What I was looking for
Whether repeating a small losing trade in a loop can make it safe.
What I found
After n rounds, the expected result is n times the edge and the spread is the square root of n times the noise. With a negative edge, more rounds make the loss more certain, not less.
Every round also pays spread and fees regardless of outcome, so the end is computable: $100 at 0.216¢ per round trip and 12 round trips an hour is gone in 1.6 days. That isn't a risk to manage. It's a date.
The move
For any repeated strategy, I compute when costs alone end it, before I ask how it might win.