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This paper explores notions of elegance and shibui in combinatorial game design, and describes simple computational models for their estimation. Elegance is related to a game's simplicity, clarity, and efficiency, while shibui is a more complex concept from Japanese aesthetics that also incorporates depth. These provide new metrics for quantifying and categorizing games that are largely independent of existing measurements such as tractability and quality. Relevant ideas from Western and Eastern aesthetics are introduced, the meaning of elegance and shibui in combinatorial games is examined, and methods for estimating these values empirically are derived from complexity analyses. Elegance and shibui scores are calculated for a number of example games, for comparison. Preliminary results indicate shibui estimates to be more reliable than elegance estimates.