Monotonicity conjecture for accurate caching-game triplets

Let $v_M(n,d,k)$ and $v_A(n,d,k)$ be the values of the Multiple and Alpern Caching Games, respectively. A triplet $(n,d,k)$ is accurate when

$$v_M(n,d,k)=v_A(n,d,k)=\frac{k^d}{\binom{n+d-1}{d}}.$$

Monotonicity conjecture. If the integer triplet $(n,d,k)$ is accurate, then the integer triplet $(n',d',k')$ is also accurate whenever $n'\geq n$, $d'\leq d$, and $k'\leq k$. This conjecture asserts monotonicity of accuracy under more boxes, fewer steps, and smaller query size. The supplied text gives no evidence that it has been resolved.