the DOW is up ... then down

There we were, having our morning coffee (the missus 'n me) and I said, "The DOW has been up three days in a row."
She says, "Then it'll be down today.".
So I started thinking ...
>A big mistake! You should've continued sipping your coffee and ...
Pay attention.
I downloaded thirty years of daily DOW closing values, whipped out a spreadsheet and got this picture
I stared at the picture and found the numbers curious.
They seemed to decrease by (nearly) a factor 1/2 each time the number of days increased:
27.0% then13.8% then 6.6% then 3.2% then 1.5%
Then it occurred to me that, if the probability of an increase (or decrease) was 50% (from one day to the next), then we would expect that
it would decrease 2daysinarow 1/4 of the time, 3daysinarow 1/8 of the time, 4daysinarow 1/16 of the time, 5days...
>Yeah, I get it. You'd expect 25.0%, 12.5%, 6.3%, 3.1%, 1.6%, right?
Right.
 
>So, did the DOW increase (or decrease) 50% of the time?
The DOW increased 51.2% of the time, from Jan 1,1970 to Jan 1,2003.
>So why did you bother to play with your spreadsheet?
Excuse me. I'm going back to my coffee
