It would be interesting to compute the advantage of having an ace without the potential gain from DD and splits. Aside from non-stake-increasing strategy, I think what would work most "optimally" may be a sort of personalized CE with regard to how much, according to one's br, would cause a heartbreaking loss. The size of bankroll seems worth noting as well; having a small initial br may devastate a ripe future opportunity by diminishing too much.
ex.) Disregarding all table conditions for the sake of simplicity; with absolute certainty of the ace, betting one hand of continuously-adjusting 40% of the initial br of $6,000, and losing 6 consecutive ace hands would bring this unfortunate player to tears with about $279.94.