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We present some elementary but foundational results concerning diamond-colored modular and distributive lattices and connect these structures to certain one-player combinatorial "move-minimizing games," in particular, a so-called "domino game." The objective of this game is to find, if possible, the least number of "domino moves" to get from one partition to another, where a domino move is, with one exception, the addition or removal of a domino-shaped pair of tiles. We solve this domino gamearXiv:1702.00806v1 fatcat:uc6aldt4kbg6pfjzxa5qompuia