  Given an integer partition of $n$, we consider the impartial combinatorial
game LCTR in which moves consist of removing either the left column or top row
of its Young diagram. We show that for both normal and mis\`ere play, the
optimal strategy can consist mostly of mirroring the opponent's moves. We also
establish that both LCTR and Downright are domestic as well as returnable, and
on the other hand neither tame nor forced. For both games, those structural
observations allow for computing the Sprague-Grundy value any position in
$O(\log(n))$ time, assuming that the time unit allows for reading an integer,
or performing a basic arithmetic operation. This improves on the previously
known bound of $O(n)$ due to Ili\'c (2019). We also cover some other complexity
measures of both games, such as state-space complexity, and number of leaves
and nodes in the corresponding game tree.
