  We make the first detailed MCMC likelihood study of cosmological constraints
that are expected from some of the largest, ongoing and proposed, cluster
surveys in different wave-bands and compare the estimates to the prevalent
Fisher matrix forecasts. Mock catalogs of cluster counts expected from the
surveys -- eROSITA, WFXT, RCS2, DES and Planck, along with a mock dataset of
follow-up mass calibrations are analyzed for this purpose. A fair agreement
between MCMC and Fisher results is found only in the case of minimal models.
However, for many cases, the marginalized constraints obtained from Fisher and
MCMC methods can differ by factors of 30-100%. The discrepancy can be
alarmingly large for a time dependent dark energy equation of state, w(a); the
Fisher methods are seen to under-estimate the constraints by as much as a
factor of 4--5. Typically, Fisher estimates become more and more inappropriate
as we move away from LCDM, to a constant-w dark energy to varying-w dark energy
cosmologies. Fisher analysis, also, predicts incorrect parameter degeneracies.
From the point of mass-calibration uncertainties, a high value of unknown
scatter about the mean mass-observable relation, and its redshift dependence,
is seen to have large degeneracies with the cosmological parameters sigma_8 and
w(a) and can degrade the cosmological constraints considerably. We find that
the addition of mass-calibrated cluster datasets can improve dark energy and
sigma_8 constraints by factors of 2--3 from what can be obtained compared to
CMB+SNe+BAO only. Since, details of future cluster surveys are still being
planned, we emphasize that optimal survey design must be done using MCMC
analysis rather than Fisher forecasting. [abridged]
