i can't see why it wouldn't work for a real money game, unless there is a rake on the table (where the house takes a cut of the profits).
It seems to me that you can only ever make a profit of the unit you start off with. If you start with $1, you will only ever make $1 total, regardless of how much you bet. If you really wanted to make some money quickly, try betting $10k, then $20k, then $40k, then $80k, you will walk away with $10k.
i tried to do a standard analytical proof but got lost in the maths:
if p = 2^n - sum (i = 1 to n) a*i*n (which i think it is)
prove:
a = 2^n - sum (i = 1 to n) a*i*n
where a is the initial bet and n is the number of bets
you could very easily do a numerical version of this if you know a little about programming (or can operate a calculator
)
it's a pretty lame way to make a living though...