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Exhaustive verification can quantify critical behaviour arising from concurrency in nondeterministic models. Rare events typically entail no additional challenge, but complex systems are generally intractable. Recent work on Markov decision processes allows the extremal probabilities of a property to be estimated using Monte Carlo techniques, offering the potential to handle much larger models. Here we present algorithms to estimate extremal rewards and consider the challenges posed by rarity.doi:10.14279/tuj.eceasst.72.1023.999 fatcat:e6vonmemivgknby7hdq525flcu