Posted: 10/15/2007 6:56:38 PM EDT
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Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice? |
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montyhallproblem.com/ |
Please tell me you're not an engineer designing airplanes. If you are, at least tell me which one you work for so I can avoid it  At the start of the game the odds of you correctly picking the right door were 33% (house had 66% chance of being right since they get two doors). So now the host has effectively eliminated one of the doors from the 66% pool. Which pile would you rather choose from? The pile that formerly had 2 choices or your single choice? Think of it with a pile of 100 boxes where you initially get to pick only one. Then the host eliminates 98 other 'empty' boxes from the pile of 99. Which pile would you rather pick from now? What airline was that again..... |
It doesn't matter, if he ALWAYS reveals what is behind one of the three doorsand gives you the chance to change, then your odds ALWAYS increase from 33% to 50% EVERYTIME. |
+1 As others have pointed out, you SHOULD switch. This is a well-known game theory exercise, and the math is solid. Switching does technically increase your odds. PLEASE let's not turn this into another .9bar thread. Why do people think that math has to be intuitive? The human brain is a squishy biological bag of watery cells - things don't have to "feel right" to be right.  |
I can only assume a 5th grader wrote that. I'm no genius, but I've had roughly 4 years of college math (from Calculus, to differential equations, to linear algebra, to random processes and noise and other probability/statistics classes). The above has no basis in fact. If you choose a door, you do have a 1 in 3 chance of getting it righ. Monty showing you that one of the others is bad doesn't increase or decrease the chances that your selected door is good or bad other than that it is now 1 in 2. Either could have the car - same odds. You have a bag with three balls - one red, one green, and one blue. What is the probability of drawing a red ball? 1 in 3. If you draw a green ball first, what is the probability of drawing a red ball then? 1 in 2. Very basic probability/statistics material. I could register a website with flawed math examples on it too, if I wanted to. Not everything on the Internet is right. I read that entire site, and I think he's really wrong. |
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Did you read this part?
Is that example not valid as the same type of problem, or does the Monty guy knowing where the car is screw up the odds somehow that is not apparent? |
Is the goat on a treadmill? |
Well now that you've demonstrated your impressive mathematics and educational credentials, I also need to know which prestigious university awarded this degree  Because the question become obvious.....are YOU smarter than a 5th grader??? I'm yanking your chain a little here but you're dead wrong on this. I hope you're just kidding because it's very simple as I explained above. In the absence of any other information you would be correct that the odds are even of picking the correct answer. But you DO have additional information that improves your odds. Take 1,000,000 boxes. One of them has a peanut in it. You get to pick one and your buddy picks the other 999,999. Who has the better odds of getting the peanut? Your buddy (who knows which box contains the peanut) opens 999,998 boxes which are shown to be empty. You are left with two boxes sitting side by side. Would you change your choice now? If you wouldn't then I'd like to invite you over to my place for some games of chance!
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While we are all impressed with your credentials , the fact remains that this is a well-known and well-supported game theoretic problem. The fact that you do not understand it doesn't make it wrong or stupid - it merely demonstrates that you didn't take any game theory classes.If you want to brag about credentials, I once briefly spoke to Roger Myerson about this very problem. |
Sweet. I wasn't trying to drop any credentials like I was a genius. I even said I wasn't one.  I'm into supercomputing, not gaming, so I have never seen this problem before. I did cheat and do a Google search on it before posting, though, and I stayed at a Holiday Inn Express last night.  I'd like to apologize right off for posting a wrong answer. I knew it was wrong, but I still posted it because it felt right to fight the system and give similar examples to see if I could get a following. I'm afraid I did the same thing at another gun board last year about the airplane on a conveyor belt, but I had great success there.  BTW, I hope you like the Bushy M4gery you won in the raffle last year. Haven't seen you since then (I got a job and got too busy to post). |
Phew - I'm relieved to see that post, because after I posted my (somewhat rude  ) response, I thought to myself, "wait a minute - I know him, and that doesn't sound like him at all" Glad to hear you were just (succesfully) yanking our chains.
I know all about being busy - especially after just finishing and getting the first job at that level! Those are stressful days, and I hope everything is going great for you! My life in the last year has been a rollercoaster, I don't mind telling you! Fortunately, things have settled down nicely now - but it's been a stressful year.The M4 was a very pleasant surprise in the middle of all the stress, and it was put to very good use. In fact, I used it to convert a new member into the ranks of the AR15 fanatics! 
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Actually, I turned down the prof job I was offered because it was at a less-prestigious university, and I would have to move (the pay wasn't going to be super-duper). I took an industry job at a wireless provider's corporate offices as a manager. I have my eyes set on Executive VP over SW development/testing in 5 years or less, and I'm pretty close already. In case that doesn't pan out, I'm keeping my CV out there to the other universities that are still hiring.
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That sure sounds a lot better than the crushing publish-or-perish grind of the research university!  |
Yep, I thought so. My thesis research was all published in peer-reviewed journals piece by piece, so I was happy to cut it off right there and leave the future work to others in my group. See you around - got to go to bed to get at corporate America in the early AM. I will have you know I was very envious of your M4 win, so I built one like the pic they posted during the raffle. It's a DPMS, but it works great anyway. I converted my father-in-law and brother with it and built two more - one for each - afterwards on their dimes using my tools.
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No. If he deliberately selects a door with a goat (rather than selecting either of the two doors at random) your odds are better if you switch. Because there was a 2 in 3 chance of the car having been behind one of the 2 doors you didn't pick the first time...eliminating a non-car door from those two means that one door you have the choice to switch to still has the 2 in 3 chance of having the car. Versus sticking with your original 1 in 3 chance. ETA: If he just selects a door at random your odds would be 50/50 but a third of the time he would reveal the car when he opened a door. |
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This is one of those questions that seems to make people answer before they consider the problem. When originally posted by Marilyn vos Savant (sp?) several prominent mathematicians made absolute fools of themselves. I built an Excel spreadsheet to demonstrate the nuts and bolts of the problem to those more visually oriented. As a side note, Marilyn is one of those very bright people who also possess considerable wisdom. |