We identify a class of stochastic control problems with highly random rewards and high discount factor which induce high levels of statistical error in the estimated action-value function. This produces significant levels of max-operator bias in Q-learning, which can induce the algorithm to diverge for millions of iterations. We present a bias-corrected Q-learning algorithm with asymptotically unbiased resistance against the max-operator bias, and show that the algorithm asymptotically converges to the optimal policy, as Q-learning does. We show experimentally that bias-corrected Q-learning performs well in a domain with highly random rewards where Q-learning and other related algorithms suffer from the max-operator bias.