Well I may have put it badly. Of course the law of large number applies, it's a law after all. But what you used is not the law of large numbers at all. Funny thing was that you can actually use the law of large numbers to "prove" the answer will be 1/3, 2/3. Here's the law of large number in case you forgot it : http://mathworld.wolfram.com/WeakLawofLargeNumbers.html
You also believe that the odds of rolling a 6 on a regular six sided dice is not 1/6? That this cannot be true because it does not apply for a single roll? Maybe there's a 50/50 chance on for each number? This may sound stupid, and it is... but it's not very different from your argument. Please read the law of large numbers again and revise your use of it. /Gustav d_j_salvia skrev: >Gustav, > >--- In [email protected], Gustav Fredell ><[EMAIL PROTECTED]> wrote: > > >>So you say it's a 100% that I win if I stay... awesome conclusion. Just >>awesome... >> >> > >Excuse me but i did not say that. > > > >>You can't drag the law of large numbers into this the way you are >> >> >doing. > > >>It has nothing to do with odds only being true for many trials or not. >>It merely states that if you do something enough times it will converge >>towards the "true" odds. Which in this case is 1/3 and 2/3. >> >> > >You just said that I can't can't put in the realm of the law of large >numberfs, and then you immediately defend its position within the >realm of large numbers. You can't have it both ways - either it >applies or it doesn't. > >The number of games is part of where you are going wrong. There is one >trial is the classic example - what effect does it have on one game? >None. In the same way that you cannot predict when a radiactive atom >will decay. > > > >> So what it >>in fact can be used for is to make the choices many times (like others >>suggested), ad them up and calculate odds that come nearer and >> >> >nearer to > > >>the real odds. In this way you can "prove" that the odds are in fact >> >> >1/3 > > >>and 2/3 if you do it enough times. I challenge you to repeat Bob's 100 >>trials and and test your hypothesis against a 95% confidence >> >> >interval or > > >>so... >> >> > >I wrote a program in Basic on an Atati 800. Making a choice between 1, >2, and 3 generated at random, I decided never to switch. Out of 100 >"games" I "won the car" 76 times. > > > >>With a solid year or so at university in probability and statistics and >>very confident in this. Ask all the probability/statistics >> >> >professors in > > >>the world if the odds are 1/3 and 2/3, and I strongly believe that the >>law of large numbers will make the will make this converge towards 100% >>agreeing. In fact I challenge you to ask a single >> >> >probability/statistics > > >>professor about this and let us all know about his/her answer. >> >> > >Why should I answer a challenge which is dependent upon how well >another person thinks? > > > >>Take on the one or both of the challenges above and then come back and >>say it's not true. I bet you my upcoming 2x2x2 average WR that you >> >> >can't > > >>do it ;) >> >> > >I'm sorry you lost the bet. You probably had your heart set on the >2x2x2 average WR. > >Regards, > >David J > > > >>/Gustav >> >>d_j_salvia skrev: >> >> >> >>>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 >>>> >>>> >>>> >>>> >>>> >>> >>> >>> >>> >>> >>> >>> >>>Yahoo! Groups Links >>> >>> >>> >>> >>> >>> >>> >>>__________ NOD32 1.1340 (20051226) Information __________ >>> >>>This message was checked by NOD32 antivirus system. >>>http://www.nod32.com >>> >>> >>> >>> >>> >>> >>> > > > > > > > > >Yahoo! Groups Links > > > > > > > >__________ NOD32 1.1340 (20051226) Information __________ > >This message was checked by NOD32 antivirus system. >http://www.nod32.com > > > > > ------------------------ 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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