This article relates a theoretical framework developed by British codebreakers in World War II to the neural computations thought to be responsible for forming categorical decisions about sensory stimuli. In both, a weight of evidence is computed and accumulated to support or oppose the alternative interpretations. A decision is reached when the evidence reaches a threshold value. In the codebreaking scheme, the threshold determined the speed and accuracy of the decision process. Here we propose that in the brain, the threshold may be controlled by neural circuits that calculate the rate of reward.