Monty Hall is a difficult task which triggers multiple biases. With sophisticated subjects and treatments that reverse and eliminate these triggers, non-rational choice is greatly reduced. Among task-familiar subjects, non-rational choice can fall to background-error levels. But as our data also show, task-form recognition is necessary but not sufficient for rational choice when the task calls for conditional probability reasoning rather than simple rule-based behavior, as in e.g. 'Switch in Monty Hall.' Task-form understanding, a more stringent requirement, proves to be necessary and sufficient for rational choice in generalized Monty Hall conditional probability reasoning tasks.