For a symmetric walk after n steps: expected position 0, variance n, so typical distance is of order sqrt(n). After 100 steps you are typically about 10 away, not 50.
Recurrence, a classic result: returns to the origin with probability 1 in one and two dimensions, but not in three (about 34%). A drunk man finds his way home; a drunk bird may not.
The subtlety. In one dimension return is certain, yet the expected time to return is infinite - the tail is that heavy. That combination is a good test of understanding "almost surely" versus "in reasonable time".