Robust Adjacent Matches in Dice Rolls

Roll a fair six-sided die $n$ times independently, producing a sequence $D_1, D_2, \dots, D_n$. An adjacent match occurs at position $i$ (for $1 \le i \le n - 1$) if $D_i = D_{i+1}$. Find the expected number of adjacent matches.

Additional robustness twist: before observation, an independent random relabeling of outcome labels is applied. Compute the same target and justify invariance.