The approach and methods used at Argonne National Laboratory to assess core damage probability in risk assessments for innovative liquid-metal reactor (LMR) designs using metal-fueled cores in pool configurations are outlined. Bounding estimates for the predicted frequency of core damage from all unprotected initiating events are developed by establishing a set of reference scenarios from traditional anticipated transient without scram events. Sources of uncertainty are described and categorized. A probabilistic treatment is used to propagate the various uncertainties through safety analyses to determine their effects on limiting reactor parameters. For example, probability distributions for safety margins to selected core temperatures are propagated from sensitivity studies and estimates of the underlying uncertainties in reactivity feedback coefficients. Considerable self-cancellation of many of the contributors to core response uncertainties is demonstrated analytically. Upper bound probabilities of core damage are then calculated for the LMR cores currently being designed. The results show that these designs have much lower probabilities of suffering core damage than are predicted in published risk assessments for commercial power reactors. Finally, design strategies that can be used to reduce these already low probabilities to almost arbitrarily low values are discussed.