Sure you can have another opionion and I would be happy to trade OTC with you if that was possible (well I am actually not sure what kind of credit risk you pose)... To answer your question. Yes, if you know the cup you remove is indeed not containing the coin then, yes, I would always initially bet on A you always take away the empty one and I would always switch and my odds of winning would double. You cannot always take away cup B because it sometimes contains the coin. The point is you have to take away one of the 2 not chosen cups that does NOT contain the coin. But in general I dont care which cup I initially pick, if you want it to be A be it A.
Good explanation to show why switch is needed for those who can not understand with 3 cups example, almost typed it myself before seeing this post.
The story tells you that the cup the dealer turns over does not have the coin underneath it. Whether or not the dealer actually knew in advance that there was no coin underneath it makes no difference to the probabilities involved. So I would say your statement of "the knowledge of where the coin is by the dealer is essenital to yield the same result" is incorrect. I mean what if the dealer is just very lucky and turns over a cup without a coin. The intent behind the dealer's actions does not change the probability of what happens next.
Thats not what I meant. Of course the intent does not make any difference. Fact is the cup taken away must not contain the coin. How I described it was that the dealer knows where there is a coin and where not, otherwise how can he take away a cup that does not contain a coin for certain if he does not know where the coin is. Hope this clarifies...
Wow, stunning logic. So according to you, after removing one cup that does not contain the coin, if you stick with your original guess you have a 1/3 chance of being right but if you switch the other remaining cup you have a 1/2 (50/50) chance of being right? Lets see, 1/3+1/2 != 1 ....looks like someone needs remedial math help since the sum of the two remaining choices winning probability must equal 100%. Yes this is the perfect example for people who dont intuitively get the 3 cup example. You did neglect to mention the important fact that the 998 cups that the dealer removes are guaranteed to not contain the coin - otherwise the act of removing the 998 cups is pointless. That is the reason that the odds of the remaining cup having the coin is so strong and why switching from your original choice is the correct answer.
The has been an interesting thread. We've established that certain individuals (1) Have no understanding of conditional probabilities (2) Cannot distinguish between probabilities and expectations. (3) No idea what statistics is. (4) No idea what trading is. (5) No concept of analytical skills, nevermind possessing them. Puts their others posts in a certain light, no?
guys, I think most of you misundersood me.. I probably didn't explain myself well. IluvVol, you're pretty rude, this is why I don't post much here lot of people like you here. And why would I bother making that story up? anyways, The answer to the cup question is of course that you should switch - I mathematically gave a clear answer why in my first post. anyone with basic understanding of probability understands why. What I was arguing on this is that this does not necessarily hold true IN THE MARKET. Let me give you an example: consider 3 stocks: A, B, C and u want to go long on one. now consider you buy A on day 1, and assume on day 2 price of A and B rise and C falls. would you switch to B? Presenting the cup probability argument as a approach to trading strategy is not perfectly practical. In fact most traders with experience may even double UP on A rather than switching. hope that makes sense..
Actually, that's not what you said, I suggest you re-read what you actually said. The interview question you gave in your first post has nothing to do with the markets or stocks. You are given an hypothetical problem and asked if you want to stay with original your choice. Your answer of "I immediately said yes. anyone with my mindframe would also stick to their original choice" is incorrect and nonsensical. There was nothing in the example about the markets, stocks or anything else. Answering the question incorrectly because you seem to think that you are actually answering a question to a different hypothetical situation (stocks) makes zero sense - apparently you think it makes you clever. Next time I suggest that you just answer the question you are given, not the one that you believe is being asked. And lastly, again, this problem has nothing to do with statistics (its probabilities) and your calculations above are incorrect. The original odds of making the right choice was 1/3. After one cup no containing the coin was removed, switching your choice improves your odds to 2/3. Now explain again where 0.16 comes from?