1.  10/17/2002, 03:32 PM Originally posted by Toby [B]I'm more of a Jeopardy person.[B]No, it doesn't. What on earth would make you think that knowing one of the wrong doors means anything? Giving you a _perceived_ 50/50 shot at it hasn't increased the original odds of you winning.[B]Let's see the math. If they always show a wrong choice that you didn't pick, your odds have not improved at all, and there's no incentive to switch, and AAMOF, the odds of pursuing a strategy of always _not_ switching are identical.If there is only one winner, what makes you think it isn't behind the door you already picked? Hey it worked. I backed you into a corner. The answer is you always switch. What're the odds of initially picking the right door? One in three. What're the odds of picking the right door when you switch? One in two. Why? Because one incorrect door was shown and so you won't switch to that!
2.  10/17/2002, 03:37 PM Originally posted by KRamsauer Now what if this disease kills people within 10 seconds of some sign (say a seizure) which I am experiencing if \$Medication isn't injected and the test to determine my allergy takes half an hour. OK, so you're only brain-damaged now. Presume there is \$Medication2 which cures the 1% allergic to \$Medication but kills the 99% who aren't. Why don't we presume that little fairies will fly down from the ceiling while we're at it. What do you do? Clearly you use statistics! Glad you're not a doctor. That is all I'm saying here. You're going to be wrong often, but you will save more people (like me!) than if you were randomly administer (in 50% - 50% ratios) the two or administer none whatsoever. You should use your knowledge of the poplution to cure me. And if a few people here and there die, no problem. ‎"Is that suck and salvage the Kevin Costner method?" - Chris Matthews on Hardball, July 6, 2010. Wonder if he's talking about his oil device or his movie career...
3.  10/17/2002, 03:40 PM Originally posted by Toby And if a few people here and there die, no problem. But many more would have died had you followed a blind strategy of using \$MEDICINE2 as much as \$MEDICINE1. BTW, my added details were put in to solidify the math behind the problem and enumerate penalties for both type one and type two error (H0: new patient is a member of the 99%; H1: he's allergic to \$MEDICINE).
4.  10/17/2002, 03:41 PM Originally posted by KRamsauer Hey it worked. I backed you into a corner. The answer is you always switch. No. What're the odds of initially picking the right door? One in three. You're correct here. What're the odds of picking the right door when you switch? One in two. Why? Because one incorrect door was shown and so you won't switch to that! You're wrong here. Why? The odds of the door you stay with being the right door are also one in two now. If I flip three coins and the first two come up heads, there is no higher chance that the next flip will come up tails. ‎"Is that suck and salvage the Kevin Costner method?" - Chris Matthews on Hardball, July 6, 2010. Wonder if he's talking about his oil device or his movie career...
5.  10/17/2002, 03:44 PM Originally posted by KRamsauer But many more would have died had you followed a blind strategy of using \$MEDICINE2 as much as \$MEDICINE1. BTW, my added details were put in to solidify the math behind the problem and enumerate penalties for both type one and type two error (H0: new patient is a member of the 99%; H1: he's allergic to \$MEDICINE). I suggested no such blind strategy, nor even the existence of \$MEDICINE2. The point was that assuming that a particular person fit into a mold simply because a certain percent of the population does is flawed. I don't know why I bothered though. ‎"Is that suck and salvage the Kevin Costner method?" - Chris Matthews on Hardball, July 6, 2010. Wonder if he's talking about his oil device or his movie career...
6.  10/17/2002, 03:45 PM Originally posted by Toby You're wrong here. Why? The odds of the door you stay with being the right door are also one in two now. If I flip three coins and the first two come up heads, there is no higher chance that the next flip will come up tails. That's not equivalent because the events in Let's Make a Deal are not independent. You know there's only one prize, and the prize is placed there before you choose your first door. So when you choose your first door there is a 1/3 chance of being right, which we agree on. Now, you also agree that there is no way of telling which door is the right one, so if you are set on a strategy of never switching, the odds of you winning are 1 in 3. But if you always switch you only lose when you pick the right one right off, or 1/3 of the time. So you win 2/3 of the time. Understand? I'd like to make sure you understand it because it is such a wonderful problem that when you really understand it, it's a great feeling. Last edited by KRamsauer; 10/17/2002 at 03:51 PM.
7.  10/17/2002, 03:46 PM Originally posted by Toby I suggested no such blind strategy, nor even the existence of \$MEDICINE2. The point was that assuming that a particular person fit into a mold simply because a certain percent of the population does is flawed. I don't know why I bothered though. Flawed in the sense that it isn't perfect? Yes. But that's like saying chemo-therapy is flawed because it doesn't save everyone. YOu do the best with what you have.
8.  10/17/2002, 03:51 PM Originally posted by KRamsauer That's not equivalent because the events in Let's Make a Deal are not independent. You know there's only one prize, and the prize is placed there before you choose your first door. So when you choose your first door there is a 1/3 chance of being right, which we agree on. Now, you also agree that there is no way of telling which door is the right one, so if you are set on a strategy of never switching, the odds of you winning are 1 in 3. However, if you always switch, you effectively choose between two (because the one revealed will never be chosen) and the winner is always in that set of two. Understand? I'd like to make sure you understand it because it is such a wonderful problem that when you really understand it, it's a great feeling. I bet it's going to be a terrible feeling when you realize that you're wrong. Such a scenario is probably where Sam Clemens's saying came from, no doubt. The non-independence doesn't only favor the switch. ‎"Is that suck and salvage the Kevin Costner method?" - Chris Matthews on Hardball, July 6, 2010. Wonder if he's talking about his oil device or his movie career...
9.  10/17/2002, 03:53 PM Originally posted by Toby I bet it's going to be a terrible feeling when you realize that you're wrong. Such a scenario is probably where Sam Clemens's saying came from, no doubt. The non-independence doesn't only favor the switch. Okay, here you go: You stand a 1/3 chance of getting it right on the first pick. So if you don't switch you have a 1/3 chance of getting it right. If you switch, the only time you're going to get it wrong is if you happen to pick the right one the first time. However, we already found that the odds of that is 1/3. Thereofre you have a 2/3 chance of winning when you switch.
10.  10/17/2002, 03:57 PM Originally posted by KRamsauer Okay, here you go: You stand a 1/3 chance of getting it right on the first pick. So if you don't switch you have a 1/3 chance of getting it right. If you switch, the only time you're going to get it wrong is if you happen to pick the right one the first time. However, we already found that the odds of that is 1/3. Thereofre you have a 2/3 chance of winning when you switch. You don't understand a damned thing about odds obviously, and I can't believe I let myself waste this much time on it. Even _if_ you stood a higher chance of getting it right by switching (which you don't), the _best_ your odds would be is one in two. This sounds like something you read out of a Marilyn Vos Savant column, and were gullible enough to buy into. ‎"Is that suck and salvage the Kevin Costner method?" - Chris Matthews on Hardball, July 6, 2010. Wonder if he's talking about his oil device or his movie career...
11.  10/17/2002, 04:02 PM Originally posted by Toby You don't understand a damned thing about odds obviously, and I can't believe I let myself waste this much time on it. Even _if_ you stood a higher chance of getting it right by switching (which you don't), the _best_ your odds would be is one in two. This sounds like something you read out of a Marilyn Vos Savant column, and were gullible enough to buy into. Why would your odds be 1 in 2 (still better than 1/3)? They are actually 2 in 3 (because the only way you can lose is to pick the "right" door initially)! Call up your local university and ask to speak to a stat prof. They will mention that this is one thing they go over extensively in class. Do you understand why you can only lose switching by picking the "right" door initially? It's because having picked the right one originally, the "host" will reveal one of two remaining losers, and you will pick the loser when you switch. However if you pick a loser initially (2/3 chance) when the host reveals the other loser you will always pick the winner when you switch. Okay, here are a whole host of links describing why it's best to switch: http://cartalk.cars.com/Tools/monty.pl http://cartalk.cars.com/About/Monty/proof.html http://dir.yahoo.com/Science/Mathema..._Hall_Problem/ http://homepage.ntlworld.com/mr.foo/monty.html