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 Sponsor --------------------~--> Get fast access to your favorite Yahoo! Groups. Make Yahoo! your home page http://us.click.yahoo.com/dpRU5A/wUILAA/yQLSAA/MXMplB/TM --------------------------------------------------------------------~-> Yahoo! Groups Links <*> To visit your group on the web, go to: http://groups.yahoo.com/group/speedsolvingrubikscube/ <*> To unsubscribe from this group, send an email to: [EMAIL PROTECTED] <*> Your use of Yahoo! Groups is subject to: http://docs.yahoo.com/info/terms/
