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JD New user Montreal, Quebec 42 Posts |
Sigh.
Stan, I wasn't trying to explain the difference between the Monty Hall puzzle and Deal Or No Deal. The first two paragraphs of my post simply pointed out that the two are different and therefore the Monty Hall principle does not apply in Deal Or No Deal. Greg Arce had introduced Deal Or No Deal to the thread in the 7th post and I was simply trying to go back on topic, because this thread's original discussion was worth exploring further. Specifically, the balance of my post, let's call it the second part, was designed to address the original rationale for this thread; i.e., finding a simple way to explain the Monty Hall puzzle. If you read through the first three posts in this thread - Greg V, then Nir Dahan, followed by Greg V's response - you'll see what I mean. Thus my third paragraph begins "As far as explaining the solution to the Monty Hall puzzle to people..." Cheers. JD |
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stanalger Special user St. Louis, MO 998 Posts |
JD,
Sigh. I knew that you knew the important distinction. And I have great respect for Greg Arce's intelligence. But when your paragraph that begins "To wit:" leaves out the crucial detail of how the 999,998 cases that are opened are chosen, I understand why Greg (and many others) get confused. Scott Cram's post in this thread is the only one that makes explicit the important way in which the host chooses the door(s)/case(s) to open. As Scott pointed out, Marilyn ("Ask Marilyn") did not state this aspect of the puzzle properly...and we know how much confusion ensued because of her poor statement of the puzzle. Stan |
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Greg Arce Inner circle 6732 Posts |
I'm still not switching.
Greg
One of my favorite quotes: "A critic is a legless man who teaches running."
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stanalger Special user St. Louis, MO 998 Posts |
Greg,
I wouldn't either, if I had your batting average. With psychic powers that strong, you "don't need no stinkin' math!" Good job! |
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JD New user Montreal, Quebec 42 Posts |
...because this thread, at its outset, explicitly assumed one understood the basis of the Monty Hall puzzle and surrounded the issue of how to explain it to people.
I was not discussing its relevance to Deal Or No Deal - and made it clear they are two, distinct topics - nor the controversy that surrounded the introduction of the puzzle. Again, I was moving back to the original discussion, Stan. The original discussion. I was pretty clear. Whatever the hell this has to do with Greg's intelligence is beyond me. Never met the man and don't know anything about him. JD |
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TomasB Inner circle Sweden 1144 Posts |
JD,
All Stan pointed out was: When you use your math free explanation to explain the Monty Hall problem to people and say "I then open all but one of the remaining 999,999 cases, show that they're empty" you really need to say that it didn't happen by accident, but that you very well knew exactly where the winning case was and your intention all along was to open all but the winning case, should it still be available. Otherwise the people you explain it to will immediately think "Hey, that'd be a great outcome of Deal or No Deal." /Tomas |
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JD New user Montreal, Quebec 42 Posts |
Tomas
If you'll note in the approach described in my original post, I still end the explanation with a question. Would you switch under those newly defined circumstances; i.e., two remaining choices out of one million versus two remaining choices out of three? It's kind of important to note that particular context. Given my take on it is intentionally designed to evoke a moment where a "light goes on", it would be self-defeating to feed them an answer. Moreover, I'm quite explicit that I am the one opening the "boxes". To be specific, I employ playing cards in the manner of the three-card monte, as this was the way I was, reading Gardner, first initiated to the puzzle. I'm sticking to playing cards lest anyone confuse me with Howie. JD |
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TomasB Inner circle Sweden 1144 Posts |
"I'm quite explicit that I am the one opening the "boxes"."
I don't see how it matters that they know that you are the one opening the boxes, unless you also explicitly tell them your self imposed rules of which boxes you are opening. That's what's missing from badly worded forms of the puzzle and also in some explanations. /Tomas |
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JD New user Montreal, Quebec 42 Posts |
I'm starting to feel like I'm banging my head against a wall.
This is my last try. Tomas, there are two possibilities in play here. Either: (a) I am a complete idiot. (b) You haven't fully grasped my approach to explaining the puzzle. I will let you decide. When I present the puzzle, I typically don't do it for retards, so I like to see people work it out on their own. It really isn't hard and I've never encountered a problem. I'm sure you're a smart guy. Tell me if the following tells you everything you NEED to know to solve the puzzle without being told absolutely EVERYTHING. I present the puzzle with three cards, in the usual manner, and ask them if they should switch at the end. As you know, they invariably say it doesn't matter, the odds are seemingly even. So, then, I follow up with this: (1) Imagine that instead of THREE face-down cards, there are ONE MILLION face-down cards in a room. (2) ONE of them is a Queen, the REMAINING 999,999 are Aces. Your job is to FIND THE QUEEN. (3) Pick one and don't look at it. What do you think the chances are you picked the QUEEN? (They always answer that the chances are extremely low. Everybody understands this.) (4) Ok. I will now turn over 999,998 cards. You will notice EVERY card I turned over is an ACE. (5) As a result, there are now TWO only two face-down cards remaining: The face-down card you initially picked and the only card I did NOT turn over. And, thus, the question: (6)Your job was to find the QUEEN. Would you like to stick with your original choice or switch with the ONE card I did NOT turn over, keeping in mind there are 999,998 FACE-UP ACES in the room? It never fails. The individual always knows what to do, i.e., switch, despite not being told HOW I turned the cards over. Common sense dictates that there's no way they picked the Queen at the outset and that I intentionally turned everything over except the Queen. Pure common sense for sensible people. Once they see the puzzle in this light, they then are able to intrapolate it to the use of only three cards, versus the one million in the extreme example. No math, just common sense. Most importantly, it is a hell of a lot more intriguing approach to understanding the puzzle than some explanation that just FEEDS you an answer. The difference between reading something in a textbook or listening to an engrossing lecture in a classroom. For a curious magician, the difference between being told how a trick is done versus figuring it out how it's done. JD |
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Greg Arce Inner circle 6732 Posts |
JD, can I add something to what you've just said? In Deal Or No Deal no one knows which case has the big money... even the host or the producers of the show. So what if you did have a million cases and opened up all but your case and the one left on the stage. Now they tell you to switch. Apparently the math tells you to switch, but what if suddenly you were the host and had to answer? You also don't know which case contains the money and you've also seen all the other cases opened. So should you switch too? Which side should switch?
greg
One of my favorite quotes: "A critic is a legless man who teaches running."
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JD New user Montreal, Quebec 42 Posts |
Greg
This is assuming only one case holds the $1 million. Of the 999,998 cases that were opened, did any of them display the $1 million? If your answer is no, then the producers knew which one contained the $1 million and were cheating on your behalf. I would switch in a New York minute. Remember that when you picked your case, your odds of being right were 1-in-1 million. There are now 999,998 cases that have something less than that on display. Would you switch for the one remaining, closed case, knowing how low the chances were when you picked your case at the outset? Best, JD |
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stanalger Special user St. Louis, MO 998 Posts |
Quote:
On 2008-04-27 21:32, JD wrote: JD, You're not saying (a) and (b) are the ONLY possibilities, are you? Stan |
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stanalger Special user St. Louis, MO 998 Posts |
JD,
You're not answering Greg's question. Greg asked you about a situation in which neither the contestant nor the producers knew which case contained the million. How would you answer Greg's question? Why? Stan |
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stanalger Special user St. Louis, MO 998 Posts |
Greg,
Excellent question! |
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Greg Arce Inner circle 6732 Posts |
JD, let me tell you something... I worked on game shows. The producers have no idea of the outcome. They are strictly guided by an outside group that makes sure everything is on the up and up. If you remember the movie that showed the 50s scandal on game shows you'll know what I'm talking about.
No one on the show, the host, backstage crew, etc, are allowed to know the outcome of the game. As I said, I worked on Price Is Right, Wheel of Fortune, Family Feud, etc... they are very strict. There is a panel that comes from an outside company that sits throughout the shows and makes sure no one cheats. If they even think somehow someone could have cheated then that particular game is throw out or replayed. So, my question still stands, the host nor the production company know which case holds which amount. 999, 998 cases have been open... you have your original case and the host has the one left on stage... you turn to the host and say, "do YOU want to switch?" What should he do? greg
One of my favorite quotes: "A critic is a legless man who teaches running."
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JD New user Montreal, Quebec 42 Posts |
I give up.
Stan, you may be a frustrated, confused old retiree with nothing better to do, the important thing is you're there for Greg. Tomas, I know you are earnest, and I think you caught the meaning in my last post. Greg, say "Hi" to Bob Barker for me. Don't worry, Stan's got your back. Whatever you do, make sure you switch to the other case. Forget the circumstances, forget the math, and just trust me. I'll see you in the Bahamas. JD |
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Greg Arce Inner circle 6732 Posts |
JD, I'm not trying to be condescending or snapping at you, but the way I see it the math works in both directions. If when it comes down to two cases and all the others don't have the million then both sides have as much chances of winning by switching or not switching.
I think the problem here is that the idea started with Let's make a Deal. I think in that show and at that time the Zonkers were kind of known by the company. It was just another level. In Deal Or No Deal the outcome is not known by anyone so when it comes down to the last two cases either one can have either thing. I've seen it happen a bunch of times where the contestant had a higher value in his case than the one left on stage. I think the math here supposes that one side knows more of what is in each case or behind each curtain. If neither side knows more than the other then I believe the last outcome is just a fifty/fifty bet. So my whole thinking was just that at the moment when the two last cases were left neither side had more info than the other side. If suddenly you stood in Howie's place and he stood in your place you both would have the same chance of having the higher case. And remember, in Deal or No Deal, it not necessary to have a million. You could end up with one case having a hundred thousand and another has ten bucks, but at that moment it's still fifty-fifty as to which one has it. It would be as if they just presented two cases and said one has nothing and one has money... pick one. Greg
One of my favorite quotes: "A critic is a legless man who teaches running."
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stanalger Special user St. Louis, MO 998 Posts |
Quote:
On 2008-04-28 00:12, JD wrote: Yes, until you know for sure...I might be a frustrated, confused old retiree with nothing better to do. That's definitely a possibility! Just like it's definitely a possibility that the contestant correctly picked the million dollar suitcase. Since you won't answer Greg's question, I will. I thought it was a very clever question that gets to the heart of the matter. Switching will not increase your chance of going home with the million. If the host/producers don't know where the million is, it doesn't matter if the contestant picks the 999,998 cases that are opened and eliminated...or if the host/producers choose the 999,998 cases that are opened and eliminated. (One of your previous posts suggests that you believe that it makes a difference who chooses which cases are opened. If neither party knows where the million is, IT DOESN'T MATTER who chooses the 999,998 cases that are opened and eliminated.) Greg's question again: You (the contestant) have eliminated 999,998 cases. None contained the million. That means the million is in either (a) your originally chosen case or (b) the only unopened case remaining on the stage (In real life, there may be more possibilities. But in the context of Greg's question, he made it clear that these are the only possibilities.) To decide whether or not to switch, you should determine the probability of each outcome occurring. If it's more likely that you're in situation (a), you shouldn't switch. If it's more likely that you're in situation (b), you should switch. The probability of outcome (a) is .000001 (You will choose the million dollar case 1 out of a million times. But if you choose the million dollar case, the probability of opening 999,998 cases and not coming across the cool million is 1. You can't come across the million when opening 999,998 because the million isn't in any of the cases on the stage. .000001 times 1 is .000001 ) What is the probability of outcome (b)? Well, the probability of you picking a case that DOESN'T contain the million is .999999 = 999,999/1,000,000, right? And if your case doesn't contain the million, the probability that the next 999,998 cases that are chosen to be opened DON'T contain the million is 1/999,999. (Choosing the 999,998 to be opened is essentially the same as choosing the 1 that is not to be opened.) So probability of outcome (b) is 999,999/1,000,000 times 1/999,999 which equals 1/1,000,000 = .000001. Since the (a priori) probabilities of ending up in situations (a) and (b) are the same, there is no advantage to switching your case for the one case still remaining on the stage. You're just as likely to be in situation (a) as you are to be in situation (b). Instead of answering Greg's question, you answered some other question... regarding a situation different than the one Greg posed. Gotta go now. I have to get to school early today because we're going on a field trip to visit the firemen at the fire department. Mrs. Lois promised to bring us milk and cookies. I hope she's my teacher again next year. She's real pretty...and makes kick-ass cookies! Stan |
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Top Hat Inner circle We peed on you! 1077 Posts |
JD - I see the point you're making, but you seem to be using it to show something that in fact does not follow. Let me explain.
If I have understood you correctly, you mean as follows: With 1 million boxes (only one of which contains the prize), my choice of box is unlikely to be correct. When the game-organiser then opens 999,998 other boxes to show them emtpy, it is an almost certainty that he KNEW which contained the prize (otherwise it is overwhelmingly likely that one of those 999,998 boxes would have contained the prize). Therefore, it is overwhelmingly likely that the remaining box contains the prize, so you should switch. I agree with all that. However (unless I have misunderstood you) you imply that that argument can be "extrapolated" down to the case of just three boxes. But it cannot. If there are three boxes, and I pick one, there are only two left. If the game-organiser then opens one to show it is empty, then my decision to switch or not becomes absolutely dependent upon whether or not I am told that the game-organiser KNEW FOR SURE that that box he was about to open was empty. If he does not know for sure, then he may have just got lucky in attempting to open an empty box and in fact doing so. In which case, you are no wiser as to whether or not your box is empty or full. This is the part of the Monty Hall problem that is hard to understand. But the game-organiser's absolute knowledge of where the prize is makes all the difference. Look at it this way: I pick a box. The chances that it is contains the prize are 1 in 3. The chances that the prize is in one of the remaining two boxes are 2 in 3. If someone else (e.g. the game-organiser) now picks AT RANDOM one of those two boxes, the chances of their box having the prize is 1 in 3. Which means that the box left on the table has a chance of 1 in 3 of containing the prize (which is no more than the chance of your own box containing the prize). So there is no advantage in switching to the box left on the table. However, if the game-organiser KNOWS which of the remaining two boxes is empty, and opens it, then you know FOR SURE that the chances of the remaining box containing the prize is 2 in 3. So you should switch. You may ask, why does the game-organiser's knowledge make any difference, since in both cases he opened an empty box? The answer is that in the second case he is GUARANTEED to open an empty box, whereas in the first case he is not. The puzzle is stated to emphasise that the box that the game-organiser opens is guaranteed to be empty. If the puzzle does not make that clear (as Tomas has said) then the puzzle is not the Monty Hall problem. Ooooh, Stan, I think you just beat me to it (although I have not yet read your post!)
TH
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Top Hat Inner circle We peed on you! 1077 Posts |
Quote:
On 2008-04-28 06:53, Top Hat wrote: Oops... I don't mean that I agree you should switch in that case - what I mean is, I understand where JD is coming from. When JD says "the organiser therefore must have known which contained the prize" he is of course changing the scenario from non-Monty Hall (where there is no advantage in switching) to Monty Hall (where there is). But it has to be one scenario or the other. The rest of my post follows on from that.
TH
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