We obtain sharp asymptotic estimates on the number of $n \times n$ contingency tables with two linear margins $Cn$ and $BCn$. The results imply a second order phase transition on the number of such contingency tables, with a critical value at \ts $B_{c}:=1 + \sqrt{1+1/C}$. As a consequence, for \ts $B>B_{c}$, we prove that the classical \emph{independence heuristic} leads to a large undercounting.

翻译：我们获得关于两个线性幅度为1美元和1美元或1美元应急表数目的精确估计。结果意味着此类应急表数目的第二阶段过渡,其关键值为:=1+\sqrt{1+1/C}。因此,对于$B>B{c}美元,我们证明传统=emph{独立超值导致大量低估。