I understand your point. I used to work in a community college math
lab once in another lifetime and every statistics student in the world
thinks this. But it is wrong.

if you flip a coin your odds are 50-50. Doesn't matter how many times
you have done it.

now if you flip it six times your odds of getting three or more heads,
or exactly two,  would would according to the formula you're using.

I am not geeky enough to go through all the permutations for you but
if you care to go through this on your own you'll see it's true. SO
then how do casinos make money you ask. Well, because a lot of people
put money in slot machines, which favor the house, and because
roulette also slightly favors the house. As Robert said, on volume.

Here's something that looks like it may explain it better:
http://www.saliu.com/bbs/messages/266.html

On 11/10/06, Gruss Gott <[EMAIL PROTECTED]> wrote:
> > RoMunn wrote:
> > More geek moments. Dana is right. Casinos make money on very, very small
> > margins (51% chance of the house winning at blackjack, is that right?) Each
> > hand, each throw, each spin is a separate event and the house makes money on
> > volume.
> >
>
> But only because she doesn't understand my point.  The odds of walking
> away an overall winner is a function of your sample size.  That is,
> winning one hand has higher odds of winning  2 >> in a row <<
>
> Here, I'll show you:
>
> The odds of flipping a heads in one toss of a coin is: 1 in 2 or 50%
>
> The odds of flipping 5 heads in a row is 1 in 32 or 3%
>
> The odds of flipping 10 heads in a row is 1 in 1024 or 0.1%
>
> The reason this analogy works is because, as every combat vet knows,
> the longer you're in combat the less chance you have of walking away
> without getting hit.  As journalists say:
>
> 1.) It can't happen to me.
> 2.) It might happen to me.
> 3.) I have to be careful or it'll happen to me.
> 4.) No matter what I do it's going to happen to me.
> 5.) I have to get out now.
>
> 

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