Why bankroll growth is multiplicative, not additive

Losing half a bankroll requires doubling what is left to get back to where you started. Percentage gains and losses of the same size do not cancel; they compound against you.

Each bet is a multiplication of what you currently hold, not an addition to a fixed pot. That is why two bets of +50 per cent and −50 per cent leave you at 75 per cent of where you began, in either order.

This is the entire mathematical case for small stakes, and it holds regardless of how good the selections are. A larger edge changes how fast a bankroll grows and does not change this asymmetry at all.

That is also the expensive part. Sizing by confidence feels like using information and is actually amplifying the term that hurts most. Confidence is correlated with recency, not with edge.

What to do with it. Fix a unit as a small percentage of bankroll, write it down, and let it change only when the bankroll changes.