 Match-biased reshuffling preserves uniform rank marginals

Accepting a fresh uniform deck permutation with a probability depending only on whether its endpoint ranks match preserves uniform individual rank marginals by symmetry. It changes their joint law. For four cards of each of thirteen ranks and rejection probability $p$ on a mismatch, the accepted matching probability is $1/(17-16p)$. The two accepted ranks are independent precisely at $p=1/4$; equality of marginals alone does not imply independence.