  Galaxy clusters provide an avenue to expand our knowledge of cosmology and
galaxy evolution. Because it is difficult to accurately measure the total mass
of a large number of individual clusters, cluster samples are typically
selected using an observable proxy for mass. Selection effects are therefore a
key problem in understanding galaxy cluster statistics. We make use of the
$(2.8~\rm{Gpc})^3$ FLAMINGO hydrodynamical simulation to investigate how
selection based on X-ray luminosity, thermal Sunyaev-Zeldovich effect or galaxy
richness influences the halo mass distribution. We define our selection cuts
based on the median value of the observable at a fixed mass and compare the
resulting samples to a mass-selected sample. We find that all samples are
skewed towards lower mass haloes. For X-ray luminosity and richness cuts below
a critical value, scatter dominates over the trend with mass and the median
mass becomes biased increasingly low with respect to a mass-selected sample. At
$z\leq0.5$, observable cuts corresponding to median halo masses between
$M_\text{500c}=10^{14}$ and $10^{15}~\rm{M_{\odot}}$ give nearly unbiased
median masses for all selection methods, but X-ray selection results in biased
medians for higher masses. For cuts corresponding to median masses $<10^{14}$
at $z\leq0.5$ and for all masses at $z\geq1$, only Compton-Y selection yields
nearly unbiased median masses. Importantly, even when the median mass is
unbiased, the scatter is not because for each selection the sample is skewed
towards lower masses than a mass-selected sample. Each selection leads to a
different bias in secondary quantities like cool-core fraction, temperature and
gas fraction.
