Can I take on your challenge and also switch every time? I'd like that :) /Gustav
Tyson Mao skrev: >No, I'm not pointing to you. It's a general "you," though at this >point, I'm surprised that no one has taken up my offer. Especially the >people who claim that the probability is even at 1/2 and 1/2. > >At the end of this, I'll even give back the money that you lost if you >concede that the probability is indeed 1/3 and 2/3. Look, there's no >money lost here. I'm giving people who believe that the probability is >1/2 and 1/2 a risk free opportunity to prove themselves, and make a >little money while they're at it if they're correct. > >Tyson Mao >MSC #631 >California Institute of Technology > >On Dec 28, 2005, at 2:25 PM, Gustav Fredell wrote: > > > >>Hey, >> >>You're not pointing on me when you say "you", do you? I'm all with you >>(and pretty much the rest of the world) on this. I now my statistics >>and probabilities well. University well :) >> >>/Gustav >> >>Tyson Mao skrev: >> >> >> >>>It's a hilarious idea, but with the sad undertone that this discussion >>>has even gone this far. The probability of winning the game if you >>>switch the door is 2/3. We make several assumptions: >>> >>>No one is "out to get you." >>>The host offers you the switch every single time. >>>The host knows which door the prize is behind. >>>Psychics are full of crap. >>> >>>Just play the game yourself. This "law of large numbers" not applying >>>is false. Probability doesn't mean that something will or won't >>>happen, it's how often it should happen. If we carry out an infinite >>>number of tests, well, and I think it's called the central limit >>>theorem but I'm not certain, the probabilities should even out to >>>about >>>2/3 and 1/3. If you do it 1000 times, the probability will generally >>>come out to 2/3 and 1/3, but it won't be exact, and it could come out >>>weird... you could win 1000 times in a row. At the same time, I could >>>tunnel through a brick wall. That's probability. >>> >>>Play the game yourself. Work out the probability, read the actual >>>text >>>of the problem as stated on that website, and if we can agree on the >>>text of the problem, and the manner of which the game is played, there >>>is no doubt that probability is 2/3 and 1/3. There is no +epsilon or >>>-epsilon because for the sake of a math problem, no one is right >>>handed >>>or left handed. No one has a preference, pure randomness is possible. >>> >>>Honestly, if you were playing the game, would you actually stay with >>>the door you chose because you believe the probability of you winning >>>is 1/2? If so, you deserve to lose that car. In fact, why don't we >>>do >>>this. I'll be the host of this game and I'll give you 100 trials. >>>The >>>prize behind the door in my game will be $5 USD. >>> >>>Then, you be the host, and you give me 100 trials. The prize behind >>>the door in your game is $4 USD. I'll switch the door every time, and >>>you keep your door every time. If the probability is 1/2, I think you >>>stand to make $50 USD in this game. Who's up for it? >>> >>>I'm putting up money here. Those who are convinced of their answer >>>should step up. I'm convinced of my answer, and I'm putting my money >>>where my mouth is. >>> >>>Tyson Mao >>>MSC #631 >>>California Institute of Technology >>> >>>On Dec 28, 2005, at 1:00 PM, Gustav Fredell wrote: >>> >>> >>> >>> >>> >>>>Thats a hilarious idea. Go Tyson! I just wish I could be there. I >>>>have >>>>a >>>>certain tactic I'm sure works, unless you pull the Lindsey Lohan card >>>>mentioned by Marco. >>>> >>>>/Gustav >>>> >>>>Tyson Mao skrev: >>>> >>>> >>>> >>>> >>>> >>>>>I'm going to set up this game, but instead of a car as a prize, as >>>>>I'm >>>>>obviously not that wealthy, I'll give away free cubes. We'll do >>>>>this >>>>>in San Francisco during the break and we'll just call up random >>>>>members >>>>>of the audience who are there spectating the competition. If I have >>>>>enough cubes, I'll do it 10 times. >>>>> >>>>>Tyson Mao >>>>>MSC #631 >>>>>California Institute of Technology >>>>> >>>>>On Dec 28, 2005, at 12:46 PM, Rune Wesström wrote: >>>>> >>>>> >>>>> >>>>> >>>>> >>>>>>"Good thinking Stefan!" ? He is contradicting himself when saying: >>>>>>"you can gain some knowledge this way and be more sure that >>>>>>changing >>>>>>would be better...but... the probability stays at 2/3". But if we >>>>>>had >>>>>>a probability of 2/3 whithout this knowledge and then bettered it, >>>>>>how >>>>>>can we still stay at 2/3? He is discussing the a priori >>>>>>probabilities >>>>>>before the first choise, *I* am discussing the probabilities before >>>>>>the second choice, that is, when the host has opened one door. >>>>>>There >>>>>>is some concensus here that the probabilities are 1/3 or 2/3. But >>>>>>if >>>>>>we accept the theoretical assumtion (Pochmann apparently does) that >>>>>>the host has an "easy" door and a "difficult" door and he chooses >>>>>>the >>>>>>first with a probability of 1/2 + epsilon and the second with a >>>>>>probability 1/2 - epsilon (epsilon not 0), the result will be >>>>>>another. >>>>>>Ask mister Pochmann to calculate the probabilities for you. Mister >>>>>>Bayes may help him. >>>>>>R >>>>>>----- Original Message ----- >>>>>>From: "pjgat09" <[EMAIL PROTECTED]> >>>>>>To: <[email protected]> >>>>>>Sent: Wednesday, December 28, 2005 5:41 PM >>>>>>Subject: [Speed cubing group] Re: (Off topic)3 doors... >>>>>> >>>>>> >>>>>>Thats the best way I have heard it put for this entire dicussion. >>>>>>Good >>>>>>thinking Stefan! >>>>>> >>>>>>Peter Greenwood >>>>>> >>>>>>--- In [email protected], "Stefan Pochmann" >>>>>><[EMAIL PROTECTED]> wrote: >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> >>>>>>>This doesn't make the argument wrong. Yes, you can gain some >>>>>>>knowledge >>>>>>>this way and be more sure that changing would be better. But it >>>>>>>doesn't make you win more often when changing. The probability for >>>>>>>that stays at 2/3. >>>>>>> >>>>>>>I knew a similar case as yours, but here's a really extreme one: >>>>>>>After >>>>>>>you pick your first door, the host opens *all* three doors and >>>>>>>let's >>>>>>>you stay or change. Even with this 100% knowledge (because you see >>>>>>>the >>>>>>>car), changing is successful exactly 2/3 of the time, namely in >>>>>>>those >>>>>>>cases where you were initially wrong. >>>>>>> >>>>>>>Cheers! >>>>>>>Stefan >>>>>>> >>>>>>> >>>>>>>--- In [email protected], Rune Wesström >>>>>>><rune. >>>>>>>[EMAIL PROTECTED]> wrote: >>>>>>> >>>>>>> >>>>>>> >>>>>>> >>>>>>> >>>>>>> >>>>>>>>A lot of intuition! >>>>>>>>You guess on door #1. The host is staying in front of door #3. >>>>>>>>Door >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>#2 is 2 meters away from him, nevertheless he opens that door. >>>>>>>What >>>>>>>would you expect to find behind door #3? A goat?! (Let us exclude >>>>>>>double-crossing!). >>>>>>> >>>>>>> >>>>>>> >>>>>>> >>>>>>> >>>>>>> >>>>>>>>----- Original Message ----- >>>>>>>>From: "Stefan Pochmann" <[EMAIL PROTECTED]> >>>>>>>>To: <[email protected]> >>>>>>>>Sent: Wednesday, December 28, 2005 3:47 PM >>>>>>>>Subject: [Speed cubing group] Re: (Off topic)3 doors... >>>>>>>> >>>>>>>> >>>>>>>>Changing wins if and only if you initially chose the wrong door, >>>>>>>>i. >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>e. >>>>>>> >>>>>>> >>>>>>> >>>>>>> >>>>>>> >>>>>>> >>>>>>>>two times of three. >>>>>>>> >>>>>>>>Can you explain why your suggestion makes this wrong? >>>>>>>> >>>>>>>>Cheers! >>>>>>>>Stefan >>>>>>>> >>>>>>>>--- In [email protected], Rune Wesström >>>>>>>><rune. >>>>>>>>[EMAIL PROTECTED]> wrote: >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>>>In real life the host is Not staying totally symmetrically in >>>>>>>>> >>>>>>>>> >>>>>>>>> >>>>>>>>> >>>>>>>>> >>>>>>>>> >>>>>>>>relation to the doors. (He is right-handed Or left-handed. Maybe >>>>>>>>he >>>>>>>>has to take a halfstep to open a certain door etc.). If he now >>>>>>>>opens >>>>>>>>the "easiest" door, Not changing wins more often than one time of >>>>>>>>three. If he opens the other door, changing will win more often >>>>>>>>than >>>>>>>>two times of three. >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>>Yahoo! Groups Links >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>> >>>>>> >>>>>> >>>>>>Yahoo! Groups Links >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> >>>>>>Yahoo! Groups Links >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> >>>>> >>>>>Yahoo! Groups Links >>>>> >>>>> >>>>> >>>>> >>>>> >>>>> >>>>> >>>>>__________ NOD32 1.1342 (20051228) Information __________ >>>>> >>>>>This message was checked by NOD32 antivirus system. >>>>>http://www.nod32.com >>>>> >>>>> >>>>> >>>>> >>>>> >>>>> >>>>> >>>>> >>>>> >>>>Yahoo! Groups Links >>>> >>>> >>>> >>>> >>>> >>>> >>>> >>> >>> >>>Yahoo! Groups Links >>> >>> >>> >>> >>> >>> >>> >>>__________ NOD32 1.1342 (20051228) Information __________ >>> >>>This message was checked by NOD32 antivirus system. >>>http://www.nod32.com >>> >>> >>> >>> >>> >>> >>> >> >> >>Yahoo! Groups Links >> >> >> >> >> >> >> >> > > > > > >Yahoo! Groups Links > > > > > > > > >__________ NOD32 1.1342 (20051228) Information __________ > >This message was checked by NOD32 antivirus system. >http://www.nod32.com > > > > > ------------------------ Yahoo! Groups Sponsor --------------------~--> Get fast access to your favorite Yahoo! Groups. 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