Chessmaster1000: My math degree is 36 years old so I'm too rusty to be sure of this . . . but I think that, while an infinite sequence of random rolls would certainly contain any *finite* sub-sequence (indeed, an unlimited number of such sub-sequences), I don't think it's correct to conclude that it will contain any given *infinite* sub-sequence . . . at least if the infinity in question is the infinity that measures the number of integers (referred to I believe as aleph-sub-naught).