--- In [email protected], Tyson Mao <[EMAIL PROTECTED]> wrote: > > Hi GameOfDeath, > > Stefan and I fully understand that running a simulation is not a > mathematical proof. However, we have given a mathematical proof many > times. In fact, Stefan has given the exact same mathematical proof, > which is why we've resorted to simulations in an attempt to convince > people that the answer is in deed 2/3 winning probability when one > switches doors. >
I guess I only read some of the posts. In that case, I take it back (about people using simulations instead of proofs) and instead congratulate you both for presenting proofs. > You know... having 76 successes out of 100 is very nearly (order of > magnitude) the probability of getting lucky on a Rubik's Cube is it > not? I don't know what the probability of getting lucky on a Rubik's cube is. (Are you talking about the Revenge - with the probability being 75% that one can skip one of the two non-standard 3x3x3 situations.) In fact, I don't even know the probablitiy of getting lucky. : ) I guess one must have P(Getting lucky on a Rubik's cube)= P(Getting lucky|one is on a Rubik's cube)= [P(Getting lucky)-P(Getting lucky|one is not on a Rubik's cube)*P(One is not being on a Rubik's cube)]/P(One is on a Rubik's cube) at least assuming P(One is on a Rubik's cube)>0. > > Tyson Mao > MSC #631 > California Institute of Technology > > On Dec 30, 2005, at 10:00 AM, Stefan Pochmann wrote: > > > --- In [email protected], "Daniel Hayes" > > <[EMAIL PROTECTED]> wrote: > >> > >> Thus, the probability of having 76 success out of 100 without > >> switching doors = 2.59697e-18 = 0.000000000000000259697% > > > > Bah, using % is a cheap trick to make it look larger. > > I prefer 0.00000000000000000259697 > > > > I did know the formula, just didn't think I have a tool good enough to > > handle these very large and very small numbers. I was wrong, actually > > even my pocket calculator easily can... > > > > It's btw close to the probability that a random scramble results in a > > solved 3x3. Just to get on-topic again... :-) > > > > Cheers! > > Stefan > > > > > > > > > > > > > > > > > > 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/
