No, not in the above example. In the example above we're strictly talking about the mathematical odds with a choice of switching.

I mentioned several posts above how revealing a non-winner might change the odds, but only if it's known that the there was a motive for revealing and giving the player a chance to switch and what that motive would be.

Once you get into that arena, you're leaving straight math and entering game theory and human psychology. If in the original example the producer knows the right door and reveals one and gives you an option to switch, then you might infer some info from that might increase your odds of making the right choice, but you would need to know the motive. What if the motive was to get you to pick the right door (increasing TV ratings maybe)??

But I thought Grimwerk was arguing it was just basic math that makes switching the better option, and I was arguing that this is not the case. If I misread Grimwerk, then I apologize to him/her profusely. It wouldn't be the first time I misread someone.

But back to game theory and motive, I would still argue it's a poor riddle because we aren't given the producer's motive. If the producer's motive is to get you to choose the wrong door, and he knows the right door, then one could argue if he gives you an opportunity to switch you should always say no because if he already knew you picked the wrong one he wouldn't give you the option to switch to the right one. This is one example of the limitations of assigning precise mathematical odds based on motive.

If you're interested in why this logic is flawed, just take the first group as an example

Car behind A, choose A, switch: lose
Car behind A, choose A, don't switch: win
Car behind A, choose B, switch: win
Car behind A, choose B, don't switch: lose
Car behind A, choose C, switch: win
Car behind A, choose C, don't switch: lose


Car behind A, choose B switch: win - NOT TRUE unless you switch to A. If you switch from B to C, you still lose.
likewise
Car behind A, choose C, switch: win - again, only true if you switch to A. If you switch to B, you still lose.

This is what's resulting in the appearance of it being better to switch. By not designating which door is being switched to, wins are assigned when they could be losses.

Motive doesn't play into this riddle. The producer's purpose (easily could be a robot) is to reveal one of the non-chosen doors that does not contain the prize. Doing this collapses the chance of a prize of the non-chosen doors into the remaining non-chosen doors.

Let's say there are ten doors. Prize is in one door. You pick one door.

1/10 is your door. 10% chance you have the prize.

9/10 is a non-chosen door. 90% chance prize is one of these doors.

A robot (knowing which doors do not contain the prize) opens 8 of the non-chosen doors.

1/10 is your door. 10% chance you have the prize.

1/10 remaining non-chosen doors. 90% chance prize is this door.

8/10 doors revealed containing no prize. 0% chance for prize.

You've still kept your door that you chose at the start. The robot is not allowed to touch it, but the robot was able to reveal the doors that he knew contained nothing of the doors you didn't choose.

If you switch, your chance goes from 10% to 90%.

I'm sorry, but this is incorrect from a math standpoint.

If the robot revealed 8 of the 10 doors and gave you the opportunity to switch, then there are only two doors left, the one you originally chose and the one of the other 9 that the robot didn't reveal.

So, you're left with a 50/50 chance if you switch, and a 50/50 chance if you don't switch.

BTW are sexist riddles allowed?? Well, I guess the riddle itself isn't sexist, but it assumes most readers are.

I'm starting to think you are the only one who understands math OldFatGuy

Edit: you are correct I meant to say

But you made your choice when there were 10 doors. A choice that persisted through the opening of 8 other doors you did not pick.

If you don't trust grimwerk's work, you can try it yourself with some cups and a token of some kind. Get 3 or more cups and put a token under one of them. Pick a random cup, and, of the remaining cups, remove any that doesn't have the token, but leave one. Do this a few times, picking different cups, and chart out how often the token is in the cup you didn't choose initially.

I doubt it. LOL

I'll go with my sexist riddle, not because I'm a sexist, but because I'm always amazed at how many people this stumps that shows how ingrained many of our sexist attitudes are, so deep we're not even aware of it.

A man and his son are driving one day and become involved in a terrible accident. The man was killed and the boy was rushed to the hospital. The nurse grabbed the emergency room Doctor to perform emergency surgery on the boy, but the Doctor refused saying "I can't perform surgery on this boy. It's my son."

How is this possible?

I would say the doctor is his mother

Of course the token will be under a cup you didn't choose most often. In fact, with 10 cups, it should be under one you didn't choose 90% of the time. That's the nature of having only a 10% chance of being right. You have a 90% chance of being wrong.

If you have 3 choices, you have a 1 in 3 chance of being right, and therefore the token will be under one of the other cups 2 out of 3 times. But just because you're chance of being wrong is 2 out of 3, it doesn't mean you're better of switching because you're still going to be left with a 1 in 3 chance of being right and a 2 in 3 chance of being wrong.

And I showed the flaw in grimwerk's work in a post above.

I'll stop responding to this stuff now. I'm just not skilled enough at explaining math to make it understandable.
Yes, yet you'd be surprised by how many hear "nurse" and "doctor" and automatically assign female to the nurse and male to the doctor and are stumped.

When you switch doors there are 2 doors left, at that time your chances are 50/50 no matter what door you go with. If you they had revealed the winning door when there was 10 doors unknown still your chances would have been 10%. With every door being revealed your chances increase of winning, but can never get higher than 50%

Probability isn't always evenly distributed among unknown variables -- see conditional probability. If there are 100 doors, you pick one, and all of the doors except the one you picked and one other door are opened (with the critical knowledge being that none of the doors that are opened will contain the prize), you have a much greater probability of winning if you switch than 50/50.

Edit: Essentially, the probability of the prize being behind the initial door, given 100 doors, is 1/100. The probability of the prize being behind the other door is the same as the probability of the prize being behind any of the remaining 99 doors, because all of the other doors will be opened except the one that it could possibly be behind. Thus in the case of 100 doors, there is a 1/100 probability of it being behind the chosen door and a 99/100 probability of it being behind the other door. The fact that there are two doors left is irrelevant -- there would only be an evenly split 50/50 probability if the prize was equally likely to be behind either door, which it is not. By switching, you "capture" the probability of the prize being behind one of the 99 doors that you did not initially choose. The same effect applies given a smaller number of doors, such as three, although the advantage of switching is less pronounced.

nm, said I was gonna stop.

But I do see where you're coming from here.

^ that is a very good explanation, combined with what Grilledfish said. It very clear that if you choose another door chances are improved. The higher the number of doors, the higher the advantage of switiching is.

Perhaps if the non-winning doors would have only be marked as "non-winning" instead of been open, then it would be more clear.

Correct.
Well yeah, if you want to make the riddle artificially easier, but when you really think about it: you are asked to empty a tub and the first that comes to mind is to smash the tub? Heh, the home improvement guys must really like those people. What do you do after you've done the dishes, tear the whole sink apart? I think the only logical solution is to remove the plug. Sure, tipping the tub over or breaking it to pieces might be faster solutions, but they aren't very sane solutions.

Ok, I agree, this actually makes sense to me.