Longest possible path from root to a leaf of a red black tree
As you can read as "Properties" in the "Wiki Red-Black Tree", "the path from the root to the farthest leaf is no more than twice as long as the path from the root to the nearest leaf.".

For a Red-Black Tree having 'N' nodes, the mean length path is 'ln(N + 1) + 1' (for 'N=10' 'Lmean = 2.397 + 1 >> 4').

Note: `ln(X) = neperian logarithm'.

So the Longest balanced-path from root to leaf is shorter than the double of the mean length '&lt; 2 * ln(N + 1) + 1'. (for 'N= 10' longest &lt; 8).