Hi Pedro, --- In [email protected], Pedro <[EMAIL PROTECTED]> wrote: > > Did you play just one time?! > Oh, no...I didn't say that switching you'll always win. I just said that you'll win more times if you switch...Ok, let me give another example. > > Suppose your friend has a bag with 3 balls inside. 2 are red and 1 is blue. So, he says that if you take a ball, without looking, and that ball is the blue one, he'll give you 10 dollars. So, you go and take one ball, but don't look at it. Say you put in on your pocket. Then, your friend looks into the bag and takes out one red ball. And ask if you want to continue with the one that is in your pocket or change with the one left on the bag? What do you do? > > Now the explanation: > your initial chance of taking the blue ball is 1/3, right?
No this is not right. "Likelihood" does not apply to humans making choices, even random ones. In the Rhine studies, with the strictest protocols, it was found that humans in general consistantly "guessed" better than the "odds" predicted. Those who believed they could do better than chance often did much better than the odds, and those who refused to believe that they could do better than chance consistantly did worst than the odds predicted. While you can artificially construct "natural numbers," often examples given of randomness, like dice throwing and Brownian motion, have been found to *not* be random. Cheers, David J > And what happens if you take the blue ball? The 2 red ones stay in the bag. So, the probability of the 2 red ones stay on the bag is the same as you taking the blue, which is 1/3. Correct? > > and your initial chance of taking one red ball is 2/3, because you have 2 red balls. So, if you take one red ball, what happens? 1 red and 1 blue stay on the bag. Right? The probability of 1 red and 1 blue ball stay on the bag is the same as you taking a red one, which is 2/3. Correct? > > Now, if your friend takes a red ball, what will happen? If there were 2 red balls on the bag, now there's 1 red ball. And if there were 1 red and 1 blue balls, now there's just the blue. So, which event has greater possibility of happen? 2 reds or 1 red and 1 blue? For 2 reds, the posibility is 1/3, and for 1 red and 1 blue the possibility is 2/3. So, you have a greater chance of winning if you change your ball for the one in the bag. You'll not win always, you'll win 2/3 of the time and lose 1/3. > > Make a test. Do it 10 times with each strategy like Stefan suggested and tell us the results... > > Pedro > > d_j_salvia <[EMAIL PROTECTED]> escreveu: > Hi Duncan and Stefan and Pedro and Evan, > > Sorry, you guys, but you aren't correct. > > In probability there's a thing called the law of large numbers. If you > generate a long enough string of numbers "randomly" that eventually > you would have every digit the same number of times. N oparticular > number is favored. Your answer relies upon this law of randomness. > > What is actually wrong with the standard answere you gave is that one > is not dealing with a large number of choices, and, as such, odds *do > not apply.* > > I went to a site with the software and made my choice and did not > switch and I won. Doing it more than once is outside the boundaries of > the game. > > Cheers, > > David J > > > --- In [email protected], "Duncan Dicks" > <[EMAIL PROTECTED]> wrote: > > > > I Had a freind who wouldnt believe this no matter how often I > explained the > > maths to him so he set up spreadsheet to test it out. Very easy to > do and > > confirmed what the maths tells you - you should switch! > > > > Duncan > > ----- Original Message ----- > > From: "aznseashell" <[EMAIL PROTECTED]> > > To: <[email protected]> > > Sent: Sunday, December 25, 2005 7:04 AM > > Subject: [Speed cubing group] Re: (Off topic)3 doors... > > > > > > Haven't we had this dicussion before? Or was it in another cubing group? > > > > The game is set up so that if you switch, a winning choice would > > become a losing choice and vice versa. In the beginning you had a 1/3 > > chance of winning and 2/3 chance of losing. Staying with your choice > > doesn't change your odds of winning (the host will always be able to > > show you a door with nothing behind it no matter which door you > > picked), but switching will turn your probabability of winning to 2/3. > > > > If my explanation makes no sense, consider the situation with 100 > > doors and one door with a prize. You pick a door, and the host shows > > you 98 doors with nothing behind them. Now it's much more obvious that > > you should switch, right? > > > > Shelley > > > > > > --- In [email protected], "richy_jr_2000" > > <[EMAIL PROTECTED]> wrote: > > > > > > It is counter intuitive, but if you are in this situation, your > > > chances would be better to switch to the other door. It's actually > > > quite interesting. > > > > > > -Richard > > > > > > --- In [email protected], Pedro > > > <[EMAIL PROTECTED]> wrote: > > > > > > > > Ok, this is off topic, but is interesting... > > > > > > > > (please forgive if I make some mistake on the english...) > > > > Suppose you are at a TV show, where you have 3 doors. 1 of the > > > doors has a car, and the other 2 don't have anything. So, the show > > > presenter asks you to choose a door. So, you choose, but he doesn't > > > open your choosen door. He opens an empty door. Then, he makes a > > > question: do you want to continue with your first choice or change to > > > the other door? > > > > > > > > What do you do? > > > > What situation gives you more chances of winning? > > > > > > > > Think about it... > > > > > > > > Pedro > > > > > > > > > > > > --------------------------------- > > > > Yahoo! doce lar. Faça do Yahoo! sua homepage. > > > > > > > > [Non-text portions of this message have been removed] > > > > > > > > > > > > > > > > > > > > > > > > > Yahoo! Groups Links > > > > > > > > > > SPONSORED LINKS > Jigsaw puzzle game Free puzzle inlay games Educational game and puzzle Word puzzle game Kid puzzle game Puzzle games > > --------------------------------- > YAHOO! GROUPS LINKS > > > Visit your group "speedsolvingrubikscube" on the web. > > To unsubscribe from this group, send an email to: > [EMAIL PROTECTED] > > Your use of Yahoo! Groups is subject to the Yahoo! Terms of Service. > > > --------------------------------- > > > > > > > --------------------------------- > Yahoo! doce lar. Faça do Yahoo! sua homepage. > > [Non-text portions of this message have been removed] > ------------------------ 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/
