  We present the Sunyaev-Zeldovich (SZ) signal-to-richness scaling relation
(Y500-N200) for the MaxBCG cluster catalogue. Employing a multi-frequency
matched filter on the Planck sky maps, we measure the SZ signal for each
cluster by adapting the filter according to weak-lensing calibrated
mass-richness relations (N200-M500). We bin our individual measurements and
detect the SZ signal down to the lowest richness systems (N200=10) with high
significance, achieving a detection of the SZ signal in systems with mass as
low as M500~5e13 Msolar. The observed Y500-N200 relation is well modeled by a
power law over the full richness range. It has a lower normalisation at given
N200 than predicted based on X-ray models and published mass-richness
relations. An X-ray subsample, however, does conform to the predicted scaling,
and model predictions do reproduce the relation between our measured
bin-average SZ signal and measured bin-average X-ray luminosities. At fixed
richness, we find an intrinsic dispersion in the Y500-N200 relation of 60%
rising to of order 100% at low richness. Thanks to its all-sky coverage, Planck
provides observations for more than 13,000 MaxBCG clusters and an unprecedented
SZ/optical data set, extending the list of known cluster scaling laws to
include SZ-optical properties. The data set offers essential clues for models
of galaxy formation. Moreover, the lower normalisation of the SZ-mass relation
implied by the observed SZ-richness scaling has important consequences for
cluster physics and cosmological studies with SZ clusters.
