The drunkard who, upon leaving a bar, takes N steps (each step independent of the previous ones, and heading downtown and uptown with equal likelihood), is likely about the square root of N steps from the bar. But what if the drunkard has a plan? What if the drunkard heads downtown on the nth step if the greatest integer of na is even, and otherwise heads uptown? For some irrational real numbers a this keeps her appreciably closer to the bar, but for others this plan is "worse than random.''