Robust Same-Rank Pairs in a Poker Hand

You are dealt a 5-card hand uniformly at random from a standard 52-card deck. A same-rank pair is an unordered pair of cards in your hand that share the same rank (e.g., two Kings). Find the expected number of same-rank pairs in your hand.

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