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 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! 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