just done a trace on random(6)+1 this is the traced results giving you an indictaion of how random this will be:-
4,1,3,5,1,5,4,4,1,4,1,1,4,2,2,1,5,2,1,4,5,5,4,3,1, 2,3,3,4,2,1,4,3,2,5,3,1,4,1,5,3,1,3,3,4,3,4,1,1,3, 5,4,1,3,3,4,2,4,1,5,2,1,1,5,2
not bad really.