We introduce a new set of large N-body runs, the MICE simulations, that provide a unique combination of very large cosmological volumes with good mass resolution. They follow the gravitational evolution of ~ 8.5 billion particles (2048^3) in volumes covering up to 450 (Gpc/h)^3. Our main goal is to accurately model and calibrate basic cosmological probes that will be used by upcoming astronomical surveys. Here we take advantage of the very large volumes of MICE to make a robust sampling of the high-mass tail of the halo mass function (MF). We discuss and avoid possible systematic effects in our study, and do a detailed analysis of different error estimators. We find that available fits to the local abundance of halos (Warren et al. (2006)) match well the abundance in MICE up to M ~ 10^{14}Msun, but significantly deviate for larger masses, underestimating the mass function by 10% (30%) at M = 3.16 x 10^{14}Msun (10^{15}Msun). Similarly, the widely used Sheth & Tormen (1999) fit, if extrapolated to high redshift assuming universality, leads to an underestimation of the cluster abundance by 30%, 20% and 15% at z=0, 0.5, 1 for M ~ [7 - 2.5 - 0.8] x 10^{14}Msun respectively ($ u = delta_c/sigma ~ 3$). We provide a re-calibration of the halo MF valid over 5 orders of magnitude in mass, 10^{10} < M/(Msun) < 10^{15}, that accurately describes its redshift evolution up to z=1. We explore the impact of this re-calibration on the determination of dark-energy, and conclude that using available fits may systematically bias the estimate of w by as much as 50% for medium-depth (z <= 1) surveys. MICE halo catalogues are publicly available at http://www.ice.cat/mice
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