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Morgan Stanley Traders Lost $390 Million in One Day in August
- Thread starter ASusilovic
- Start date
Quote from sprstpd:
The story says the host turns up the cup without the coin. It is a given fact. It does not matter whether the host did it by luck or by knowing.
I hope I am not making any logical errors in the following analysis.
Suppose the player chooses door 1
1st case (Host knows the empty doors)
Event A: car behind door 1
Event B: host opens empty door
Event AB : car behind door 1 AND host opening empty door
Event A|B : car behind door 1 conditional that host opened empty door
P(A) = 1/3
P(B) = 1
P(AB) = 1/3
P(A|B) = P(AB)/P(B) = (1/3) / 1 = 1/3
Conclusion: It makes sense to switch
2nd case (Host doesnât know the empty doors)
P(A) = 1/3
P(B) = 2/3
P(AB) = 1/3
P(A|B) = P(AB)/P(B) = (1/3) / (2/3) = 1/2
Conclusion: It makes no difference switching or not
Quote from sprstpd:
The story says the host turns up the cup without the coin. It is a given fact. It does not matter whether the host did it by luck or by knowing.
For the paradox to work, the host MUST know that the cup he/she turns over does not contain the coin. When this condition is met, you are better off switching because the chance that the coin is under your cup is 1/3 while the chance that the coin is under the other cup is 2/3.
In the case where the host does not know where the coin is and randomly turns up a cup that does not contain the coin, there is no benefit to switch because the chance that the coin is under your cup is now 1/2 and the chance that the coin is under the other cup is also 1/2.
Joe.
Ahahah... Morgan Stanley loses $400 MILLION DOLLARS in ONE day and what is the big hubbub about?
Lets make a deal (door switch) probability question.
This is why the US is great and the rest of the world hates us.
By the way, this is not an easy problem.
By the way, when this question first came out many PhDs couldn't figure this one out.
The person that famously solved the problem had the world's highest known IQ at that time.
It was and still is one of the harder puzzles to conceptualize the answer.
It is however easy to copy the solution from Google. And that is what 99% of the thread is.
So to the person that got this question wrong, don't feel so bad. It's a difficult problem.
Also, good chance the person asking you couldn't get it without studying the Teacher's Edition first.
Lets make a deal (door switch) probability question.
This is why the US is great and the rest of the world hates us.
By the way, this is not an easy problem.
By the way, when this question first came out many PhDs couldn't figure this one out.
The person that famously solved the problem had the world's highest known IQ at that time.
It was and still is one of the harder puzzles to conceptualize the answer.
It is however easy to copy the solution from Google. And that is what 99% of the thread is.
So to the person that got this question wrong, don't feel so bad. It's a difficult problem.
Also, good chance the person asking you couldn't get it without studying the Teacher's Edition first.
Quote from u21c3f6:
For the paradox to work, the host MUST know that the cup he/she turns over does not contain the coin. When this condition is met, you are better off switching because the chance that the coin is under your cup is 1/3 while the chance that the coin is under the other cup is 2/3.
In the case where the host does not know where the coin is and randomly turns up a cup that does not contain the coin, there is no benefit to switch because the chance that the coin is under your cup is now 1/2 and the chance that the coin is under the other cup is also 1/2.
Joe.
You've got to be kidding me, right? The coin knows the intent of the host? If there were 100 cups and the host randomly flipped over 98 of them and there was no coin underneath them (the host got very very lucky), you are telling me you wouldn't switch?
The crux of the problem is related to possibilities of what the host will do.
If you know that the host will not turn over the winning cup, then you would switch and this is why:
If the host doesn't know where the coin is, there is a 1% chance that it is under any of the cups. If the host turns over cup after cup and finally 2 of them are left, the same original 1% probality apply to both cups that is was originally under the 2 remaining cups.
On the other hand, if the host does know where the coin is and leaves 1 cup overturned, there is a 99% probability that the cup left has the coin.
Here's why, in the case where the host doesn't know where the coin is, if you were to play the game 100 times, let's say you have perfect execution of the probability. In this case, the host overturns the coin 98 times before the end of the game and 2 times he doesn't. The 2 times he doesn't, you get to play the game. (again, I'm considering ideal situations where all possibilities are executed in order). So in the 2 games where it isn't turned over, once it's under your cup and once it's under the host's cup, so your chances of winning whether you switched or not were 1 out of 100
In the case where the host does know, all 100 times you will be left with a cup to choose from. In this game, if you played all 100 times, you would win 99 times out of 100 by switching.
This is why the host knowing where the coin is located is important, because otherwise, the possibility of the host overturning the cup with the coin disrupts the advantage that you'll get by knowing that the host knows.
yes it is confusing, I even didn't consider this in my first post until I thought about it.
If you know that the host will not turn over the winning cup, then you would switch and this is why:
If the host doesn't know where the coin is, there is a 1% chance that it is under any of the cups. If the host turns over cup after cup and finally 2 of them are left, the same original 1% probality apply to both cups that is was originally under the 2 remaining cups.
On the other hand, if the host does know where the coin is and leaves 1 cup overturned, there is a 99% probability that the cup left has the coin.
Here's why, in the case where the host doesn't know where the coin is, if you were to play the game 100 times, let's say you have perfect execution of the probability. In this case, the host overturns the coin 98 times before the end of the game and 2 times he doesn't. The 2 times he doesn't, you get to play the game. (again, I'm considering ideal situations where all possibilities are executed in order). So in the 2 games where it isn't turned over, once it's under your cup and once it's under the host's cup, so your chances of winning whether you switched or not were 1 out of 100
In the case where the host does know, all 100 times you will be left with a cup to choose from. In this game, if you played all 100 times, you would win 99 times out of 100 by switching.
This is why the host knowing where the coin is located is important, because otherwise, the possibility of the host overturning the cup with the coin disrupts the advantage that you'll get by knowing that the host knows.
yes it is confusing, I even didn't consider this in my first post until I thought about it.
Quote from sprstpd:
You've got to be kidding me, right? The coin knows the intent of the host? If there were 100 cups and the host randomly flipped over 98 of them and there was no coin underneath them (the host got very very lucky), you are telling me you wouldn't switch?
Quote from tradestrong:
This is why the host knowing where the coin is located is important, because otherwise, the possibility of the host overturning the cup with the coin disrupts the advantage that you'll get by knowing that the host knows.
yes it is confusing, I even didn't consider this in my first post until I thought about it.
There is a story. In the story, you play the game only once. The story mentions nothing of whether the host randomly turns over the 98 cups or actually knows that those 98 cups do not have anything under them. You just know that all 98 cups turned over do not have the coin. Do you switch? Yes, of course you do.
You are telling me that in this one game, that if I told you that the host was randomly guessing which cup to turn over or if I told you the host knew where the coin was would make a difference in your final decision?
Quote from dividend:
It was and still is one of the harder puzzles to conceptualize the answer.
Well said. It's hard to remember when you didn't know something because once you walk across the line and get it you can't imagine how anyone can still not get it.
One way to conceptualise it rather than getting lost in conditional probability maths is to consider this:
The host removes all the incorrect doors except one, so you are left with two doors: your door and another. When there are only 3 doors it is intuitively difficult to see what has just happened with the introduction of this new information.
But if there were 1 million doors and we apply the same logic the host removes all the incorrect doors from consideration except one, leaving two doors including the door you originally chose. Now it is patently obvious that your original choice is vanishingly unlikely to be the winning door, so you switch without hesitation. (Of course there is still the possibility that your first choice was correct all along.)
The key to all this is that the host will leave the correct door available in the second round - this is crucial to understanding the logic. This is the revised information.
Quote from PointOne:
But if there were 1 million doors and we apply the same logic the host removes all the incorrect doors from consideration except one, leaving two doors including the door you originally chose. Now it is patently obvious that your original choice is vanishingly unlikely to be the winning door, so you switch without hesitation. (Of course there is still the possibility that your first choice was correct all along.)
That's about as clearly as it can be put. If you don't get it after reading this, you likely won't get it, ever.