Strange Dice Math Puzzle

We have four strangely marked dice. Each die has one digit, 0-6, on each face.

Die "A" has four 4's and two 0's.

Die "B" has six 3's.

With random tosses, die "A" should beat die "B" two-thirds of the time, with no ties. The same is true for

"B" over "C"

"C" over "D" and

"D" over "A"

How are dice "C" and "D" marked?

This type of die is called "nontransitive." It is discussed in Martin Gardner's column in Scientific American, December, 1970 issue.

Click to find the answer to this math puzzle.