I'm not sure I really agree with the entire concept of "going bust" in these terms. To nit pick, you don't go bust if you lose 99.97% of your money. The real point is from whereever you start 5 losees will take away 99.97% of your money and it's asymmetrical- after those 5 losses you don't need 5 wins to make back your original sum of money because now your wealth is much smaller so you need far more consecutive wins to regain your wealth. It's counter intuitive because most people don't really think about the implications that you're betting a fraction of your wealth and your wealth at each timestep is a compounded function of the previous timesteps. They think of wealth as a constant where it's not.
You’re totally right and my rationale was mistaken.
My two examples were based on the idea that there’s some limit on how we can divide the original bet. For example, if a person starts with $10 and loses 99.97%, they have nothing left because rounding. Likewise for losing 99.999% of $1000.
In hindsight, though, the risk of consecutive losses wasn’t the point of the math. As you point out, the asymmetry is the problem. Loss occurs over time even with intermittent losses.
Here’s an example of how to half $100 in capital, despite a 70% win rate.
