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For random walks with steps drawn uniformly from $[-1,1]$, we show an ordinal pattern occurs with probability $\\frac{|[1,w]|}{2^n n!}$, where $[1,w]$ is a weak order interval in the affine Weyl group $\\widetilde{A}_n$. For random walks with steps drawn from a symmetric Laplace distribution, the probability is $\\frac{1}{2^n \\prod_{j=1}^n \\mathrm{lev}(\\pi)_j}$, where $\\mathrm{lev}(\\pi)_j$ measures how often $j$ occurs between consecutive values in $\\pi$. 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