The anticipation–scaling conjecture for wager sets

Let $A,B e\subset \mathbb R_+$ be sets of nonnegative real numbers. The set $B$ anticipates $A$ when the regular gamblers' wagers from $B$ can be evaded against gambler 0's wagers from $A$, and $A$ scales into $B$ when the relevant scaling condition between the two wager sets holds. If

$$0\notin\overline{B\setminus\{0\}},$$

then $B$ anticipates $A$ only if $A$ scales into $B$. This would unify the boundedness and well-ordering results for anticipation; whether the proposed condition holds in full generality is left as further research.