The inheritance of no discrepancy for dominant three-action subtraction sets

Let $S=\{s_3,s_2,s_1\}$ with $s_3<s_2<s_1$, and let a friendly/antagonistic discrepancy mean a difference between the FvF and AvA self-interest games. Dominant three-action inheritance conjecture. If

$$s_1\geq 2s_2$$

and the two-action set $\{s_3,s_2\}$ has no discrepancy for any heap size $x$, then $S$ has no friendly/antagonistic discrepancy for any heap size $x$. The claim is an empirical conjecture about extending the two-action pattern to three actions; no proof or resolution is supplied.