puzzling probability and roulette a la Mark Brown

["David Folster" <mr_bond@xxxxxxxxx>]

Perhaps someone who knows could explain this probability question to me.

Curious as to whether that simple roulette system mark spoke about could
work consistently, I decided to try it out for myself.  I went to one of
those "play for fun" casinos and, starting with a bankroll of $2000, decided
to be a bit more conservative and wait for four in a row of one color to
come up before betting the opposite color.  If I lost, I would double up and
bet the same color again, and so forth until my color came up.  Well, this
worked fabulouly for the first while.  I was betting in $50 increments and
had increased my acount all the way up to $2900.  This was great!

But then I hit a string of 10 blacks in a row, and the betting limit (of
which I was previously unaware) kicked in and so I was only able to bet
$1000 instead of $1600 (actually I would only have been able to bet the rest
of my bankroll, which was 1400).  Anyhow, after that, I quit with $2400 in
my account.

So the next day I was discussing with this with my brother in law, who is a
programmer and has taken probability and statistics in university.  But I
was not able to wrap my pea brain around what he told me.  He said that my
betting system wasn't valid because each bet was an event independent of
previous events and that my next bet would therefore always have a 50/50
chance of going my way.  Yet when I asked him what the odds of one color
coming up, say, 5 times in a row, he said that the chance of that happening
was about 3% (.5 * .5 * .5 * .5 * .5).

Now in my mind, these two different probabilities are measuring the *same
event*.  So how, on the one hand, can my probability of winning be only 50%,
and on the other hand, just 3%?

I just can't figure this out.  Anyone?

Dave