Black height ($\mathrm{bh}(v)$)

For a node $v$ of a red-black tree, count black nodes strictly below $v$ on any path to an absent-child sentinel, including that black sentinel. The red-black invariants make this count independent of the path. Other conventions omit the sentinel or count $v$; specify the convention when using numerical values. Equality of the counts, rather than their common additive offset, is what the balancing condition requires.