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Another well-known 'controversial' problem

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Vabjekf	Posted - 2008.09.09 19:35:00 - [31] It took me quite a bit of thinking and internet arguing before i realized how this one worked. The easiest way to understand it is to actually DO it. Not with doors and cars and goats, but with say, flash cards. Two with a picture of a goat, one with a picture of a car (or just playing cards, one face card and two not face cards). It should not take long to figure it out. Switching under these circumstances is always your best bet.
Slade Trillgon Siorai Iontach	Posted - 2008.09.09 19:47:00 - [32] Well, if I am ever on a game show and I have to make this type of decision I will go with what yall have said and if I loose I will come for all your pods To Duban, I bet their a many instances throughout history where great people have gone against the odds and succeded. Do you call these people stupid? Or would they just be stupid if they had failed according to what the numbers may have said had they been computed? My logic has been corrected, but that does not mean that I would always choose to go with the statistically proper choice. They are odds for a reason and sometimes my gutt trumps my logic. I guess I am an idiot for life Slade Originally by: Crumplecorn NerfBat is now known as the WaveMachine. DesuSigs
Amandin Adouin Minmatar	Posted - 2008.09.09 20:01:00 - [33] Edited by: Amandin Adouin on 09/09/2008 20:01:15 Door #1 - the door you chose Door #2 - the winner Door #3 - the empty/goat door Slade - I don't even know if I'd call this a statistical question - more like a psycological logic question. The host knew which door had a goat behind it, so him choosing to open Door #3 actually upped the odds for the other unopened door (#2) being the winner. Get it? If the host didn't interject in any way, it would have been a matter of pure statistics.
Slade Trillgon Siorai Iontach	Posted - 2008.09.09 20:07:00 - [34] Edited by: Slade Trillgon on 09/09/2008 20:08:27 Originally by: Amandin Adouin Edited by: Amandin Adouin on 09/09/2008 20:01:15 Door #1 - the door you chose Door #2 - the winner Door #3 - the empty/goat door Slade - I don't even know if I'd call this a statistical question - more like a psycological logic question. The host knew which door had a goat behind it, so him choosing to open Door #3 actually upped the odds for the other unopened door (#2) being the winner. Get it? If the host didn't interject in any way, it would have been a matter of pure statistics. Either I don't get it or the host just upped the odds that either of the remaining closed doors is the winner. Slade Originally by: Crumplecorn NerfBat is now known as the WaveMachine. DesuSigs
Vabjekf	Posted - 2008.09.09 20:14:00 - [35] Originally by: Slade Trillgon Originally by: Amandin Adouin Edited by: Amandin Adouin on 09/09/2008 20:01:15 Door #1 - the door you chose Door #2 - the winner Door #3 - the empty/goat door Slade - I don't even know if I'd call this a statistical question - more like a psycological logic question. The host knew which door had a goat behind it, so him choosing to open Door #3 actually upped the odds for the other unopened door (#2) being the winner. Get it? If the host didn't interject in any way, it would have been a matter of pure statistics. Either I don't get it or the host just upped the odds that either of the remaining closed doors has the car behind it. Slade The first door you picked had a 33% chance of having a car behind it. That left 66% chance it was behind one of the other two doors. By removing one of the other doors in the group of two you did not pick, the host has effectively made it a 66% chance it is behind the remaining door you did not pick, because you KNOW that he host removed a goat door. Or look at it like this. G is a goat door, C is a car door, the \| divides the two you did not pick from the one you picked. These are the possible combinations; G G \| C G C \| G C G \| G As you see, by picking a door you have a 1 in 3 chance of winning. Now Lets look at those same combinations, but the host removed one door that HAS TO BE A GOAT DOOR from the ones you did not pick. Removed doors are represented by an R R G \| C R C \| G C R \| G As you see, in this situation, if the first door you picked was a goat door, switching would reward you with a car. The ONLY way to lose by switching is if you picked the right door from the start. Therefore switching in this situation gives you 66.6% chance of winning, and a 33.3% chance of losing.
Amandin Adouin Minmatar	Posted - 2008.09.09 20:43:00 - [36] Nevermind what I said about it not being statistical, it is. I'm trying to explain this without the math, but it's impossible. You took Door #1 out of the host's options of opening by choosing it first. (33%) The Host was left with #2 and #3 to open. (33%) + (33%) = (66%) But the host knew which one not to open. So out of the two doors he had left, he knew which one not to pick. He couldn't eliminate Door #1. You already eliminated that from his choices. You look at the two doors left as a combined probability (66%) vs. the first one you took out of the equation. Because you had already taken Door #1 out of his options, his choosing to open Door #3 increased the odds of Door #2 being the winner, over and beyond it's normal statistical probabiliy.
Akita T Caldari Navy Volunteer Task Force	Posted - 2008.09.09 20:52:00 - [37] Originally by: Slade Trillgon Except that the game has been reset, there are now two doors and your decision is to stay or to switch is based on a 50%. Two choices not 3. It is total seperate decision at that point. If you stay yes your original choice was made at a 33% probability, but if you switch now you have a 50% chance of being wrong . I would rather stick with the 33% chance of being wrong then the 50% chance of being worng It is really a matter of which numbers you want to bank on. Errr... your INITIAL choice was made at 66% chance of being wrong, not 33%... Also, let's have a really, REALLY expanded problem, to see it much more clearly. There aren't just 3 doors, there's a MILLION doors. Behind ONE of the doors, there's a car, behind the rest, a total of 999,999 goats. You pick a door. The gameshow host opens 999,998 doors with goats behind them. Do you keep your choice or do you switch ?
Vabjekf	Posted - 2008.09.09 21:02:00 - [38] Again: G is a goat door, C is a car door, the \| divides the two you did not pick from the one you picked. These are the possible combinations; G G \| C G C \| G C G \| G As you see, by picking a door you have a 1 in 3 chance of winning. Now Lets look at those same combinations, but the host removed one door that HAS TO BE A GOAT DOOR from the ones you did not pick. Removed doors are represented by an R R G \| C R C \| G C R \| G If this does not explain it, then i don't know what will. Its right there, i even drew a picture.
Slade Trillgon Siorai Iontach	Posted - 2008.09.09 21:30:00 - [39] Edited by: Slade Trillgon on 09/09/2008 21:31:30 Originally by: Akita T Errr... your INITIAL choice was made at 66% chance of being wrong, not 33%... Well this is probably one of my main problems with these threads, interpreation. In what you quoted I ment that the choice was made with a 33% chance of being correct. The way I wrote it could have been interpreted either way. I can honestly say that I understand the odds, but staying with only 2 choices, in this type of situation, makes sense to me since I trust my instincts, not that they really affect the outcome of this type of situation. Wrong statistically, but hey what can I say, if the choice was good enough to begin with then I am going to follow through with it, ** stats. Sue me or laugh if you ever see me make this choice and lose, but know that I lost knowing that I had a better chance of winning if I chose the other door. Wow, I bet yall are laughing at that one Originally by:** Akita T Also, let's have a really, REALLY expanded problem, to see it much more clearly. There aren't just 3 doors, there's a MILLION doors. Behind ONE of the doors, there's a car, behind the rest, a total of 999,999 goats. You pick a door. The gameshow host opens 999,998 doors with goats behind them. Do you keep your choice or do you switch ? This was probably the best example, at least the one that made the most sense. I guess I need to stay away from these threads in the future. This is the second time I have been drawn in on one of these **ing threads. Slade, AKA Stubborn SOB Originally by:** Crumplecorn NerfBat is now known as the WaveMachine. DesuSigs
Chr0nosX Ore Mongers Black Hand.	Posted - 2008.09.09 21:46:00 - [40] Im so confused.
Eternal Error Exitus Acta Probant	Posted - 2008.09.09 21:56:00 - [41] I just wikipediaed it since I knew I wouldn't figure it out myself. My head hurts a bit.
Kyrall A Few Killers	Posted - 2008.09.09 21:59:00 - [42] Originally by: Slade Trillgon This was probably the best example, at least the one that made the most sense. I guess I need to stay away from these threads in the future. This is the second time I have been drawn in on one of these **ing threads. Slade, AKA Stubborn SOB and Originally by:** Chr0nosX Im so confused. My work here is done For any still not convinced, you really do have a 2/3 chance of winning by switching. Read all you ever wanted to know about it (and much more) on its Wikipedia page: Monty Hall Problem. Oh, and it's a problem, not a paradox. It's not even an apparent paradox, it's just a problem that's slightly awkward to think through! _____ Originally by: Pwett You sir, underestimate the things I have and will pee on.
Sharupak Minmatar Brutor tribe	Posted - 2008.09.09 22:11:00 - [43] Yeah I saw the movie 21 too... _______________________________________________ RuntimeError: ChainEvent is blocking by design, but you're block trapped. You have'll have to find some alternative means to do Your Thing, dude.
Slade Trillgon Siorai Iontach	Posted - 2008.09.09 22:13:00 - [44] Edited by: Slade Trillgon on 09/09/2008 22:13:29 I do not feel so bad if close to 1000 PHd's wrote in claiming the soultion was incorrect. I guess I am not in that bad of company. Slade Originally by: Crumplecorn NerfBat is now known as the WaveMachine. DesuSigs
Baldour Ngarr Interwarp Plexus Controlled Chaos	Posted - 2008.09.09 23:29:00 - [45] Edited by: Baldour Ngarr on 09/09/2008 23:31:06 Originally by: Slade Trillgon Edited by: Slade Trillgon on 09/09/2008 22:13:29 I do not feel so bad if close to 1000 PHd's wrote in claiming the soultion was incorrect. I guess I am not in that bad of company. Definitely not; I didn't see how it could possibly be right, the first time I came across this problem. It took a couple of reads of the explanation before I got it. I think there's something instinctive in the way the human mind works, that makes us think "this is now a problem involving two doors, one of which has a car behind it." But that's not the whole problem; it ignores the bit about the host knowing which door he could open that had a goat behind it. Incidentally, to go off at a tangent - the problem is misnamed. On the show presented by Monty Hall, he never did offer contestants a chance to switch - at least, his own words were "I do not recall ever doing so. I asked all of the production team if they could remember me ever making that offer, and all but one of them said no." The other point to be made is the whole premiss of the question relies on the host always revealing one door. If he does so only sometimes, the chance of winning by switching could be as low as zero (if he's malevolent, and only opens a door when he knows you've chosen the car). ________________________________________________ "I tried strip mining, but I lost, and it's cold flying around in space naked."
Slade Trillgon Siorai Iontach	Posted - 2008.09.10 03:06:00 - [46] Originally by: Baldour Ngarr The other point to be made is the whole premise of the question relies on the host always revealing one door. If he does so only sometimes, the chance of winning by switching could be as low as zero (if he's malevolent, and only opens a door when he knows you've chosen the car). That was my biggest problem with this question. I kept wanting to make a reference to a game show in my earlier arguments, but I did not want to do that since I did not have proof that this did not happen in some game show. What I wanted to say was that no game show host would give you the second chance unless they new that you had chosen the correct door to begin with. All the time hoping that you would realize the statistical probability was in your favor to change your choice, so if you changed your choice you would save the game show the money cost of the car. I do not think that this type of situation would happen very often if at all in the real world. That is why I said that I would go with my initial gut choice in the beginning, even though my logic was skewed. Slade Originally by: Crumplecorn NerfBat is now known as the WaveMachine. DesuSigs
Spaztick Canadian Imperial Armaments EVESpace	Posted - 2008.09.10 03:26:00 - [47] What you have to realize is that switching to the other remaining door or keeping the door you have will still be a 50% chance. Think of it as resetting your choice when a door is removed: either you can pick the door your originally chose or the second remaining door. But seriously, more people should have some type of spacer in their sigs to show it's not part of the post.
Woodwraith Digital assassins G00DFELLAS	Posted - 2008.09.10 03:34:00 - [48] the idea behind it is a collapsing probability wave. you gain information when the dead door is opened, your odds go up. they have to, the more information about a system you have, the 'more correct' your decision will be, the idea of having a million doors all but one with a goat is a really good way to make it more obvious whats going on. its probably easier still if you take the people out of the picture, say you drop a marble out of an airplane, it could fall in any one of 10 buckets, and you dont want it to get wet, you need to choose the bucket and everytime i tell you wich one has water in it, you get better odds of having a dry marble.
Baldour Ngarr Interwarp Plexus Controlled Chaos	Posted - 2008.09.10 07:16:00 - [49] Originally by: Spaztick What you have to realize is that switching to the other remaining door or keeping the door you have will still be a 50% chance. It will not, for reasons detailed in several different ways above. ________________________________________________ "I tried strip mining, but I lost, and it's cold flying around in space naked."
Shadowsword COLSUP Tau Ceti Federation	Posted - 2008.09.10 07:59:00 - [50] Originally by: Kyrall Originally by: Shadowsword I wouldn't swap, statistically it wouldn't improve your chances. Care to elaborate? Please work through your logic for people to follow and agree/disagree/improve upon. Once the game host opened a goat door, there's two doors remaining, and you choosed one of them. That mean you now have 50% chances of already having the right door. Changing now would still get you 50% chance, so there's no point doing it. However, there might be other factors, like, say, the goat making some noise, that could make you change. ------------------------------------------
Mark Lucius Kinetic Vector	Posted - 2008.09.10 08:46:00 - [51] Originally by: Vabjekf Again: G is a goat door, C is a car door, the \| divides the two you did not pick from the one you picked. These are the possible combinations; G G \| C G C \| G C G \| G As you see, by picking a door you have a 1 in 3 chance of winning. Now Lets look at those same combinations, but the host removed one door that HAS TO BE A GOAT DOOR from the ones you did not pick. Removed doors are represented by an R R G \| C R C \| G C R \| G If this does not explain it, then i don't know what will. Its right there, i even drew a picture. What other people see: Initially. G G \| C G C \| G C G \| G Host removed a door from the problem. G \| C C \| G See, 50% chance. Again: the keyword is 'switching'. This implies that the initial chance is factored in when calculating what the new chance is, as opposed to just making a 'fresh' pick. ---
Norwood Franskly Minmatar Fleet of the Damned Dark Trinity Alliance	Posted - 2008.09.10 10:02:00 - [52] We had a TV show a bit like this problem in Australia called "Deal or No Deal" it had 21 (I think) suitcases one suitcase had a million dollars in it the rest had varying amounts of money in increasing increments (eg $5, $10 $ 100, $500 etc), the contestant from the audience would pick a suitcase and the host would remove it from the stack then he'd get the guy to open suitcases 1 by 1 eliminating the cash in the suitcase from the prize pool at the end when there was 1 suitcase left he'd ask if the guy wanted to open he's suitcase he'd put aside or the suitcase that was left. Similar premise to the problem except you still walked out with something if you failed. It was slightly more complicated as they had a bank as well which would make you an offer (I think the offer was made when 50% of the suitcases were taken away), the offer was done on a formula I think based on how much of the money had been removed from play, if you thought the offer was worth it you could walk away with the banks money. Was quite a fun Tv show to watch (as far as any game show can be)...
Nyphur Pillowsoft	Posted - 2008.09.10 10:32:00 - [53] Originally by: Shadowsword Once the game host opened a goat door, there's two doors remaining, and you choosed one of them. That mean you now have 50% chances of already having the right door. Changing now would still get you 50% chance, so there's no point doing it. This has already been disproven in many earlier posts. There's a 33% chance of you picking the right door on your first choice. The chance of you having chosen the wrong door is 66%. Those probabilities don't change when the presenter opens one of the doors. The chance that you picked the wrong door is still 66% but since one wrong choice of the remaining doors has been eliminated, the chance that the remaining door is correct is the full 66%. The key things here are that the car doesn't move and the presenter deliberately opens a wrong door. He doesn't just eliminate one choice out of three, he eliminates one WRONG choice out of the two you haven't chosen. Since the car isn't reshuffled, you're just as likely to have picked the wrong door as when you began. Pillowsoft - Join the Pillowsoft Gallente Militia, get free ships and support.
Slade Trillgon Siorai Iontach	Posted - 2008.09.10 11:51:00 - [54] Edited by: Slade Trillgon on 10/09/2008 11:51:36 Originally by: Nyphur This has already been disproven in many earlier posts. There's a 33% chance of you picking the right door on your first choice. The chance of you having chosen the wrong door is 66%. Those probabilities don't change when the presenter opens one of the doors. The chance that you picked the wrong door is still 66% but since one wrong choice of the remaining doors has been eliminated, the chance that the remaining door is correct is the full 66%. The key things here are that the car doesn't move and the presenter deliberately opens a wrong door. He doesn't just eliminate one choice out of three, he eliminates one WRONG choice out of the two you haven't chosen. Since the car isn't reshuffled, you're just as likely to have picked the wrong door as when you began. He obiously skipped over my "rant" from last night, LMAO!!! Boy was I turned upside down and all bent out of shape. Shakes fist at Kyrall Slade Originally by: Crumplecorn NerfBat is now known as the WaveMachine. DesuSigs
Baldour Ngarr Interwarp Plexus Controlled Chaos	Posted - 2008.09.10 19:05:00 - [55] Edited by: Baldour Ngarr on 10/09/2008 19:05:43 Edited by: Baldour Ngarr on 10/09/2008 19:05:19 Find a friend and a deck of playing cards. Pick out the Ace of Hearts and two random other cards. Deal them randomly, face down, so that you know which is which but your friend does not. Ask him to pick the card he thinks is the Ace. Then show him one of the other two cards, that you know is NOT the Ace. Ask him if he wants to switch. See how many times you have to do this before his success rate closes towards 50% regardless of whether he switches or not. Hint : it never will. The odds are 2/1. ________________________________________________ "I tried strip mining, but I lost, and it's cold flying around in space naked."
Mankirks Wife	Posted - 2008.09.11 02:41:00 - [56] Easiest way to understand this one is to scale it up. Instead of three doors there are a million doors. You pick one, and the host opens up 999,998 doors that all reveal goats. Now should you switch? ---
Atomos Darksun Infortunatus Eventus Obsidian Empire	Posted - 2008.09.11 02:47:00 - [57] I shoot the host, open all the doors, grab the keys, and drive off. Originally by: Amoxin My vent is talking to me in a devil voice... Atomos' Guide to Forum Flaming
Vabjekf	Posted - 2008.09.11 02:55:00 - [58] I don't understand why you people don't trust us. Most of us trying to tell you that you have a 66% chance of winning if you switch are only bothering to post in this thread because we ourselves once thought you had a 50/50 chance until it finally dawned on us that you are better off switching. We are trying to save you the hassle of waiting for it to dawn on you as well. Look it up on Wikipedia if you want. The airplane takes off, and you have a better chance of winning the car by switching. You are going to make these same flawed arguments when you can even sit there at home and test this with a deck of playing cards and test it. Thats how it finally dawned on me. Stop arguing, go TRY IT.
Lrd Byron	Posted - 2008.09.11 10:11:00 - [59] best way I have thought of to think of it is, say you pick a door with a goat, then you know that after the host opens a door, the one left has to be the car. Since there is a 66% chance you picked a door with a goat originally, there is a 66% chance of getting the car if you switch.
Crumplecorn Gallente Eve Cluster Explorations	Posted - 2008.09.11 11:12:00 - [60] Edited by: Crumplecorn on 11/09/2008 11:13:06 There are 10000 doors. You pick one, the host opens 9998. Two are left. One is guaranteed to be the prize. Now which is more likely, that you just happened to pick the correct one out of ten thousand the first time, or that it was among the other OVER NINE THOUSAND the host had to 'choose' from? So, you gonna swap? Edit: Just saw that this was already done above. Meh. - DesuSigs

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