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! 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