing being to switch, if the host always picks a goat.

[TykeMerc]

Tune in tomorrow when we do an airplane on a treadmill: will it take off?

No it wouldn't as lift is reliant on the velocity of the air over the aerofoil wings generating a vacuum effect and has nothing to do with ground velocity.

That's why you can get an aircraft to fly in a wind tunnel despite it having a ground speed of zero.