The maximizer conjecture for the Trail of Lost Pennies

Let $\lambda_{\rm \max}:(0,1]^2\to[1,\infty)$ be the function measuring the maximum value associated with the game. Maximizer conjecture. The maximum value of $\lambda_{\rm \max}:(0,1]^2\to[1,\infty)$ is attained at the point $(1,1)$. This conjecture is prompted by numerical investigations of the function and concerns the strength and robustness of the discouragement effect; the supplied text does not state a proof or resolution.