This is especially important in what we would call capital cases.

这在我们称之为死刑案件中尤为重要。

Randolph's betting big on the capital case.

兰多夫很重视这个案子。

A " capital case" is a case where the person is sentenced to death, or could be sentenced to death.

“死刑”是指被判处死刑或者可能被判处死刑的案件。