Well put!. Although this has already been mentioned with 100 and 1000 cups, the "intellectual giants" amongst us beg to differ. Now wait for the next village idiot on ET try and tell you how that view is wrong - or you are forgetting about this and that - or decision trees BS, blah blah... Quite frankly, any in-duh-vidual who cannot see this - after so much discussion and many examples - should not be entrusted with using even plastic cutlery. But I firmly believe they should "play" the markets. Someone has to take the other side of the trade. Next!
All right..one last post. If I know that the host knew where the coin was, the probability at that exact point that the coin is under the cup in that game is 99%. I have a 100% probability of making it to the point of being able to even make this choice in this game. The probability that the coin is under my cup is 1%. If I knew that the host was randomly selecting cups and he made it to the end, the original probability of it being under either cup is 1%. That doesn't change. I had a 2% probability of making it to the point of even having a choice in this particular game. So, it's 50/50 at that point. My odds are exactly the same whether I switch or not.
That's exactly what my cab driver told me the other day. Isn't it supposed to be a sign of something when your cab driver says things like that?
a) I dont get your logic about why someone would "hate" you because losing 400mn is not that big of a deal for big blue in the US. I think you are forgetting that many parts of the world have by far reached/outpaced the US' wealthiest. A Mexican is the richest man of the world now, the top 20 richest people contain a number of Russians and Asians. So, you sound as if the rest of the world is still nibbling crackers while Americans savor Caviar. Even Thai dont anymore stutter pronouncing "1 billion". If you suggested another logic then please enlighten me as I then really did not get it. b) The thread (most of it) was not about solving the problem but understanding the solution. c) The person who got this question wrong interviewed for a quant position at an investment bank. Working myself as rates trader at a an IBank I have no clue how he got this interview, judging from his attitude and how he described his conversation with his interviewer. Fact is, he did not do his homework. EVERY quant in the world who applies for a quant position SHOULD KNOW this puzzle and its solution. The point of half the puzzles in interviews is to test whether the interviewee has done his homework or not because the puzzles are very hard/impossible to solve in such short time even by very smart people. It comes down to whether you know the puzzles or not. The other half of the puzzles test conceptual thinking and analytical problem solving skills.
Nope. Hint: This problem is about risk-neutral pricing. It is very related to how you would price an option, using binomial trees.
There is no paradox here. It is an issue of transparency: A number of ex-college mates who are engineers, accountants, sales managers,etc. asked me if I could trade for them since they have no time to monitor their trades and could only invest long term in mutual funds/ETFs/Bank Structured products(which included subprime CDOs). Some proposed a 40%:40% scheme, meaning at the end of a period (3 mths or 1 year), I take 40% of the net profit or compensate 40% of the loss if it is a net loss. A gambler I met, after hearing this, straight away told me it's a fantastic deal. I ask why? "Just tell them you lost everything and you get to keep 60% of whatever they gave you" So did these Billions dollar funds really lose that much? Was is clearly stated that the cup taken aside did not have the coin under it? If not, then it remains that every cup still has the probability of 1/3, so you DO NOT need to switch your decision. But the real question is: if a new person comes along to play the game when there are only 2 cups to choose from, he could be the patsy because the coin could be under the cup taken away. How do you know if there is a coin under any cup in the first place?
Heidegger, I like cab drivers ! Point is, I am just waiting for the next 25-standard-deviation-we-aplogize-for-this to-happen-because-we-thought-to-be-smarter-then-the-rest-of-the-market-letter ! Translation : Sorry for being Quant !
Maybe we should give this thread another "dimension" and discuss about a much more interesting topic, i.e. chaos theory ! In mathematics and physics, chaos theory describes the behavior of certain nonlinear dynamical systems that under specific conditions exhibit dynamics that are sensitive to initial conditions (popularly referred to as the butterfly effect). As a result of this sensitivity, the behavior of chaotic systems appears to be random, because of an exponential growth of perturbations in the initial conditions. This happens even though these systems are deterministic in the sense that their future dynamics are well defined by their initial conditions, and with no random elements involved. This behavior is known as deterministic chaos, or simply chaos. Question : Did we experience a butterfly effect during August ?
So you are telling me that if you played this game once, and the host turned over 98 cups and no coin was underneath and he did not mention whether his actions were based on knowing or luck, that you would not have enough information to switch even though the physical result of his actions is exactly the same?
This is a totally different problem definition. Each definition has a different solution. 1. Host knows --> you have to switch 2. Host doesnât know --> It makes no difference switching (I have explained why a few pages ago) 3. You are uncertain about Host Knowledge --> start with a prior belief and after each turn update posterior belief with the new evidence