>If you flip a (fair) coin and it lands head 8 times in a row (a 1 in 256 chance), what are the odds of it landing heads the next time.
>if it's really a fair coin, the chance is 1 in 2
Yep, and it's amazing how many well educated numerate people don't get this (I once had a friend who was an astrophysicist who thought tails was more likely)
The way I explain it is this, the coin doesn't have a memory or a conscience, it just reacts to a bunch of forces which are hard to predict, and have been around since that Newton fellow invited gravity in 1964.
111111111 is just as likely as 100110100 etc, it's just that people recognize or interpret the 111111111 as a pattern and think, wow what are the chances of that...
111111111 is just as random a number as anything else because you can't predict the tenth flip.
Now if the coin landed on it's side 10 times in a row...
If you really want to wind somebody up (and I generally do) try telling someone who works in the financial industry to plot a histogram of the daily percentage movements for the last 25 years of the SP500, of the FTSE all share and ask what curve they get :-)
Then ask what their commission is actually buying you!