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The ordered Ramsey number $\\overline{R}(\\mathcal{G})$ is the minimum number $N$ such that every $2$-coloring of the edges of the ordered complete graph on $N$ vertices contains a monochromatic copy of $\\mathcal{G}$.\n  We show that for every integer $d \\geq 3$, almost every $d$-regular graph $G$ satisfies $\\overline{R}(\\mathcal{G}) \\geq \\frac{n^{3/2-1/d}}{4\\log{n}\\log{\\log{n}}}$ for every ordering $\\mathcal{G}$ of $G$. 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