Hi Ted,
    I believe the original question was "What is the probability of tossing
6 heads in a row out of 20 coin
tosses?". "In a row" implies 6 seperate actions in a time sequence and not a
physical arraingement as though 20 coins were tossed simultaneously. "The
last 6 times were all heads" that you refer to could just as well have been
"actions" 5-10 or 7-12  out of the 20 which supports my observation that the
gamblers-fallacy applies to Jeff's question.

                      Eric Sand
                      [log in to unmask]


> Thus it was written in the epistle of Eric H. Sand,
> > Hi Folks,
> >     I just completed a little bit a research and found a couple of items
> > that can shed some light on what we're trying to understand.
> >     The first one is parallel to most of the postings and explains the
> > "odds" when 20 coins are tossed "simultaneously".
> >
> > http://westgard.com/lesson36.htm#scores
> >
> >
> >     The second one, I believe addresses Jeff's situation, where the odds
> for
> > each subsequent toss of the coin(20 times), is always 50/50. The
> resultant
> > behavior of "X" coin tosses cannot be derived from the result of any
> > previous toss nor any subsequent toss.
> >
> > http://www1.ca.nizkor.org/features/fallacies/gamblers-fallacy.html
>
> The problem is that the question was poorly stated.  If the question had
> been:
> "I've flipped this coin 20 times and just realized that the last 6 times
> were
> all heads, what's the chance of that?"
> then the gamblers-fallacy would apply.
>
> Ted
> --
> Ted Ashton ([log in to unmask]), Info Sys, Southern Adventist University
>           ==========================================================
>
> If "Number rules the universe" as Pythagoras asserted, Number is merely
> our
> delegate to the throne, for we rule Number.
>                                       -- Bell, Eric Temple (1883-1960)