Great Puzzle
- Thread starter 261252
- Start date
Here is a very simple explanation:
If you do not switch your choice, the only way you win the car, is if you picked the correct door the first time, when your odds were 1 out of 3.
But, the odds of picking the wrong door on your first try were 2 out of 3.
By switching your choice, nothing has changed. You're simply gambling that you did not pick the right door on your first try. The odds remain the same, 2 out of 3.
If you don't get it, I recommend that you stay away from casinos.
If you do not switch your choice, the only way you win the car, is if you picked the correct door the first time, when your odds were 1 out of 3.
But, the odds of picking the wrong door on your first try were 2 out of 3.
By switching your choice, nothing has changed. You're simply gambling that you did not pick the right door on your first try. The odds remain the same, 2 out of 3.
If you don't get it, I recommend that you stay away from casinos.
Again DistantVoyeur you are missing the key to the argument. What you are thinking is true only if Monty (love that name) did not know which door held the car and opened all doors randomly. If by some miracle he opened all doors randomly and it came down to 2 doors, one of which was your original selection, then your thinking would be correct.DistantVoyeur said:
However, Monty does know and it is his behaviour based on his knowledge that adds new information that will increase your odds if you understand this info, which you do not.
This is called the variable change effect. As new info is added so do your odds.
Let us go back to three doors. The key is that Monty knows which door has the car.
If the car is behind door one then it does not matter which door Monty opens first as they are both empty and no new information has been added, so your odds have not increased.
HOWEVER
If door one is empty then Monty has to open the remaining door that is also empty thus revealing with certainty which door has the car ( door two.) This is the new information that is added although it is not a certainty this information will be added. If it was a certainty then your odds are 100%however this new info only has a 50% chance of being added.
But the chance that it may be added increases your odds to 66% only if you change doors.
Told you this was a good one.
The 3rd door is no longer a factor. Why can people not see that? It has been eliminated as a variable and you are down to exclusively 2 doors. When the problem started you had a 33.3% chance, but you changed the entire scenario by eliminating a choice and creating a new scenario. The only way the odds could be cumulative in nature is if the outcome of the previous scenario had a direct influence on the new condition.
If you started with only 2 doors, would you ever assume that switching gave you a 66.6% chance of being correct? At that moment in time, you only have two doors and one choice, regardless of whether you started with 3, 4, 5 or more doors.
If you started with only 2 doors, would you ever assume that switching gave you a 66.6% chance of being correct? At that moment in time, you only have two doors and one choice, regardless of whether you started with 3, 4, 5 or more doors.
no you're not getting it mr. 261252... I'm agreeing with you!! Read my post again. I said the odds of winning if you switch are 2 out of 3. In other words 66%
This takes in the presumption that Monty is always going to open a door that has no car. That is where the assumption of past behaviour is expected to influence the odds. If Monty is obligated to ask you if you want to switch, regardless of whether the car is behind the door or not, then that is a change in behaviour and the pattern is broken. A new scenario is created and the odds are changed. You are now down to 2 choices, each with an equal probability of giving you a car.261252 said:
DistantVoyeur said:
I REPEAT. WHILE DOOR 3 IS ELIMINATED THE INFORMATION THAT DOOR THREE GIVES HAS NOT. Indeed, the information that door three gives has been added. You now have more information then if ,say, someone came in after the fact door three was eliminated and was told to chose only door 1 or 2 and did not know MONTY HAD INTENTIONALLY ELIMINATED DOOR 3. THIS IS THE KEY. If you use this info correctly you icrease your odds. Go back a couple of threadlets to see my deeper explanation.
DistantVoyeur said:
I REPEAT. WHILE DOOR 3 IS ELIMINATED THE INFORMATION THAT DOOR THREE GIVES HAS NOT. Indeed, the information that door three gives has been added. You now have more information then if ,say, someone came in after the fact door three was eliminated and was told to chose only door 1 or 2 and did not know MONTY HAD INTENTIONALLY ELIMINATED DOOR 3. THIS IS THE KEY. If you use this info correctly you increase your odds. Go back a couple of threadlets to see my deeper explanation.
Sorry you're still wrong Distantvoyeur ... what you need to do is perform the experiment on your own about 30 times. You will discover that when you switch your choice, statistically, you will win roughly 2 out of 3 times. When you don't switch your choice, you will win roughly 1 out of 3 times. The more times you perform the experiment, the closer you will come to matching the odds precisely.
In the meantime, stay away from casinos
In the meantime, stay away from casinos
Guys, guys. This is a very counter-intuitive problem that has been solved. It turns out that it is better to choose the other door, no matter how crazy that sounds.
This is the most simple, elegant, and amusing explanation you'll ever find:
http://www.youtube.com/watch?v=mhlc7peGlGg&feature=related
This is the most simple, elegant, and amusing explanation you'll ever find:
http://www.youtube.com/watch?v=mhlc7peGlGg&feature=related
We're going to have to agree to disagree. I've read all the arguments, looked at all the links and still see it as flawed. Not going to argue any more.
Edit: Looked at stinky's link and see the logic flaw. They say that after the first goat is revealed the odds are still 66% that you picked a goat. Bullshit. At that point there is one goat, one car (2 choices). The odds are now 50%.
If you can't see that flaw, we will never find a common ground. Still not going to argue any more though.
Edit: Looked at stinky's link and see the logic flaw. They say that after the first goat is revealed the odds are still 66% that you picked a goat. Bullshit. At that point there is one goat, one car (2 choices). The odds are now 50%.
If you can't see that flaw, we will never find a common ground. Still not going to argue any more though.
Just do the experiment ... problem solved ... unless you don't want to know.DistantVoyeur said:
thanks buddy ... I understand your frustration ... with some people you just can't win, no matter what the odds261252 said:
First let me state that I find your reasoning is intelligent IMHO. So let us not call each other stupid because neither of us are.DistantVoyeur said:
One more time and that is it. Two doors have goats. Monty knows which doors have goats. So by Monty choosing a door that he knew had the goat DOES NOT INCREASE YOUR FIRST CHOICE TO 50%. It stays at 1 in 3.
Actually, I have found this rather stimulating.
261252 said:
Actually, it increases to 66%. Click on the youtube link that I posted, and if you still don't think you're wrong, then something is wrong with you.
Not IMHO. It increases to 66% if you use this new info and reselect door 2. If you keep door one the odds are still 1 in 3 not 50% as Vouyeur would have it.stinkynuts said:Actually, it increases to 66%. Click on the youtube link that I posted, and if you still don't think you're wrong, then something is wrong with you.
One more attempt at logic.
When you have 3 choices then you odds can be 1 in 3. By eliminating one choice you no longer have 3 choices. You have your choice and the only other alternative that is now available. You either have the correct one, or it is behind the other door. The only way you can use the three choices at that point it to assume that Monty is going to always pick a goat door, which he can no longer do or your chance of getting a car will be 100%.
Your odds have changed because your number of alternatives has changed. You can no longer use the percentages for that scenario because that scenario is no longer in existence.
There are not 3 choices, Monty will not always pick a goat door or prompt you towards a specific door even. He is trying to get you to switch doors regardless of whether he knows it has a car or not. His intention is solely to get you to change your mind.
I wanted to stop before it got heated, but glad to see you are keeping perspective as am I.
When you have 3 choices then you odds can be 1 in 3. By eliminating one choice you no longer have 3 choices. You have your choice and the only other alternative that is now available. You either have the correct one, or it is behind the other door. The only way you can use the three choices at that point it to assume that Monty is going to always pick a goat door, which he can no longer do or your chance of getting a car will be 100%.
Your odds have changed because your number of alternatives has changed. You can no longer use the percentages for that scenario because that scenario is no longer in existence.
There are not 3 choices, Monty will not always pick a goat door or prompt you towards a specific door even. He is trying to get you to switch doors regardless of whether he knows it has a car or not. His intention is solely to get you to change your mind.
I wanted to stop before it got heated, but glad to see you are keeping perspective as am I.
