Caught In A Circle
You are trapped in the center of a flat circular area of radius 1000 by an evil maniacal tyrant. You have to walk out by taking steps of size 1. However, for each step, you can only choose the direction to walk in, and the tyrant will dictate if you move in the positive or negative direction.
What is the minimum number of steps you need to take to guarantee that you can reach the circumference?