Interestingly, even over an infinite grid you should get to your target with probability 1: http://www.math.cornell.edu/~mec/Winter2009/Thompson/randomwalks.ht

Interestingly, even over an infinite grid you should get to your target with probability 1: http://www.math.cornell.edu/~mec/Winter2009/Thompson/randomwalks.html http://www.math.cornell.edu/~mec/Winter2009/Thompson/randomw...