

It’s not sound actually because it trivially ends up in nonsensical amounts of money and any sufficiently long series of rolls will have an increasing chance of having a sufficiently long series of losses such that no reasonable person can possibly recover from it. For instance who that can afford to bet 1024x 100 or $100,000 on a single game of chance is excited by betting $100?
It’s nonsense.
The math doesn’t work because given enough rolls you literally always go bankrupt no matter what bankroll you start with. Take the simplest option a fair coin where you win on tails and lose on heads. Real actual random flips will contains runs of heads. Let N be the number of rolls required to bankrupt you for any value of N. The more you roll the more the probability of such a run increases towards 1.
You could end up bankrupting a billion dollar bank starting with 10 dollar bets. It’s only sound if you have a literally infinite bank. For any finite bank you just have to play longer to lose but you always end up losing.