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Luminous Red Galaxies (LRG) from the Sloan Digital Sky Survey are consideredamong the best understood samples of galaxies, and they are employed in a broadrange of cosmological studies. Because they form a relatively homogeneouspopulation, with high stellar masses and red colors, they are expected tooccupy halos in a relatively simple way. In this paper, we study how LRGsoccupy massive halos via direct counts in clusters and we reveal severalunexpected trends suggesting that the connection between LRGs and dark matterhalos may not be straightforward. Using the redMaPPer cluster catalog, wederive the central occupation of LRGs as a function richness, Ncen({\lambda}).Assuming no correlation between cluster mass and central galaxy luminosity atfixed richness, we show that clusters contain a significantly lower fraction ofcentral LRGs than predicted from the two-point correlation function. At halomasses of 10^14.5 Msun, we find Ncen=0.73, compared to Ncen of 0.89 fromcorrelation studies. Our central occupation function for LRGs converges to 0.95at large halo masses. A strong anti-correlation between central luminosity andcluster mass at fixed richness is required to reconcile our results with thosebased on clustering studies. We also derive P_BNC, the probability that thebrightest cluster member is not the central galaxy. We find P_BNC ~ 20-30%which is a factor of ~2 lower than the value found by Skibba et al. 2011.Finally, we study the radial offsets of bright non-central LRGs from clustercenters and show that bright non-central LRGs follow a different radialdistribution compared to red cluster members, which follow aNavarro-Frank-White profile. This work demonstrates that even the most massiveclusters do not always have an LRG at the center, and that the brightest galaxyin a cluster is not always the central galaxy.

Luminous Red Galaxies in Clusters: Central Occupation, Spatial Distributions, and Mis-centering