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.
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.
The impact of the asymmetry seems obvious in hindsight. I might have to agree with the original post that it’s a bit counterintuitive.