You only did the first four rows on your tree, out of eight. I did all eight and found the answer to be equivalent to the first answer, as expected. You can apply the geometric series' closed form to prove this analytically if you're interested.

Even though after 8 bets you would expect to make $1 with 99.411% probability, you have might lose $1+2+4+8+16+32+64+128=$255 with 0.589% chance. You would then have an expected profit of $1*0.99411=$0.99411, and an expected loss of $255*0.00589 = $1.50195. Overall, you'd expect to lose $1.50 - $0.99 = $0.51 with this betting technique.

If you had infinite money and a casino willing to take arbitrarily large bets, you could make money with this scheme eventually with arbitrarily high probability (keep doubling indefinitely). Too bad casinos don't extend infinitely large lines of credit or I'd be rich tomorrow....