In Time Travel and Other Mathematical Bewilderments, Martin Gardner presents a set of four nontransitive bingo cards designed by Donald Knuth (pp. 61). The rules are that the first player to complete a horizontal row wins. Gardner does not delve into the mathematics but merely mentions that, probabilistically, A beats B, B beats C, C beats D, and D beats A.
I was so baffled that I immediately went on to to verify those results. He was right.
Now, with dice or heads tails sequences, I can understand nontransitivity; can someone please give the mathematical explanation of how and why nontransitivity occurs in the above game.