Sacrifice-size conjecture for cumulative subtraction games

Let a cumulative subtraction game be played with a finite action set, and suppose optimal play includes sacrifices by both players. Sacrifice-size conjecture. In such a game, Negative's sacrifice is smaller than Positive's sacrifice. The claim concerns the relative sizes of sacrifices when both players sacrifice during optimal play; the paper supplies an example with action set $S=\{2,10,13,14\}$ in which Positive sacrifices $4$ and Negative sacrifices $1$. The supplied text gives no evidence of a proof or disproof, so its resolution remains open.