The Drunkard's Walk

There once was a drunk man who wandered far too close to a cliff. From where he stands, one step forward would send the drunk man over the edge. He takes random steps, either towards or away from the cliff edge. At any step, his probability of taking a step away from the cliff is 2/3, and his probability of taking a step towards the cliff is 1/3. What's the chance of escaping the cliff?